Origami/Examples 2

 This is the "E:/WikiversityStuff/FoldingWithTheStars.txt" file, which was created WED 2012 MAR 28 09:05 PM, revised TUE 2012 AUG 07 05:29 PM. 

A much better name for this page would be, "RCB_FoldingWithTheStars". I have asked one of the custodians for help. Ray Calvin Baker (talk) 18:40, 11 August 2012 (UTC)

A friend of mine recently asked me to publish my instructions for folding a simple hopping frog. So, I am "rushing" to add this information, below. As always, making the illustrations is, for me, a VERY slow process. If you do not have patience, you had better find an activity more exciting than origami. Ray Calvin Baker (discuss • contribs) 14:46, 4 September 2013 (UTC)

 THIS IS A COMPLETELY FRESH UPLOAD (If I must, I can upload it again.), primarily to break a large lesson plan into more manageable sections. (Each section is numbered to facilitate maintenance.) I still need to correct some known MISTAKES, and add material and PICTURES to incomplete sections. A big hurdle for me is simply to get material "out there". After that big step is taken, I can ask the entire world to help me with maintaining/correcting/improving it. This is a wiki, right? :-)

This lesson plan is really about making geometric star-shaped decorations. It is not really about dancing with the stars. 

Watch out for the sections which are INCOMPLETE! #1 of 23. I'm still working on several of these. There are at least 20 altogether. I found some serious MISTAKES in what I have written so far, so I need to correct those ASAP. I found those while preparing to present this material at the Caroline County Senior Center in Denton, Maryland. I look forward to actually having a CLASS—real, live people interested in some of the decorations and models I know how to make. Interaction and use of this material should help enormously to improve the accuracy and relevance of the information. PICTURES! I need to add lots of pictures, too. I know several ways "how to", but it takes time to create pictures using only PAINT.EXE. The regular pentagon layout diagram is proof that I CAN DO THIS! :-)

Ray Calvin Baker (talk) 21:44, 7 August 2012 (UTC)

 Do Folding with the stars! (even if you have two left feet and need a clock to keep time). Hopefully, you will be able to sit in a comfortable chair next to a suitable work table. You won't even need to work up a sweat!

Folding with the Stars -- Improved version -- better than Dancing with the Stars -- no losers! Everybody wins, and every winner takes home a handmade (made in USA) trophy -- or several trophies!

THIS IS NOT A COMPETITION! It's a CO-OPERATION!

Teachers are especially invited! You will be able to share important, interesting, educational and cultural activities with your classes.

FREE! to the first ten people (any age above third grade) who sign up. After ten sign up, others will go on a waiting list for a possible follow-up session. Each meeting will consist of HANDS-ON activities; be prepared to have some good, clean fun! Be prepared to succeed in making something you've never before even imagined!

Paper and supplies will be provided.

An entertaining afternoon of unusual, but easy, craft projects is planned at the Caroline County Public Library in Greensboro. Mathematics only -- no arithmetic allowed, except by request. (Do you mean to tell me there is a difference between Mathematics and Arithmetic? I most certainly do! Come and find out what the difference is.)

[ INCOMPLETE #2 of 23] VENUES FOR CLASSES Permissions, support, and survey of available facilities is needed. Possible Additional venue -- The Caroline County (Maryland) Senior Center

Activities may include: Origami (to fold paper) Storigami (to tell a story, and illustrate it with origami) Paper Sculpture Paper Engineering and some other useful craft materials

- - - - - - - - -

Above is a possible plan for the flyer, intended to attract attention, and to encourage people to sign up and attend. 

1. PLAN OF EVENTS
 Below is the plan of events. I hope that by posting this as a lesson plan at the Wikiversity I can establish some credibility for my outrageous claims. This should also allow me to post stories, pictures, and diagrams for participants to preview, download, and bring with. Of course, anyone on planet earth with access to the Wikiversity is free to use this material, once I post it.

Since by opening this project to the entire Greensboro community (to the entire world, via Wikiversity), I expect a wide range of ages, abilities, and prior experience, I plan to introduce some of the easiest, most fundamental crafts projects. Easy does NOT exclude four-dimensional geometry, vector calculus (without arithmetic, as much as possible), and discussion of non-orientable surfaces, and other topics as they arise. There are many strange, unusual, and unexpected things in Mathematics! Emphasis will be on hands-on, actual construction of interesting models. My goal is to make the "How to Make (Almost) Anything" course, popular at M. I. T., (though I have only read about it), accessible to a larger and younger audience.

NOTE: More activities must be planned than are expected to be actually used at any one event. Also, sometimes one must move on to another activity, due to lack of interest, or unexpected difficulties. Moreover, once a lesson plan is posted here, it is immediately available for anyone who wishes to use it. I intend to use the material myself, if there is ever another sequel event.

- - - - - - - - - 

2. THE ORIGAMI TOOL KIT
 Part of the beauty and wonder of origami is that NO TOOLS (other than the paper itself) are really REQUIRED. However, some folders like to use the handle of an ordinary butter knife to crease their folds. (If you fold a LOT or origami, your thumbnail may get uncomfortably HOT. And, you may wear grooves into your nails that interfere with other activities.) Scissors or a paper cutter are, of course, necessary to cut paper to specific sizes and shapes. (Even some authentic and historic Japanese origami sometimes requires cuts or slits in the paper.) Toothpicks, skewers, and tweezers are sometimes useful to put a stubborn flap into its proper place.

Paper (almost all kinds -- except paper napkins) Knife with smooth handle (and no sharp blade) Scissors Toothpicks Skewers Tweezers Paper cutter Glue, tape, wire (These supplies are used mostly to 		stabilize models for long-term display, so 		they don't unfold themselves and look sloppy.)

- - - - - - - - -

NOTES TO PARENTS AND TEACHERS 

3. HOW TO PREPARE MATERIALS
 Inasmuch as not everyone has received the benefits of growing up in a family where construction engineering, drafting design, and other scientific and technological activities were everyday occurrences, I feel it to be necessary to give instructions for the preparation of the materials I expect to use.

I am planning to bring prepared materials for these special projects, in order to allow you to begin working without delay.

I. SUMMARY OF POPULAR 3-D SHAPES

Summary of Requirements for Popular Shapes, by shape and by number required (see the source books) Name			Shape	#	Shape	#	Shape	# Regular Tetrahedron	3-sides	X 4 Cube			4-sides	X 6 Regular Octahedron	3-sides	X 8 Regular Dodecahedron	5-sides	X 12 Regular Icosahedron	3-sides	X 20

Truncated Tetrahedron	3-sides	X 4	6-sides	X 4 Truncated Cube		3-sides	X 8	8-sides	X 6 Truncated Octahedron	4-sides	X 6	6-sides	X 8 Truncated Dodecahedron	3-sides	X 20	10-sides X 12 Truncated Icosahedron	5-sides	X 12	6-sides X 20 AKA Soccer ball, AKA Bucky ball Cuboctahedron		3-sides	X 8	4-sides	X 6 Icosadodecahedron	3-sides	X 20	5-sides	X 12 Rhombicuboctahedron	3-sides	X 8	4-sides X 18 Rhombitruncated		4-sides	X 12	6-sides	X 8	8-sides	X 6 Cuboctahedron Rhombicosadodecahedron	3-sides	X 20	4-sides	X 30	5-sides	X 12 Rhombitruncated		4-sides	X 30	6-sides	X 20	10-sides X 12 icosadodecahedron Snub Cube		3-sides	X 32	4-sides	X 6 Snub Dodecahedron	3-sides	X 80	5-sides X 12

Prisms			n-sides X 2	4-sides X n Anti-Prisms		n-sides	X 2	3-sides	X 2 X n

Note: Some of these shapes are obviously precursors of the geodesic dome, invented by architect R. Buckminster Fuller, and featured in some museums of art. I did not make up the names of these shapes! But various (allegedly authoritative) sources sometimes get some of the names mixed up. 

4. MAKING POLYGONS FOR 3-D SHAPES
 Materials: Ordinary Poster Board (white, or colored, one or both 		sides. What I get in Mayland, USA, is usually 		22 inches by 28 inches.)

Tools: Yardstick (or meter stick, if outside United States) ( I can use my computer to convert 1 inch to 25.4 mm) Ball-point Pen, or pencil Scissors

Procedure: 

5. GENERAL HINTS
 Turn your measuring stick onto its edge when laying out the dimensions. This puts the graduations on the measuring stick closer to the poster board, which should improve the accuracy of your lay out.

Sight down along the edge of your straight-edged measuring stick to be sure that it really is straight. You want to draw straight line segments, not curves.

The taper of a ball-point pen or a sharpened pencil, when held against the straight-edge, leaves a small gap between the edge of the straight instrument and the location of the line which will be drawn. This small gap is good; it helps prevent smearing of ink, if you use a pen. But you will need to estimate the size of this gap, carefully and accurately, in order to draw the lines exactly where you want them to be.

Clamp the straight-edge FIRMLY against the poster board with one hand. You do NOT want it to move as you are drawing the lines. With the pen or pencil held in the other hand, far enough above the poster board so as to leave NO MARK, practice a few times making a smooth, sweeping stroke, while letting one finger gently touch the guiding edge. After you gain confidence that you can make a smooth, sweeping stroke with a comfortable movement of your entire arm, lower the pen or pencil to touch the poster board, RELAX, and draw your first line. If that line looks good: smooth, straight, and well-positioned, continue. If it doesn't look so good, take a deep breath, try to figure out what went wrong, reposition your straightedge, clamp, RELAX, practice for a smooth stroke, and try again.

After a few years, all of these hints will become automatic for a skilled draftsman. But you probably want to help your kids with their homework THIS WEEK. So, I try to share all these hints with you. Relax! If you can cut the pieces accurate within a sixteenth of an inch, you are doing very well, indeed.

I have calculated (there goes my ban on arithmetic!) dimensions to make many of the shapes, to the nearest quarter of a sixteenth of an inch, in hopes of making it easier for you to lay out these shapes. (I have also calculated the metric dimensions to use.)

The same materials and tools are used for making all of these shapes.

Note: You will want to use regular poster board, that you can easily cut with ordinary scissors. I am using poster board, because I need to make a lot of these shapes, and poster board (in various colors) looks a 	lot nicer for public presentation than a wonderful substitute.

WONDERFUL SUBSTITUTE:

Salvage the cardboard from cereal boxes, snack boxes, and other sources. Throw them away if they are stained by garbage, but keep and use them if they are clean and dry. Cut the boxes along the seams, so they can lay flat for storage. The back side is usually a 	plain gray or light brown color; ball-point pen ink shows up well to mark your lines for cutting out shapes. It's FREE, (or at least, already paid for), readily available, and ecologically GREEN! Once upon a time (decades ago, before TV became popular), packagers would print designs intended for paper engineering and paper sculpture on their boxes, to be cut out and assembled into model cars, and trains, rockets, and airplanes. START YOUR OWN TOY FACTORY!

ADDITIONAL BENEFITS:

As you disect boxes to salvage the cardboard, you also have an unusual opportunity to explore the many ways professional packaging engineers have solved problems important in manufacturing and commerce. Some boxes are stapled together, some are die-cut, with flaps and slots which lock tother, but most boxes are glued.

Interesting problem: In how many ways can you unfold a cubical box? Kunihiko Kasahara uses many of these ways in his famous "Panorama Cube", as published in 	_Origami_Omnibus:_Paper-folding_for_Everybody_, Japan Publications, Inc., Tokyo, New York, ISBN 0-87040-699-X, (paperback 384 pp.). This book also contains his instructions for folding modules to make ALL of the regular and semi-regular using only origami folding techniques.

Most boxes for commercial packaging are also printed, often in may colors. You were probably taught in 	school that the "primary colors" (for SUBTRACTIVE color 	mixing) are red, yellow, and blue. These colors work fairly well, for painting posters, but did you know that professional printers usually use magenta, yellow, cyan, and black inks? (OK. so they sometimes call 	these colors "process red", "process yellow", 	"process blue", and black. Still they refer to a "MYCK" 	color system.) You will find their calibration marks and the symbols used to align high speed printing presses, printed in magenta, yellow, cyan, and black ink on many boxes, if you look for them.

Speaking of colors, your computer monitor uses a different color system -- ADDITIVE color mixing. The primary colors used for this are red, green, and blue. Red and green, added together, make yellow, which is the color of one of the inks used by printers. Green and blue add to make cyan, and red and blue add to make magenta. People who use computer monitors or 	color television equipment often use these names for colors.

Materials: Poster board (Do NOT try to use foam-core board for 	these projects!)

Tools: Yardstick Ball-point pen, or pencil Scissors 

6. TO MAKE SQUARES
<PRE> Squares make a regular tessellation, so this should be easy and obvious. I can usually trust the corners of machine-made poster board to be accurate 90 degrees angles (i. e., square).

Procedure: (1) Be sure to measure from the same short side each time when you make evenly spaced marks one inch (25.4 mm) apart along each long side of the poster board. (2) Be sure to measure from the same long side each time when you make evenly spaced marks one inch (25.4 mm) apart along each short side of the poster board.

RIGHT WAY		WRONG WAY

++		++	Do you see |   |    |  |		|    |    |  |	the difference? |           |		|            |	Do you |           |		|            |	understand |   |    |  |		|  |    |    |	why it is ++		++	important?

The above instructions will be important for many other projects which require the laying out of grids.

+--+--+--+--+--+	| |  |  |  |  |	+--+--+--+--+--+	You are trying | |  |  |  |  |	to make a grid, +--+--+--+--+--+	something like | |  |  |  |  |	this, only much +--+--+--+--+--+	more extensive. | |  |  |  |  |	+--+--+--+--+--+

(3) Connect all of the marks by drawing parallel line segments, as indicated in the diagrams above. (4) Cut the poster board into strips along the lines you have drawn. (5) Cut each strip into squares.

Yield: A piece of poster board 22 inches by 28 inches should make 616 1-inch squares. </PRE>

7. TO MAKE TRIANGLES AND HEXAGONS
<PRE> Although triangles and hexagons each make regular tessellations, I prefer to use a semi-regular tessellation which includes both shapes instead; this makes it so much easier to cut out the hexagons.

a           b                   f           d	.            ________________________________. /   \  /    \  /    \  /    \  /	           /      \/      \/      \/      \/	          /\      /\      /\      /\      /	         /__\____/__\____/__\____/__\____/  	        /    \  /    \  /    \  /    \  /	       /      \/      \/      \/      \/	      /\      /\      /\      /\      /\	     /__\____/__\____/__\____/__\____/__\ 	            /    \  /    \  /    \  /    \  /    \	   /      \/      \/      \/      \/      \	  /\      /\      /\      /\      /\      /\	c/__\____/__\____/__\____/__\____/__\____/__\.e

Procedure: It is easy to make angles of 30 degrees and 60 degrees with a yardstick or ruler, when you know how. In the diagram above, line segment "bc" should be 6 inches long. To 	construct this line segment, measure off 3 inches from the corner at "a".

Note: This diagram is intended only to show the princples of the construction! You will achieve more accurate angles if you use longer baselines. I suggest "ab" should be 12 inches (or 30.48 centimeters), and "bc" should be 24 inches (or 60.96 centimeters). In any case, you want the edges of the shapes you finally cut out, to be 	one inch (or 2.54 centimeters) long.

Mark point "b" with a pen or pencil. Keeping one of the graduations of the yardstick at 	point "b", swing the yardstick (or meter stick) until you find point "c", 6 inches away, at the edge of the poster board. Now you can draw line segment "bc". Mark off equal 1-inch (2.54 mm) intervals along this line segment. Mark off equal 1-inch (25.4 mm) intervals along the edge "abfd" of the poster board. Measure length "ac", then mark point "e" at that same distance from edge "abfd". Now you can draw line segments "ce" and "ef", then mark off equal 1-inch (25.4 mm) intervals along each line segment. This should give you enough grid points to 	cover the poster board with triangles and hexagons. Note: all lines should be parallel to the edge "abfd", to line segment "bc", or to line segment "ef".

Once the grid is drawn, you can cut strips of hexagons and triangles. Trim off all of 	the triangles from each strip, and you should be left with a pile of hexagons, and another pile of equilateral triangles.

Yield: [ INCOMPLETE #3 of 23 -- RCB ] YIELD I got [ ?? -- RCB ] hexagons and [ ?? -- RCB ] equilateral triangles from my sheet of poster board. There was some scrap near the edges of the sheet. </PRE>

8. TO MAKE REGULAR PENTAGONS
<PRE> Although the above polygons nest together to 	form space-filling tessellations, regular pentagons cannot fit closely together.

There will be gaps between these and all of the following shapes. I think that the easiest way to make a lot of these shapes is to first make a grid of carefully calculated measured rectangles, then connect the grid points with line segments which outline the desired shapes. You have already used this method once; since a network of 	rectangles is also a network of squares, if the dimensions are correct. I will do the rest of the (ugh!) arithmetic for you, or show you ways to avoid most of the arithmetic. </PRE>

After some experimentation, I was able to upload my first picture into Wikimedia Commons. Here it is!



<PRE>

Example Calculations: (You may skip down to "Procedures", if trigonometry 	scares you. I'm trying to be a counter-terrorist, 	myself.) There is an incredible irony here! I know a very easy way to arrive at the measurements without arithmetic, but I have a computer instead of a drafting table and instruments. (Hey! I'll 	keep the computer!) That very easy way (without 	arithmetic) is simply to make a scale drawing (using a protractor and a ruler) of a pentagon, and measure the relevant dimensions.

C	g+--_+-+j |  _-  |\    |	This diagram of a regular |_-    | \   |	pentagon is about as good as B+---|--\--+	I can make it in text mode. |      |   \ |	Computer graphics is an	 |       |    \|	enormously complicated m+-+-+-+D	subject which I prefer |    O |f   /|	to postpone until some |      |   / |	later time. A+_--|--/--+ | -_   | /   |	 |     -_|/    |	This is diagram one, h+---+-+k	which will be mentioned E 		below.

This diagram will serve for the purpose of	being an example for the calculations, whose results follow. It also indicates how the outline of the regular pentagon will fit on the grid you will construct.

We want line segment "AB" to be 1 inch (or 2.54 centimeters metric). Point "O" is supposed to be the center of our pentagon. 360 / 5 = 72	Angle "AOB" is one fifth of a circle, or 72 degrees. Half of this angle is 36 degrees. 72 / 2 = 36 	Let "m" be the midpoint of line segment "AB". Then angle "mOB" is 36 degrees, angle "BmO" is 90 degrees, and line segment "mB" is 1/2 inch (or 12.7 mm, if you are using metric 	measurements). C	g+--_+-+j 90 18_- |\54 90	Let's see if I can emphasize |_- 54|54\   |	the important angles. B+54   |   \36+ | -_ 72|   \ |	360/5 = 72	 | 36-_|72  54\|	m+-+---+D 	180 - 72 = 108 | 36_-O72 54/| | _- 72|   / |	A+_54   |   /36+	108 / 2 = 54 |72-_54|54/  |	 90  18-_|/54 90	90 - 54 = 36	 +---+-+                 E

Line segment "mOfD" is supposed to be a 	horizontal diameter of the circle with center "O", which passes through all five vertices of the desired regular pentagon, and is a line of symmetry.

This is enough information to apply 	Length("Bm")/Length("mO") elementary trigonometry (tri = three, 	= tangent(36 degrees)	gono = angle, metry = measure), to 	calculate other measurements of the 	Length("mO") = triangle "BOm". Length("Bm")/tangent(36)

Having emphasized the angles and the triangles, (and having thouight for 	several days about how best to provide 	this information), I find that the relevant facts are these:

H * cos(18) g+---_+C H * |90     18_- sin |      _- (18) |72_- H	    B+-

(1) Right triangle "BCg" has acute angle 18 degrees and hypotenuse H = 1 inch (25.4 mm). Elementary trigonometry (this 	is what I was searching for) gives Length("gC") = Length("BC") * cosine of 18 degreees. I also found that Length("Bg") = Length("BC") * sin of 18 degrees.

H * sin(18) C+---+j \     |	   \     | H * \   | cos H \  | (18) \36|	      \ |	        \|	         +D

(2) Right triangle "CDg" has acute angle 36 degrees and hypotenuse H = 1 inch (25.4 mm). Then Length("Cj") = Length("CD") * sin (18 degrees), and Length("Dj") = Length("CD") * cosine(18 degrees).

A quick little QB64 BASIC program gives the measurement numbers we want to mark. </PRE>

9. SOLVING AN OPTIMIZATION PROBLEM WITHOUT CALCULUS
[ INCOMPLETE! #4 of 23—RCB ] OPTIMIZATION CALCULATION

10. SOURCE CODE FOR THE QB64 BASIC COMPILER
<PRE> Pi = 4.0 * ATN(1.0) ' Computers and calculus students have an easier time calculating ' trigonometric functions when the angles are expresed in radians. ' Multiply the angle by Pi / 180 to convert degrees to radians. PRINT "Pi ="; Pi

PRINT "This program calculates dimensions for grid to make regular pentagons. " PRINT "16 * cos(36); 16 * sin(36):" PRINT 16 * COS(36 * Pi / 180) PRINT 16 * SIN(36 * Pi / 180) PRINT PRINT "16 * cos(18); 16 * sin(18):" PRINT 16 * COS(18 * Pi / 180) PRINT 16 * SIN(18 * Pi / 180) PRINT "(Dimensions in sixteenths of an inch.)" PRINT PRINT "25.4 * cos(36); 25.4 * sin(36):" PRINT 25.4 * COS(36 * Pi / 180) PRINT 25.4 * SIN(36 * Pi / 180) PRINT PRINT "25.4 * cos(18); 25.4 * sin(18):" PRINT 25.4 * COS(18 * Pi / 180) PRINT 25.4 * SIN(18 * Pi / 180) PRINT "(Dimensions in millimeters.)" END </PRE>

11. RESULTS OF RUNNING THE PROGRAM
<PRE> Pi = 3.141593 This program calculates dimensions for grid to make regular pentagons. 16 * cos(36); 16 * sin(36): 12.94427 9.404564

16 * cos(18); 16 * sin(18): 15.2169 4.944272 (Dimensions in sixteenths of an inch.)

25.4 * cos(36); 25.4 * sin(36): 20.54903 14.92975

25.4 * cos(18); 25.4 * sin(18): 24.15684 7.849032 (Dimensions in millimeters.)

But it was so much easier just to make the scale drawing and measure off the dimensions I wanted! Here is a picture!

[ INCOMPLETE #5 of 23 ] PENTAGON PICTURE </PRE>



<PRE> Here is how to find the necessary dimensions WITHOUT ARITHMETIC! (1) Tape a piece of paper to your drawing board. (2) Using your T-square pressed against the edge of the drawing board as a guide, draw a horizontal line near the middle of your paper. (3) Using a drafting triangle, (pressed against the 	T-square, which is still pressed against the edge 	of your drafting table) as a guide, draw a second line near the center of your paper, perpendicular to the first line you drew. (4) Put the center of your protractor over the intersection of the two lines. Align the 0 and 180 degree marks with the first line you drew on your paper. (5) Using the aligned protractor, put a mark at 72 degrees. Then, put another mark at 144 degrees. (6) Turn the protractor 180 degrees, then re-align it. (7) Make two more marks, at 72 and 144 degrees. (8) Now, using a straightedge as a guide (a straight 	side of your drafting triangle will do nicely), draw four line segments which connect the marks you made with the protractor, to the intersection of the first two lines you drew (Where the center of the protractor 	went). (9) Make two marks 1/2 inch (12.7 mm) from the first line you drew (one mark on each side.). (10) Using your T-square as a guide, draw two new lines, parallel to the first line you drew. These lines, 1 inch (25.4 mm) apart, establish the size, or scale, of the regular pentagon you are constructing. They intersect the lines you drew at 144 degrees at points "A" and "B" per diagram one. (11) Use your drafting compass to draw a circle through points "A" and "B", having its center at the intersection of the first two lines you drew. This will establish points "C", "D", and "E", according to diagram one. (12) Now that you have located the five vertices of your regular pentagon, connect them by drawing line segments "AB", "BC", "CD", "DE", and "AE". (13) Complete your drawing of the rectangle "gjkh" about regular pentagon "ABCDE". Measure the parts of this rectangle, then use these dimensions to lay out your grid on your poster board.

After you find the answer to a problem, sometimes you wonder why it took you so long to find the answer!

Information summary:

What's in the diagram	US Measure 	Equivalent Metric measure

Length("gB")		5/16 inch	7.85 mm  Measure off these Length("Bm")		8/16 inch	12.7 mm  distances along Length("mA") = "Bm"	8/16 inch	12.7 mm	 one edge of your Length("hA") = "gB" 	5/16 inch	7.85 mm	 poster board.

Length("gC")		15.25/16 inch	24.16 mm  Measure these along Length("Cj")		9.5/16 inch	14.92 mm  perpendicular edge.

Procedure:

(1) Measure off and mark the four lengths "gB", "Bm", "mA", and "hA" along one edge of your poster board. (2) Repeat step (1), until you have marks all along one edge of your poster board. (3) Repeat steps (1) and (2) all along the opposite edge of your poster board. (4) Connect corresponding marks with a series of parallel line segments. (I recommend using a long 	straightedge to draw these lines.) (5) Two edges of your poster board have not been marked yet. Along one of these edges, measure off and mark the two lengths "gC" and "Cj". (6) Continue measuring and marking lengths "gC" and "Cj", all along the edge you have started marking. (7) One edge of your poster board has not been marked yet. Use lengths "gC" and "Cj" to mark this edge. (8) Connect corresponding marks with a series of parallel line segments. (I recommend using a long 	straightedge to draw these lines.) (9) Use a short straightedge as a guide to draw all five sides of each regular pentagon in your grid. (10) Cut your poster board into strips, so that each strip contains an entire row of regular pentagons. (11) Cut each strip into rectangles, so that each rectangle contains a regular pentagon. (12) Trim each rectangle. Keep all of the regular pentagons. Discard all of the triangular scraps.

Yield:	[ INCOMPLETE #6 of 23 ] YIELD I got [ ?? -- RCB ] regular pentagons from my sheet of poster board. Some scrap had to be trimmed from each rectangle. </PRE>

12. TO MAKE REGULAR OCTAGONS
<PRE>

+m   +---+    n+	Note: This diagram is /C      D\     	distorted. (It's too	   /           \    	tall.) Technical /            \   	difficulties such as	  /               \  	this often arise when /                \ 	one tries to push +B                E+	equipment beyond the |                  |	limits for which it |                  |	 was designed. Word |                  |	processors were never |        O         |	designed for making |                  |	diagrams. But creative |                  |	thinking often requires |                  |	that one thinks beyond +A                F+	the normal limits. \                /	  \               /  	This shape has four-fold \            /   	rotational symmetry, so 	    \           /    	a lot of the lengths in \H      G/	the diagram are identical. +q   +---+    p+

Angle "mBC" is supposed to be 45 degrees. A true scale diagram, or trigonometric calculation, would establish this as a fact. Triangle "mBC" is thus an iscoceles right triangle, with some interesting and unusaul properties. If Length("BC") = 1 inch (25.4 mm) then length("mC") = length("mB") = cosine(45 degrees) = sine(45 degrees) = 1/2 the square root of 2 = 0.7071.

Table of measurements: Length("mB") = Length("mC")	11.25/16 inch	(17.96 mm) Length("AB") = Length("CD")	1 inch		(25.4 mm) Length("qA") = Length("Dn")	11.25/16 inch	(17.96 mm)

Procedure: (1) Measure off the dimensions for one cell of the grid along one edge of your poster board. (2) copy these measurements along the edge to make as many grid cells as possible along that edge. (3) Repeat steps (1) and (2) along each of the other three edges of your poster board. (Remember to start 	all of your measurements from the correct edge of the 	poster board.) (4) Use a long straightedge as a guide to draw line segments connecting corresponding measured marks. (5) Cut your poster board into strips along the grid lines you have drawn. (6) Cut each strip into squares along the grid lines. (7) Trim away the triangles from each square. (8) Discard the triangular scraps.

Yield:	[ INCOMPLETE #7 of 23 ] YIELD Four triangles of scrap had to be trimmed from each square to make [ ?? -- RCB ] regular octagons -- "stop signs". </PRE>

13. TO MAKE REGULAR 10-SIDED POLYGONS
<PRE> The computations for laying out the grid for this shape are somehat like the process for laying out the regular pentagons, except for the essential fact that there are twice as many sides for this 10-sided shape.

Table of measurements:

Procedure:

Yield:

[ INCOMPLETE! #8 of 23 -- RCB ] YIELD

14. TO MAKE REGULAR 12-SIDED POLYGONS
None of the regular or semi-regular polyhedra require this shape, but it can be used nicely to 	make a pretty semi-regular tessellation, prism, or anti-prism, so I try to include a few instances of this shape.

Table of measurements:

Procedure:

Yield:

[ INCOMPLETE! #9 of 23 -- RCB ] YIELD </PRE>

14. A SAMPLE CONSTRUCTION
On top of everything else, I messed up the numbers. Easy fix! Ray Calvin Baker (talk) 21:06, 9 August 2012 (UTC)

<PRE> [ INCOMPLETE! #10 of 23 -- RCB ] DIAGRAM NEEDS EXPLANATION

c  c   c   c   c	  /\  /\  /\  /\  /\ a/__\/__\/__\/__\/__\a \ /\  /\  /\  /\  /\      	 b\/__\/__\/__\/__\/__\b \ /\  /\  /\  /\  /     	    \/  \/  \/  \/  \/	     d   d   d   d   d

This diagram needs an explanation! and further instructions. </PRE>

It is a good idea to put together as much of a model as you can on a flat surface, such as a table. This allows you to apply maximum pressure to taped or glued joints, to make a stronger model.

< - - Click there to see 20 Equilateral Triangles assembled.

Here is an animated, stereoscopic picture (3-D, if you know how to look at such images. If you have experience with the once-popular "Magic Eye" pictures, then you know how to do this.),which I found in Wikimedia Commons. It illustrates how the above diagram should be assembled. Wikimedia Commons used a slightly different "net", but the assembly principles are the same. Ray Calvin Baker (talk) 00:37, 10 August 2012 (UTC)

== 15. MAKING TOOLS FOR BUILDING A TRADITIONAL FOLK ORNAMENT --

<PRE> III. MAKING TOOLS FOR BUILDING A TRADITIONAL FOLK ORNAMENT The special tool you will want for this project is 	a loop of wire which will fit through a drinking straw, to pull a length of string through the straw.

Materials: Wire (light gauge doorbell hookup wire from a 		hardware store works just fine)

Tools: Wire cutters Pliers (needle-nosed pliers work best) Ruler Ball-point pen or pencil

Procedure: (1) Measure off a piece of bell wire about 50 per cent longer than a drinking straw. (Drat! More of that 	arithmetic!) (2) Form a loop at each end of the piece of wire, using the needle-nosed pliers. DON'T POKE YOUR EYE OUT! To minimize the danger of that, I recomment a loop at each end of the piece of wire. (3) Twist the short end of the loop around the wire several times. Do this with each of the two loops. (4) Squeeze each loop down to size, so that it will fit easily through the drinking straws, while keeping the loop large enough to slip a piece of string through it. </PRE>

15. PREPARING MATERIALS TO MAKE KEPLER'S STAR
Still fixing the numbers! Ray Calvin Baker (talk) 21:08, 9 August 2012 (UTC) <PRE> IV. PREPARING MATERIALS TO MAKE KEPLER'S STAR

Materials: Take one sheet of paper 8+1/2 inches by 11 inches for each star you wish to make.

Tools: Ruler Ball point pen or pencil Scissors

Procedure: The end of a ruler or yardstick sometimes gets battered and worn, and may not be well aligned with the graduations of the measuring instrument. To avoid these possible errors, I usually align the 1-inch mark with the place from which I wish to measure. This can cause its own type of 	errors, but it is usually easy to spot and fix if your measurements are off by exactly one inch.

(1) Align your ruler with the 1 inch mark at the edge of the paper. Mark along both of the short edges at 3 inches, at 5 inches, at 7 inches, and at 9 inches. This will leave 1/2 inch of waste along the long edge. (2) Align your ruler with the 1 inch mark at the edge of the paper. Measure and mark along the long edges at 4+1/2 inches, at 8 inches, and at 11+1/2 inches. (I avoid using 	a hyphen in mixed numbers like these; it can too easily be 	mistaken for a "minus" sign, leading to subtraction instead 	of addition.) This process of measuring and marking will leave 1/2 inch of waste along the short edge. (3) Using the ruler as a straight-edge, draw line segments to connect the marks. There should be four lines running the long way, and three lines running the short way. (4) Cut the paper along the lines.

Yield: Twelve paper rectangles, each 2 inches by 3+1/2 inches, sufficient to make one Kepler's Star.

I was so amazed that the proportions for this project worked out within a sixteenth of an inch, that I wondered if variations of this folding technique would work. I found two more stars that make very nice decorations.

Several other types of stars (Projects VI. and VIII., as described below) can be constructed using variations of the techniques used to make Kepler's Star. Instructions for preparing the paper for these stars is fully described below, as an essential part of these additional projects.

Materials for all other projects are so basic, and no special tools are required. so instructions given for all of the other projects should be sufficient and complete, as described below.

- - - - - - - - - </PRE>

16. MAKING 3-D SHAPES
I'll get there someday, even if I need to take baby steps. Ray Calvin Baker (talk) 21:12, 9 August 2012 (UTC) <PRE> I. MAKING 3-D SHAPES (Paper Sculpture)

Although this is the simplest activity, even graduate students at George Washington University found it extremely interesting when I shared it with them.

Materials: Cardboard shapes (carefully measured and cut out, each side about one inch long) Equilateral triangles Squares Regular pentagons, hexagons, octagons Regular ten- and twelve-sided shapes (Consult the source books to estimate	the numbers required for each shape.) Instructions and hints for making these are given above. Masking tape Illustrations of the five regular and thirteen semi-regular polyhedra (These may be compared with the three regular and eight 	semiregular tessellations)

Tools: Scissors (to cut the masking tape)

Source books: Ball, W. W. Rouse and H, S. M. Coxeter, _Mathematical_ _Recreations_and_Essays_ (Thirteenth Edition), Dover Publications, Inc., 1987, ISBN 0-486-25357-0 (pbk.) Fuse, Tomoko, _Multidimensional_Transformations_Unit_ _Origami_, Japan Publications, Inc., 1990, ISBN 0-87040-852-6 (pbk.) Wells, David, _The_Penguin_Dictionary_of_Curious_and_ _Interesting_Geometry_, Penguin Books, ltd., London, 1991, ISBN 0-14-011813-6 (pbk.)

Procedure: Make the materials and tools available to the students. Construct a simple shape, such as a cuboctahedron, by sticking the necessary pieces together with squares of masking tape. During construction, show that parts of the structure can lie flat, until other parts are added, requiring that folds be made to allow the developing structure to take its final three-dimensional shape. Compare the final shape with its descriptive diagram.

Instruct the students to (1) select the shape they would like to build, (2) gather the necessary pieces, (3) cut squares of masking tape, and (4) assemble their model.

Inexperienced students may need to select additional pieces and cut additional masking tape. Accuracy in making the necesssary estimates comes with experience. Encourage cooperation: for example, one student may cut masking tape for several other students, with the understanding that he will receive help later, in building his own model. Note to helpers: Be a helper; don't "take over" someone else's model. Although neatness is commendable, any model which holds together and allows the student to see the relationships between the descriptive diagrams and the final, intended shape should be instructive. As time permits and interest persists, and supplies last, students may gain proficiency by building several models. </PRE>

17. SHAPES IN SPACES
One step at a time. Ray Calvin Baker (talk) 21:14, 9 August 2012 (UTC)

<PRE> This is an open-ended activity, which COULD lead from the regular and semi-regular tessellations, and the regular and semi-regular polyhedra, prisms and anti-prisms, to the four Kepler-Poinsot polyhedra, to five more convex deltahedra, to 53 additional uniform polyhedra, to 92 convex polyhedra with regular faces, not to mention compound polyhedra and other stellated polyhedra. There is a LOT of territory here, not all of it well known or thoroughly explored. And then, many of these can be used in the constuction of polytopes, of which there are 16 regular polytopes, etc. After all that, I'm sure I missed a few. And there are some of these shapes which I have never yet seen myself.

Some shapes may be rigid enough to leave some "windows" -- places where you deliberately do not tape in a shape. Instead, put a small knick-knack or an origami bird, flower, or angel into your model for a different way to display your folding skills.

If this activity is going well, I may be able to demonstrate a few simple, traditional folds that create sequences of origami models, while some students are completing their paper sculptures. One example of this is "the multi-fold", which includes the oldest documented paper fold in Western culture, "Pajarita, the little Spanish bird". Another example is "the salt cellar" (formal title), which changes from "cootie catcher" to "the lover's knot", to "anvil", "sawhorse", and "crown". Another sequence, based on the "triple blintz fold", includes "perfume vial", "Japanese lantern", "Yokosan", and a "cross". Historically, such sequnces have inspired several story-tellers.

- - - - - - - - -

II. A MOST USEFUL ORIGAMI MODEL </PRE>

18. A BOX WITH LID
1 -- 2 -- 3 -- The Wikiversioty is free! but not yet free of all my stupid mistakes. Still Working! Ray Calvin Baker (talk) 21:17, 9 August 2012 (UTC)

<PRE> (storigami: "Brothers Tall and Brothers Short")

Historical Note: [ INCOMPLETE #11 of 23 -- RCB ] SEE "The Paper" I made up my own poem for this project. But the essential idea was mentioned in - [source needed]

Materials: Two sheets of 8+1/2 inch by 11 inch paper (One sheet for the box, one sheet for the lid)

Source book: Sakoda, James Minoru, _Modern_Origami_, Simon and Schuster, New York, NY, 1969, ISBN 0-671-20355-X (pbk.)

Procedure: Since this is "storigami", the paper folding is intended to illustrate the story. The words of the story contain important clues concerning the sequence of folds, and the appearance of the paper after each fold (or series of folds).

"Brothers Tall and Brothers Short"

(Stage directions -- instructions how to fold and display the paper -- are included between a pair of parenteses, like this. The actual story is enclosed in quotation marks. Give each student two sheets of ordinary 8+1/2 inch by 11 inch paper. Invite them to watch carefully, and try to fold along, as the story is told. Try to pace the story, and intervene as necessary, so that no one gets left behind. This story is told in a way which will help everyone remember the essential steps. Adults and older children should find that the boxes with lids are extremely useful for storing household items, and items for hobbies and crafts.)

"This is the story of the Brothers Tall, Who didn't like extras creases at all."

[ INCOMPLETE #12 of 23 -- RCB ] Illustrations are needed, if possible.

(Place a single sheet of paper on the table in front of you, with the long edges running from left to right. Pick up the nearest edge, and place that edge exactly over the farthest edge. The paper should roll smoothly into a cylinder-like shape. Gently and carefully flatten the cylinder. Make a single length-wise crease down the middle of the sheet of paper. This is a valley fold.

Note FYI: The first six creases, as described in the following steps, should all be valley folds, all facing upwards.

Lift your creased paper up off the table, and display the Brothers Tall. Let your imagination fill in the picture of the two brothers. Since this is the first crease, there are NO extra creases whatsoever, which the Brothers Tall dislike so much.)

"And they lived in a plain, long tent, To save money on rent."

(Display the plain, long tent shape formed by one crease. The tent shape clearly demonstrates that what is a valley fold on one side of the paper, is a mountain fold on the other side.)

"Each fell in love with a girl from next door; Soon they were married, now there are four."

(Make two more long creases to meet the previous crease in the middle. Note: When making the lid, leave a gap about the size of these words: "It is OK". Lift the paper to display the two couples. Let imaginations fill in the features of these two lovely couples.)

"They moved into a plain, long house, Because each had a spouse."

(Display the long house shape formed by the three parallel creases.)

"When they went to the cupboard, the cupboard was bare. There weren't even any shelves in there!"

(Hold the paper so the creases are all vertical. Open and close the cupboard doors. Notice that there are no shelves, because there are no extra creases.)

"That was the story of the Brothers Tall, Who didn't like extra creases at all. So short! So sad! Don't cry or make the paper wetter. Just place it on the table, and give it a turn, I hope, a turn for the better."

(Place the paper flat on the table, then rotate it 90 degrees. This is the "turn for the better".)

"This is the story of the Brothers Short, Who liked to wear stripes just for sport."

(Make a single crease down the middle of the paper. This crease should cross the three creases left from the previous story. Let imaginations fill in the picture of the Brothers Short, but point out that the stripes are real -- the creases.)

"They lived in a short, striped tent, To save money on rent."

(Display the short tent form, with its stripes.)

"Each fell in love with a girl from next door. Soon they were married; now there are four."

(Make two more short creases to meet the short crease in the middle. When making the lid, leave a gap about the size of these words: "It is OK". Notice that the girls like stripes, too. What lovely couples!)

"They moved into a short, stiped house, Because each had a spouse."

(Display the shape of the short, striped house.)

"They went to the cupboard; each shelf was filled with stuff. Plenty of stuff, and plenty's enough."

(Hold the paper so that the three short creases are all vertical. Open and close the cupboard doors. The shelves are real (they are the creases left from the first part of the story), but you'll have to imagine the "stuff".)

"With enough in the cupboard, each family begins. Soon each mommy is the mother of twins. Pick up each corner, and fold to the line, You've done it just right, you've done it just fine. Now pull up the blanket, over their toeses, Until all that sticks out is the tips of their noses. "

(Follow the instructions. My, what big noses these children have!)

"Turn everything 'round; the paper spins, so the other mommy can see both of HER twins. Pick up each corner, and fold to the line, You've done it just right, you've done it just fine. Now pull up the blanket, over their toeses, Until all that sticks out is the tips of their noses."

(Follow the instructions. My, these children have big noses, too! Is it nice to tease? Of course not!)

"See how cleverly each corner locks. Now, reach in and pull up, to open your box."

(Do I need to draw you a picture? This really is a very clever way to fold a box. To make a lid for your box, just take another sheet of paper, and repeat the story all over again, with two minor changes. Leave small gaps in the middle, "It is OK", when you make the folds which introduce the girls from next door. This will make the lid wider and longer than the box, but not quite as deep. Each lid has a folded rim, which can serve as a convenient label for the intended contents of each box. Just be careful to notice how the lid will fit on the box, so you don't write the label up-side-down!)

(Now that you have mastered this story, if you ever get paid for it, you will be a "professional boxer"! (A joke. Ha, ha.))

- - - - - - - - - </PRE>

19. A TRADITIONAL FOLK ORNAMENT
Learn humility! Try to program a computer! Ray Calvin Baker (talk) 21:20, 9 August 2012 (UTC)

CORRECTIONS in progress! Ray Calvin Baker (talk) 21:05, 11 August 2012 (UTC)

<PRE> III. A TRADITIONAL FOLK ORNAMENT THIRD STELLATION OF THE REGULAR PENTAGONAL DODECAHEDRON (other materials)

My apologies are in order. I had an incorrect diagram in this section. The old diagram is good for taping equilateral triangles together (see above) to make the regular icosahedron. but it is totally incorrect for making that shape with string and plastic straws. A complete rewrite of this section is in progress.

Materials: 75 Plastic soda straws (to make one ornament) String white glue (optional)

Tools: Scissors wire loop (narrow enough to fit through the hollow 		straws. Instructions to make this tool are 		given above.) Ball-point pen Ruler (optional)

Procedure: CUT 15 STRAWS IN HALF

WARNING! Pieces this size will make an enormous ornament nearly 1 meter in diameter! That's suitable if your Christmas tree is a Giant Sequoia or a Giant California Redwood. But, you may wish to cut eaqch piece in half, to make two smaller ornaments instead.

Place two straws side-by-side. Estimate the location of the center of the straws, then make a short mark there with the ball-point pen. Turn one of the straws end-for-end, then place it back beside the other marked straw. If the marks line up, you did a good job of finding the center. If the marks are off by a fraction of an inch, estimate the location of the place midway between the short marks, then make a longer mark there. (This process should reduce your 	error by half.) OR, use the ruler to measure off half the length of the straws. Cut both straws in half at the marked 	places. Use these half straws to measure off the halfway point on thirteen more straws. Mark and cut those straws in half.

Now you should have 30 half length pieces, and 60 full length pieces. </PRE>

20. BUILD THE CENTRAL CORE OF THE ORNAMENT
CORRECTIONS (actually a complete rewrite of this section) are in progress. It's still not complete yet, and it needs pictures (this is a "how to" lesson).

Ray Calvin Baker (talk) 23:35, 15 August 2012 (UTC)

There are three kinds of people in the world: those who can count, and those who can't. -- One of Ian Stewart's mathematical jokes. (page 1, _Professor_Stewart's_Cabinet_of_Mathematical_Curiosities_, ISBN 978-0-465-01302-9)

<PRE> | DIAGRAMS:                                  | |                      (2)                   |        Two general principles are important to keep in mind at  |       |             /  |  \       These are | all times while trying to build the core of this model. |      |           /    |    \     SKETCHES, | (1) Exactly FIVE straws must meet at every vertex. | (1)   (2)(1)(2)  not exact | (2) Every vertex must be surrounded by a ring of FIVE   |      / \         \    / \    /    scale     | straws in a pentagon shape. |    /   \         \  /    \ /     drawings! |                                                                |                    (2)(2)               |                                                                 | Principle 1       Principle 2               | |                                            |                                                                 |                                          |                                                                 |       /  |  \                               |                                                                 |     /    |    \                             |        As you approach the end of building the core, you will   | --                         | find that adding the last few straws will require that  |  |\     / \    / |     Severe distortion    | you observe both general principles at the same time. | | \   /   \  /  |     results from trying  | Some straws are simultaneously the fifth straw to be    |  |  =====  |     to show a 3-D        | added to a vertex, and the fifth straw to make a        |  |  / \    /  \  |     structure on         | pentagon ring. Eventually, you will get to the last     |  | /   \  /    \ |     a flat surface! |       straw, which completes TWO vertices AND two pentagonal   | --                         | rings. |    \    |    /                             |                                                                 |       \  |  /                               |                                                                 |                                          |                                                                 | The last straw (=====) does multiple duty. |

It takes thirty (30) pieces to make the central core. I will list the numbers of the pieces involved at the beginning of each paragraph of the following instructions.

Once you have made a few stars using this method, you are free to use your own plans. However, there are many ways to get stuck, or to miss tying a knot where one belongs. Thus, I recommend that you stick with my        printed plan. Besides that, you may help me find and eliminate mistakes (if there are any) if you follow a       written plan consistently.

NOW START: (1, 2, & 3) Push the wire loop down the hollow middle of one of the short pieces (1). Thread one end of the string through the wire loop, then pull the wire (with the string) back out of the piece of        plastic straw. Repeat this process two more times, until you have three pieces threaded onto the string (1, 2, & 3).

Tie a knot in the string, then pull it tight (not TOO        tight, or you may split a plastic straw!) so that the three plastic pieces (1, 2, & 3) outline an equilateral triangle. Note: when I say, "tie a knot" while building this model, I really mean, "Tie three or four knots". No one wants a model that comes apart too easily. When ln doubt, tie another knot!

You should have something that looks like this. (The dot indicates the location of the knot)

(2)	  ________	   \      /    Pieces 1, 2, & 3. \   /          (1)\  /(3)	      \/.

(4 & 5) Stretch out a length of string from the knot (about the length of your arm should be fine.) You can tie on more string any time, if you find that you need more string. Just try to plan it so that your splices will be hidden deep in the middle of a straw. Thread two more pieces (4 & 5) of straw onto the string. Tie another knot. Now you should have something like this.

(2)	  ________.)	   \      /\       Pieces 4 & 5 added.          (1)\ (3)/  \(5)             \  /    \	      \/______\                  (4)

(6 & 7) Keep on threading short pieces of plastic straw and tying knots until you have a network something like this.

(2)    (6)           ________A_______      Notice that there are FOUR \     /\      /      straws at vertex A.             \ (3)/  \(5) / (1)\ /    \  /(7)              \/______\/.        Pieces 6 & 7 added. (4)   )

(8 & 9) Add two more pieces of plastic straw, until you have a flat structure like this.

(2)    (6)           ________A_______.)            \      /\      /\            \ (3)/  \(5) /  \(9)   Pieces 8 & 9 added.           (1)\  /    \  /(7) \               \/______\/______\                  (4)  D  (8)

(10 & 11) Keep in mind that there are already four straws at point "A". My strategy is to add the fifth straw there, as soon as possible. Add straw pieces (10 & 11) as shown below. Your structure should still lie flat on your work table.

C                               /\           Pieces 10 & 11 added. (11)/ \(10)            (2)    / (6)\         Notice that we have five B ______(./______\E      straws together now,          \      /\A     /\       where point "A" had been.         (1)\ (3)/  \(5) /  \(9)   Also, 4 straws come together             \  /    \  /(7) \     at "D" and at "E".             \/______\/______\                 (4) D   (8)

Since we now have five straws coming together at one vertex, it is time to tie a final knot in this piece of        string. Cut the string about 1/4 inch from the knot. If you cut the string too close to the knot, the knot may come loose, and your model may fall apart.

(12) Next, we start with a fresh piece of string. Tie this new string to the corner at point "B", per the diagram above. Thread plastic straw piece (12) onto the string, then loop the string around the corner at "C". Pull the string tight, so that no        excess of string is visible at either end of plastic piece (12). This will cuase you model to pucker up        into the shape outlining a pentagonal pyramid. It        will no longer lie flat. I will need to switch from the diagrams which have served until now, to use pictures of the model. (Diagrams will be distorted        because the shape is now 3-D and cannot be well         displayed, except by pictures.)

Note: Each picture will be drawn independently of all other pictures. I do not expect that the labels of the vertices will be consistent between pictures. The labels will apply only to the paragraph which explains how to build the core of         the ornament, up to the stage shown in the picture. (Perhaps I should try extra hard to make the labels        consistent throughout all of the pictures.)


 * (B)               Vertex B actually lies |
 * // || \\             behind vertex A;       |
 * (1)//   ||   \\(12)       I lies behind F;       |
 * //  (2)||     \\         K lies behind D; and   |
 * // (3)   ||  (11) \\ .)    L lies behind E.       |
 * (G)=========(A)=========(C)   Actually, A and F      |
 * |\\      // \\       //|     should be farther      |
 * | \\ (5)//   \\(6)  // |     apart.                 |
 * (4)\\ //       \\  //(10)    B and I should be      |
 * |  \\//   (7)   \\//   |     closer together.       |
 * | K (D)=========(E) L  |     Severe distortion      |
 * |  /  \\       // \    |     results from trying    |
 * | /    \\     //   \   |     to show a 3-D          |
 * | /  (8)\\   //(9)  \  |     structure on           |
 * |/       \\ //       \ |     a flat surface!        |
 * (J)-(F)-(H)   Vertex A has 5 straws; |
 * \        |         /       B has 3; C has 3;      |
 * \      |       /         D has 4; E has 4;      |
 * \    |     /           F has 2; G has 3.      |
 * \  |   /             H, I, J, K, and L      |
 * (I)               have 0 straws.         |

Maybe I can use this diagram after all, to plan the pictures. I am the only person who needs to see it, and I understand the nature of the distortions, and can compensate. However, it may be good for my pupils to learn how to interpret diagrams, and to understand how they compare with pictures, so I'll leave the diagram in place. -- RCB Double lines in the diagram indicate straws already in place. </PRE>



EXPLANATION OF THE COLOR-CODED PICTURE: Five straws around corner "A" are shown in black. Straws (1), (4), (7), and (10) are shown in orange. The last straw to be installed, (12), is shown in red. These five straws form a pentagonal ring around corner "A". Corner "A" is higher above the gray tabletop than the pentagonal ring. A string hangs loose from corner "C". We will use this string later, if it is long enough. If it is not long enough, we will splice on more string. A loop of two straws, (8) and (9), shown in yellow-orange, hangs below the model, from edge "D" -- "E".

<PRE> (13 & 14) So, tie a string to the corner at D.       Put two plastic pieces (13 & 14) onto the string. Loop the string around corner F, then pull it        tight. Tie a knot at F.

Then we have this: </PRE>
 * (B)               Vertex B actually lies |
 * // || \\             behind vertex A;       |
 * (1)//   ||   \\(12)       I lies behind F;       |
 * //  (2)||     \\         K lies behind D; and   |
 * // (3)   ||  (11) \\ .)    L lies behind E.       |
 * (G)=========(A)=========(C)   Actually, A and F      |
 * |\\      // \\       //|     should be farther      |
 * | \\ (5)//   \\(6)  // |     apart.                 |
 * (4)\\ //       \\  //(10)    B and I should be      |
 * |  \\//   (7)   \\//   |     closer together.       |
 * | K (D)=========(E) L  |     Severe distortion      |
 * |  // \\       // \    |     results from trying    |
 * (13)//  \\     //   \   |     to show a 3-D          |
 * | // (8)\\   //(9)  \  |     structure on           |
 * |// (14) \\ //       \ |     a flat surface!        |
 * (J)=========(F)-(H)   Vertex A has 5 straws; |
 * \        |         /       B has 3; C has 3;      |
 * \      |       /         D has 5; E has 4;      |
 * \    |     /           F has 3; G has 3.      |
 * \  |   /             H, I, K, and L         |
 * (I)               have 0 straws.         |
 * J has 2 straws.       |

[I need another picture—13 & 14—here. It may be from a slightly different vantage point. This picture should be based upon a projection of an icosahedron. -- RCB]

<PRE> (15 & 16) Put two more plastic pieces onto the string, then tie a knot at E. Since you have tied the fifth plastic piece at E, you may cut and trim the string.

Then we have this: </PRE>
 * (B)               Vertex B actually lies |
 * // || \\             behind vertex A;       |
 * (1)//   ||   \\(12)       I lies behind F;       |
 * //  (2)||     \\         K lies behind D; and   |
 * // (3)   ||  (11) \\ .)    L lies behind E.       |
 * (G)=========(A)=========(C)   Actually, A and F      |
 * |\\      // \\       //|     should be farther      |
 * | \\ (5)//   \\(6)  // |     apart.                 |
 * (4)\\ //       \\  //(10)    B and I should be      |
 * |  \\//   (7)   \\//   |     closer together.       |
 * | K (D)=========(E) L  |     Severe distortion      |
 * |  // \\       // \\   |     results from trying    |
 * (13)//  \\     //   \\(16)    to show a 3-D          |
 * | // (8)\\   //(9)  \\ |     structure on           |
 * |// (14) \\ //  (15) \\|     a flat surface!        |
 * (J)=========(F)=========(H)   Vertex A has 5 straws; |
 * \        |         /       B has 3; C has 3;      |
 * \      |       /         D has 5; E has 5;      |
 * \    |     /           F has 4; G has 3.      |
 * \  |   /             I, K, and L            |
 * (I)               have 0 straws.         |
 * J and H have 2 straws. |

[Third picture—15 & 16—goes here.]

<PRE> (17) Use the string hanging from corner C. Put a        piece of plastic straw (17) onto the string. Loop the string about corner H, then pull it tight so        there is no excess string showing at either end of         piece (17). This should cause your model to "pucker        up" around corner E, in a way similar to the way the model puckered when you completed the ring around corner A, earlier. CAUTION! You have just formed a second pentagonal ring, around corner E!        Be sure that both corners, A and E, will end up at         the same distance from the place where the center of your ornament will be, eventually. You do not want any part of your central core to be "inside        out"!

After the second ring has formed, around corner E, we have this:
 * (B)                    Vertex B actually lies |
 * // || \\                  behind vertex A;       |
 * (1)//   ||   \\(12)            I lies behind F;       |
 * //  (2)||     \\              K lies behind D; and   |
 * // (3)   ||  (11) \\            L lies behind E.       |
 * (G)=========(A)=========(C)        Actually, A and F      |
 * |\\      // \\       //||         should be farther      |
 * | \\ (5)//   \\(6)  // ||         apart.                 |
 * (4)\\ //       \\  //(10)         B and I should be      |
 * |  \\//   (7)   \\//   ||         closer together.       |
 * | K (D)=========(E) L  ||(17)     Severe distortion      |
 * |  // \\       // \\   ||         results from trying    |
 * (13)//  \\     //   \\(16)         to show a 3-D          |
 * | // (8)\\   //(9)  \\ ||         structure on           |
 * |// (14) \\ //  (15) \\||         a flat surface!        |
 * (J)=========(F)=========(H)        Vertex A has 5 straws; |
 * \        |         /  (         B has 3; C has 4;      |
 * \      |       /     )        D has 5; E has 5;      |
 * \    |     /                F has 4; G has 3.      |
 * \  |   /                  H has 3. I, K, and L   |
 * (I)                    have 0 straws.         |
 * H has 3, and J has 2. |

</PRE>

[Fourth picture—17 -- goes here. -- RCB]

<PRE> (18 & 19) These complete 5 straws at F. </PRE>

[Fifth picture—18 & 19—goes here. -- RCB]

Essential error-correcting rewrite still in progress. Pictures may have to wait a while. I need to create them, then upload them to Wikimedia Commons.

Ray Calvin Baker (talk) 23:35, 15 August 2012 (UTC)

End section 20.

21. ADD THE STAR-LIKE POINTS
Limit(anything) as time approaches infinity AND a programmer keeps trying = PERFECTION! Hopefully, that's worth waiting for. Ray Calvin Baker (talk) 21:35, 9 August 2012 (UTC)

<PRE> The core has 20 equilateral triangles. Our next task is 	to tie three full-length straws above the three corners of each of these equilateral triangles. This should be a fairly obvious matter of adding straws and tying knots. I think the easiest to manage this in a systematic fashion is this. Work on one triangle at a time. (1) Take a piece of string about three times as long as a straw. (2) Tie one end of the piece of string to one of the corners of the triangle you have elected to work on. (3) Thread two full-length straws onto this string. (4) Tie the loose end of the string to a second corner of the triangle you are working on. (5) Take another piece of string almost twice the length of a straw. (6) Tie one end to the third corner of the triangle you are working on. (7) Thread a full-length straw onto this string. (8) Tie the loose end to the joint between the first two straws you added in steps 2, 3 and 4. This should position a rigid point above one of the 20 triangles of the core of the ornament.

Repeat this process for each of the remaining 19 triangles. </PRE>

22. FINAL FINISHING
Seven or eight more to go! Then I can start working on the SERIOUS problems! Ray Calvin Baker (talk) 21:38, 9 August 2012 (UTC)

<PRE> You will probably wish to trim loose ends of string, or tuck them out of sight. You may wish to leave a large loop for hanging your ornament. A few drops of white glue may help secure the knots and keep loose ends out of the way.

When you make your next star, see how many ways you can figure out to save string, and make the tying of the knots a more efficient process. I tried to keep things as easy as possible for you, while we worked on your first star.

- - - - - - - - - </PRE>

23. KEPLER'S STAR
Don't lose your sense of humor. You're gonna need it! Ray Calvin Baker (talk) 21:40, 9 August 2012 (UTC)

<PRE> IV. KEPLER'S STAR (Compare with M. C. Escher's "Two Worlds".) (Paper sculpture using business cards)

Materials: 12 cards or thick paper 2 inches by 3+1/2 inches (Instructions for cutting these cards are 		given above.) white glue or glue sticks (technically optional, 		but highly recommended, especially for 		beginners.)

Procedure: FOLD EACH CARD

[ INCOMPLETE! #15 of 23 -- RCB ] NEEDS DIAGRAMS & INSTRUCTIONS

AsSEMBLE THE FOLDED CARDS

[ INCOMPLETE! #16 of 23 -- RCB ] GROUND BREAKING! Many who have published designs for modular origami have done a great job of describing how to make the modules, but (except for a few hints) have left it up to the folder how to assemble those modules into complicated final models. This is understandable, if one is discouraged by the large number of detailed diagrams which would be required for a large, complex design.

I may be the first to completely document this phase of the construction, if I can persuade my computer to make the necessary diagrams. -- RCB

- - - - - - - - - </PRE>

24. THE HOPPING BUNNY
Every problem you encounter is really an opportunity to improve this world, in a clever disguise. Ray Calvin Baker (talk) 21:43, 9 August 2012 (UTC)

<PRE> V. THE HOPPING BUNNY (quick, easy origami toy, with 	a story: "The Lonely Little Japanese Lady")

Materials: 3 inch by 5 inch index card

Procedure: (Follow along with the story; adapted from the video, "A Peace of Paper".)

"The Lonely Little Japanese Lady"

[ INCOMPLETE #17 of 23 -- RCB ] This story also may benefit with pictures.

"Once upon a time there was a Japanese Lady, who would wake up every morning and begin her exercises. She lived by herself, and was lonely, so she was always hoping for company."

(Display a 3 by 5 index card, which represents the Japanese lady.)

"She stretched out her right arm, then bent over and touched her left knee. Then she stood up straight again."

(Bend the top right corner of the card, so that what was the top edge lies over the left edge of the card. Crease, then unfold the card.)

"Then, she stretched out her left arm, bent over, and touched her right knee. Then she stood up straight again."

(Bend the top left corner of the card, so that what was the top edge lies over the right edge of the card. Crease, then unfold the card.)

"After many years of doing these stretching exercises every morning, she was so flexible that she could stretch out both arms, bend over backwards, and touch the backs of both knees. Then she stood up straight again."

(Don't you try this at home on yourself! You are not a three by five index card! But fold the card backward so that the corners, which were on top, lay on the creases left by the first two folds.)

"Would you like to see the little house the lonely Japanese Lady lives in? Just walk up to her door. There in the middle of the door, where the lines cross, is the doorbell button. Press the button to ring the doorbell, then pull the roof down into place to see the house."

(Hold the card up, with the top bent back slightly away from you. This represents the door, with lines that cross in the middle. Press the doorbell button. The two sides of the card should snap toward you. Pull the roof down into position, and look at the little house.)

"Now, imagine that the little Japanese Lady has come to the door. She feels that it is rather chilly outside today, so she wraps her shawl about herself. 'Would you like to come inside to warm up?', she asks. 'I'm sorry. I have other things I must do today, so I must be on my way. Perhaps you will have another visitor today.', you reply."

(Pull both vertical edges of the "house" forward, so that these edges of the card meet in the middle. Crease the new folds firmly.)

"The little Japanese lady still feels chilly, so she claps her hands together in front of her, several times."

(Pull the two triangular flaps, which represent her arms, forward several times, as if she's clapping her hands.)

"Thinking she is a bit stiff from the chill, she repeats one of her stretching exercises. She bends backward so far that the top of her pointed hat touches the bottom of her heels."

(Bend the pointed top of the card back until it touches the bottom of the card, in the middle.)

"Thinking that more vigorous excercise may help her warm up, she leaps into the air, and kicks out both her feet so far that her toes touch her tummy. She lands quickly and gracefully on her feet."

(Bend the bottom of the folded card forward, so that the lowest edge meets the crease which marks the lady's waist. Fold the card into a compact shape, to suggest how she lands quickly and gracefully.)

"When the Japanese Lady turns around again, she sees that, indeed, she does have another visitor today. There, on the doorstep, she sees a little bunny. She leans down to pet the bunny, but it hops away."

(In its compact shape, the folded card resembles a rabbit, with big ears. If you stroke your finger down its back, the bunny may hop for you!)

"'Perhaps I will see him again tomorrow', the Lady says to herself. Indeed, she will, if you take another three by five index card, and share this story with someone tomorrow."

- - - - - - - - - </PRE>

25. A STAR REVISITED
The real reason I am such a klutz is this: to give YOU an opportunity to do SO MUCH BETTER! Ray Calvin Baker (talk) 21:47, 9 August 2012 (UTC)

<PRE> VI. A STAR REVISITED (a starry paper sculpture 	from ordinary sheets of paper)

[ INCOMPLETE! #18 of 23 -- RCB ] NEEDS DIAGRAMS & INSTRUCTIONS

- - - - - - - - - </PRE>

26. AN INTRODUCTION TO MODULAR ORIGAMI
Close, but NO CIGAR! Ray Calvin Baker (talk) 21:50, 9 August 2012 (UTC)

<PRE> VII. AN INTRODUCTION TO MODULAR ORIGAMI Part One: A SIMPLE MODULE

Part Two: ASSEMBLING SEVERAL MODULES (I may be among the first to completely document 	this important phase of the construction.) 3

[ INCOMPLETE! #19 of 23 -- RCB ] but I have an old file, in which I began to describe this project. -- RCB ]

- - - - - - - - - </PRE>

27. FIRST STELLATION
Closer, but still NO CIGAR! Ray Calvin Baker (talk) 21:52, 9 August 2012 (UTC)

<PRE> VIII. THE FIRST STELLATION OF 	THE REGULAR PENTAGONAL DODECAHEDRON (Compare with M. C. Escher's prints, "Gravitation" 	and "Order and Chaos".) (The beauty of modular origami is that the same 	module can be assembled in several, completely 	different ways. Learn to fold just one module; 	but be able to learn how to make several 	different models using that module.)

[ INCOMPLETE! #20 of 23 -- RCB ] 1st STELLATION

- - - - - - - - - </PRE>

28. A SIMPLE JUMPING FROG
Ray Calvin Baker (talk) 21:54, 9 August 2012 (UTC)

<PRE> IX. A SIMPLE JUMPING FROG (origami toy)

[ INCOMPLETE! #21 of 23 -- RCB ] JUMPING FROG

- - - - - - - - - </PRE>

Coming ASAP—an INCOMPLETE ROUGH DRAFT! I am working on a poster for traditional classroom use. I hope this will help me make good illustrations for Wikimedia Commons, which I can reference within this topic. Ray Calvin Baker (discuss • contribs) 14:46, 4 September 2013 (UTC)

<PRE> This is my "E:/WikiversityStuff/Paper&Prep_1.txt" file, created FRI 2013 AUG 26 11:20 AM, revised SUN 2013 SEP 08 10:46 AM.

12345678-1-2345678-2-2345678-3-2345678-4-2345678-5-2345678-6-2345678-7

Origami paper is very good for use in origami, but it is expensive, and not often available in the large sizes which beginners will find most useful. It is usually white on one side, and brightly colored on the other side.

When I was a professional computer programmer, I usually had access to huge boxes of slightly used computer paper. It was thin, flexible, and precisely cut to go flawlessly through high-speed printers. Also, it came in LARGE 11 inch by 14 inch sheets.

Now that I have retired, I usually use 8 + 1/2 inch by 11 inch copy machine paper. It is widely available from office supply stores, prepackaged in reams of 500 sheets, for a price usually less than $7 per ream. (Sometimes white paper is available on sale for less than $5 per ream.) It comes in a wide range of beautiful colors (mostly pastel colors), and is frequently available in several thicknesses.

The thickness of the paper is important, as it affects the flexibility and folding characteristics of the paper. I usually use what is called "20 pound" paper. This is the usual stuff one would use in a copy machine. Some of the brighter, bold colors come only in the "24 pound" thickness, which is somewhat stiffer. Card stock is usually available (but more expensive). It is very nice for greeting cards and some types of paper sculpture. I have even used poster board (NOT the foam-filled kind) for making large free-standing angels, and Christmas tree ornaments.

I recommend that you experiment with every kind of paper you can find, to experience as wide a range of folding characteristics as possible. Magazine pages, (glossy and not glossy), newspaper pages, brown paper from shopping bags and from wrapping paper rolls, even paper towels, have their uses for various models. The only types of papers I have not had success with are lotion-soaked tissues, and paper napkins. (Paper place mats are sometimes amusing to fold in restaurants.)

Additional topics: Gift-wrap paper Foil-laminated paper Using paper from ROLLS

A section on "Preparing Paper" should follow this section, but it is still INCOMPLETE.

The end of the "E:/WikiversityStuff/Paper&Prep_1.txt" file.

</PRE> Ray Calvin Baker (discuss • contribs) 15:23, 8 September 2013 (UTC)

<PRE> This is my "E:/WikiversityStuff/ FrogFolding_1.txt" file, which was created WED 2013 AUG 28 03:56 PM, revised SUN 2013 SEP 08 10:58 AM. </PRE> Ray Calvin Baker (discuss • contribs) 19:46, 25 September 2013 (UTC) <PRE> HOP 1 (DARK GREEN COLOR). This is the STARTING SQUARE, actual size.

NOTE 2 (LIGHT YELLOW COLOR) "WHY 1/2 SCALE?" Why do I make most of my pictures at 1/2 scale? So I don't waste space on the posters or in the pictures! The initial folds for most models require showing the entire piece of paper, and there are no small details until later. Later, (see NOTE 16), when the folded paper model is more compact, and small details will be important, I will again make my illustrations in their full actual size.

HOP 3 (GRAY COLOR). Observe the starting square, shown at 1/2 scale. I don't want you to be confused -- I have merely drawn the starting square a second time, at the smaller scale.

Sometimes in origami books, just part of a model will be drawn, so as to show how to develop details, without redrawing parts of the entire model which have not changed. Changes of scale are also common in origami books, for the reasons I have already mentioned.

NOTE 4 (LIGHT YELLOW COLOR). "INTRODUCING RANDLETT-YOSHIZAWA NOTATION"

Now I would like to introduce Randlett-Yoshizawa notation. On the model for HOP 5, The dashed line from corner "B" to corner "D" indicates a "valley fold". (In my computer drawings, I usually show valley folds as GREEN lines -- think, "lush GREEN valleys. GREEN lines are easier for me to draw on my computer than dashed lines.) The back-and-forth arrow indicates, "Fold, Crease, then Unfold".

To make a "valley fold", lift an edge, a corner, or some other part of your model, move it over, then press it down against some other part of your model. For example, to get to HOP 7, you must move corner "A" and press it down against corner "C". These are the "anchor points" for this fold -- they help you position the fold very precisely.

The "anchor points" are points between which you expect to form a fold or crease. Usually, but not always, you will want a sharp crease, because a sharp crease does allow the paper to fold as if it had a hinge. I generally sharpen a fold into a sharp crease by running my thumb nail along the fold.

Origami books usually show you where the folds belong, but they don't always show you the "anchor points", which define the fold which is supposed to form midway between them. You must learn to figure out for yourself where the "anchor points" for each fold belong. When you have identified the "anchor points" correctly, making the fold is usually much easier.

The way origami folds are usually drawn in books might suggest to you that the paper folds like a hinge. But, it does NOT work that way at all (until and unless you have made a sharp crease)! HOP 6 is intended to show you that the paper tends to bend into a cylinder or cone shape, somewhat like a stylized teardrop shape. Actually, the flexibility of the paper in that cylinder or cone shape allows you to position the "anchor points" of your fold quite accurately.

Some complicated models described in origami books require a lot of "prefolding". You will fold and crease and unfold for many steps, and it may not seem that you are accomplishing anything, because you unfold so much. But, in a later step, many of the creases you have formed will act as hinges, and large portions of the model will be shaped by those hinges.

At other times, you will fold, crease and unfold, just to form a crease line. Sometimes, crease lines are used as "construction lines". They are not part of the final model, but they act as guide lines, to help you construct other folds more easily.

Origami is not about strength, or using brute force to coerce the paper. Such force may tear the paper, spoiling your model. Rather, origami is more about using gentle coaxing to persuade the paper to drift into the position you desire. So, never rush, or allow yourself to be rushed. You need accuracy, not speed!

Here is a secret that may help you position your folds exactly. Once you have established the "anchor points" for your fold, and bent the paper so that one anchor point lies on top of the other, hold the paper down with one finger. Be very careful that you do not allow those held-down anchor points to be moved. Hold them securely with the fingers of one hand. Then, slide one finger on your other hand from a place near the "anchor points" to a place near the middle of your intended fold. This will tend to flatten the paper cylinder, and start your fold in its middle. Then, gently brush the paper from where the fold has started to one of the places where the fold ends. Brush the other half of the fold in a similar way. Now, when you move a finger along the newly formed fold, you should feel it squash into exact position. You may need to try these moves several times until they work well for you. Be gentle!

HOP 5 (RED COLOR). Observe the GREEN dashed line. This shows you where to make a valley fold. Observe the back-and-forth arrow. This tells you, "Fold, crease, then unfold".

The letters, "A", "B", "C", and "D", are intended to help you identify the four corners throughout the next few "hops".

HOP 6 (RED-ORANGE COLOR). Observe that the paper tends to form a cylinder. It will not act like a hinge here until you have made a sharp crease here.

HOP 7 (LIGHT ORANGE COLOR). Flatten the cylinder, as suggested in NOTE 4. Congratulations! You have made your first valley fold!

Crease the fold sharply, then unfold it, leaving only the crease mark.

On the poster, corners "B", "C", and "D" are glued to the poster board. Corner "A" tends to lie slightly away from the poster board, because of the valley fold in the paper.

HOP 8 (YELLOW-ORANGE COLOR) Observe a second dashed line, this time from corner "A" to corner "C". For this fold, your "anchor points" will be established by placing corner "B" on top of corner "D". Again, the back-and-forth arrow tells you, "Fold, crease, then unfold".

NOTE 9 (YELLOW COLOR). "A SHORTCUT TO SAVE ME SOME WORK"

It is rather wasteful of space on the poster or in the drawings for one "HOP" to show the results of a fold, and for the next "HOP" to show the notation for the next fold. So, from now on, wherever it seems practical, I will show the results of one fold, and the notation for the next fold, all on the same drawing.

HOP 10 (LIGHT GREEN COLOR). Observe the results of the first two valley folds. They intersect in the middle of the paper square.

</PRE> Ray Calvin Baker (discuss • contribs) 20:29, 25 September 2013 (UTC) <PRE>

SPECIAL INSTRUCTION 11 (PINK COLOR). Turn the model over. The easiest way to do this, is to let the left edge of your model remain on the table, as if there were a hinge there. Then lift the right edge of your model, push it towards the left, then let it drop back onto the table. Yes, there are several different ways to turn a model over. Each different way may leave your model with a different orientation, so always look ahead at least one diagram to see exactly how you should turn your model over.

HOP 12 (TEAL COLOR). Observe the other side of your partially-folded model. Observe that the folds which formerly looked like valleys now look like mountain ridges. Folds like these are called "mountain folds", and are usually shown in origami books as "dash dot" lines. I usually draw them as purple lines in my computer drawings. Think, "Purple mountain majesties".

"Lush green valley" or "Purple mountain majesty"? It's always just the same fold, depending only on the direction from which you view it. And this is really all there is to origami -- valley folds and mountain folds -- although sometimes you will form a cluster of folds, all at the same time. You will see this happen when you lift a cheek of your frog model and form an eye, all at the same time, as in hops 36, 37, and 38.

HOP 13 (LIGHT BLUE COLOR). Observe the dashed line which runs parallel to the top edge of the model. This is sometimes called a "book fold", because it leaves edges of your model parallel, like the edges of the pages in a book are parallel.

NOTE 14 (LIGHT YELLOW COLOR). "A CHANGE OF CONFIGURATION"

Take your model up off the table with one hand. Gently press up, in the center of the model where three creases intersect, using a finger on your other hand. The model should snap into another configuration. it.

HOP 15 (LIGHT VIOLET COLOR). Observe that the model has started to take up the shape of an isoceles right triangle (It was a square before). Help your model take up that shape.

It may bulge a little bit. Try to press it flat. (Try to get the middle to lie flat first, then crease the edges again) You may need to let some of the creases shift slightly.

NOTE 16 (WHITE ON YELLOW). "BACK TO ACTUAL SIZE"

As promised earlier, in NOTE 2, I am going to resume making my models and drawings full actual size.

HOP 17 (WHITE ON YELLOW). Observe the final result of part one. It resembles an upside-down basket. Turn it around, and it will hold water, at least until the paper gets soggy. This is called, "the Water Bomb Base", because it is an early stage of folding the traditional Japanese Water Bomb. It is called a Base because it is also an early stage of folding many other models.

The end of the "E:/WikiversityStuff/ FrogFolding1.txt_" file. </PRE> Ray Calvin Baker (discuss • contribs) 15:28, 8 September 2013 (UTC)

<PRE> This is my "E:/WikiversityStuff/ FrogFolding_2.txt" file, which was created SUN 2013 SEP 08 11:13 AM, revised SUN 2013 SEP 08 11:13 AM.

12345678-1-2345678-2-2345678-3-2345678-4-2345678-5-2345678-6-2345678-7

HOW TO FOLD A SIMPLE HOPPING FROG -- PART TWO

</PRE> Ray Calvin Baker (discuss • contribs) 20:29, 25 September 2013 (UTC) <PRE>

HOP 18 (WHITE ON YELLOW). Part two starts with the "Water Bomb Base", which you completed in part one. Observe that I have added a dashed line, to indicate where to start folding the frog's left front leg.

Observe that this time, the arrow is NOT a back-and-forth arrow. This time, the arrow means, "Fold, Crease, and Leave the paper Folded".

HOP 19 (GRAY COLOR). Observe that the left front leg has been started. Observe the dashed line, which tells you where to start folding the right front leg.

HOP 20 (RED COLOR). Observe that both front legs have been started. I hope you have made your frog symmetrical!

SPECIAL INSTRUCTION 21 (PINK COLOR). Turn the model over.

HOP 22 (RED-ORANGE COLOR). Observe the frog's back. His front feet will be formed underneath his head.

</PRE> Ray Calvin Baker (discuss • contribs) 20:29, 25 September 2013 (UTC) <PRE>

NOTE 23 (LIGHT YELLOW). INTRODUCING 'JUDGEMENT FOLDS'"

Until now, you have had well-defined anchor points to guide your folds -- corners, edges, or previous creases. But to fold the frog's left hind leg, you need to estimate the position of the fold. Too narrow, and your frog will look weak. Too wide, and your frog may not hop at all. Making folds like this takes experience and good judgement. So look carefully at the model I have provided, and try to fold your frog so that it looks like mine.

HOP 24 (LIGHT ORANGE COLOR).

HOP 25 (DARK ORANGE COLOR).

HOP 26 (BROWN COLOR).

SPECIAL INSTRUCTION 27 (PINK COLOR). Turn the model over.

HOP 28 (YELLOW-ORANGE COLOR).

</PRE> Ray Calvin Baker (discuss • contribs) 20:29, 25 September 2013 (UTC) <PRE>

HOP 29 (LIGHT GREEN COLOR).

HOP 30 (TEAL COLOR).

HOP 31 (LIGHT BLUE COLOR).

HOP 32 (DARK BLUE COLOR).

HOP 33 (DARK BLUE-VIOLET COLOR).

HOP 34 (LIGHT VIOLET COLOR).

</PRE> Ray Calvin Baker (discuss • contribs) 20:29, 25 September 2013 (UTC) <PRE>

SPECIAL INSTRUCTION 35 (PINK COLOR). Turn the model over.

HOP 36 (DARK VIOLET COLOR). Observe how the frog's "cheeks" protrude slightly from underneath his head. This is a tricky fold which wraps the "cheek" around the edge of the frog's head, and simultaneously forms one of the frog's bulging eyes.

HOP 37 (RED-VIOLET COLOR).

HOP 38 (YELLOW-GREEN COLOR). At last! The completed frog! This frog is glued to the poster board, to keep the set of instructions complete, so that other people can fold frogs, too. But the simple hopping frog is not much fun until it starts hopping.

NOTE 39 (WHITE ON YELLOW) How to make your frog hop. Put the frog on a firm surface. Then, put a finger on top of the frog's back, and press down. You should feel some "springiness" in your frog as you compress him. Then slowly slide your finger away from the frog's nose. He should hop suddenly!

HOP 40 (DARK GREEN ON YELLOW). This completed frog is attached to the poster only by a paper clip, so that you may remove it and try him out. Please do not lose the frog or the paper clip. Please re-attach the frog, using the paper clip, when you are done playing with him, so that other people may enjoy him, too -- at least, until they learn how to fold a simple hopping frog, too!.

Here is a local Eastern Shore Maryland joke. (It won't make sense elsewhere.) "Remember, frogs cost less in Preston!"

The end of the "E:/WikiversityStuff/ FrogFolding_2.txt" file. </PRE> Ray Calvin Baker (discuss • contribs) 15:30, 8 September 2013 (UTC)

29. ANGEL
Only ONE MORE to go~ Ray Calvin Baker (talk) 21:55, 9 August 2012 (UTC)

<PRE> X. ANGEL (a simplified origami ornament or finger puppet)

[ INCOMPLETE!#22 of 23 -- RCB ] ANGEL

- - - - - - - - - </PRE>

30. THE SITTING CRANE
Thank you for your patience. :-) Next time, I get to begin more work on the SERIOUS problems. Ray Calvin Baker (talk) 21:57, 9 August 2012 (UTC)

<PRE> XI. THE SITTING CRANE (authentic traditional Japanese origami)

[ INCOMPLETE! #23 of 23 -- RCB ] TRADITIONAL CRANE

The end. </PRE>