Learning Mathematics with Origami: Dynamic Geometry Files

Tung Ken Lam, Mar 20, 2016

These files show some of the constructions and objects in the book "Learning Mathematics with Origami" published by the Association of Teachers of Mathematics. You can demonstrate them to learners or let them interact with them: [list] [*]What mathematical concepts does this construction use? [*]What improvements could you make? [*]How would you make this construction? [*]How could you generalise this construction? [/list] Some hints: [list=1] [*]Some constructions use the Sequence command (see [url]https://www.geogebra.org/wiki/en/Sequence_Command[/url]). This powerful command lets you do a FOR … NEXT loop and assign the results to a LIST object. Not only does this save you repeatedly using the same user interface objects, you can also refer to the member objects in the list e.g. set the colour of all members, obtain the first or nth object, etc. [*]Some dynamic geometry versions of origami models move the planes of “paper” away from their theoretical positions so that they do not overlap. [*]In general, you can interact with construction by either dragging a point or a slider. The former gives you the feeling of direct manipulation. However the latter allows you to hide the point and animate the construction to an animated GIF file. You can easily change from the former to the latter: create a slider and define a point using the slider, then redefine the interactive point to be the point defined by the slider. [*]You can use 2d views of planes other than the x-y plane. In a 3D window, right click a plane and select “Create 2d view from ...”. [/list]

Table of Contents

  1. A single fold
    1. LMOrigami06 Haga Theorem (Square)
  2. Folding strips of paper
    1. LMOrigami08 Trisect Length Iterative Thirds Fujim…
  3. Exploring angles
    1. LMOrigami12 Trisect Acute Angle Abe Method
    2. LMOrigami12 Triangle Angles Sum to 180 degrees an…
    3. LMOrigami13 Trisect Right Angle Iterative Strip
  4. Polygons
    1. LMOrigami18 A Paper Series Spiral
    2. LMOrigami18 Cairo Tessellation
    3. LMOrigami18 Tessellation Hexagon and Triangle wit…
    4. LMOrigami18 Cairo Tessellation Variable Animation
    5. LMOrigami18 Equilateral triangles, squares and regular hexagons Tessellation Variable Animation
  5. Modular origami
    1. LMOrigami20 Robert Neale Pinwheel-Ring-Pinwheel a…
    2. LMOrigami22 Belt Cube
    3. LMOrigami23 Skeletal Cuboctahedron variable to tr…
    4. LMOrigami23 Skeletal Octahedron Eversion
    5. LMOrigami23 Skeletal Octahedron variable to Rhombicuboctahedron and Cube
    6. LMOrigami20 Robert Neale Pinwheel-Ring-Pinwheel aka Magic Star
  6. Modular poyhedra
    1. LMOrigami24 Sonobe 03 piece Jewel Hexahedron
    2. LMOrigami24 Sonobe 12 piece Octahedral with variable pyramids
    3. LMOrigami25 Sonobe 30 piece Icosohedral with vari…

1.

A single fold

  • 1. LMOrigami06 Haga Theorem (Square)

1.1.

LMOrigami06 Haga Theorem (Square)

[br]Page 6 of “Learning Mathematics with Origami” by Tung Ken Lam and Sue Pope published by the Association of Teachers of Mathematics[br][br][br]
Interaction
Move the big red point to see what happens if the fold meets at a point other than one half of the square's width.[br]Set the size of the square so that the units are more convenient e.g. 24 units if the location point is half of the square's width.
What happens if you try this with an oblong e.g. A paper, 1:sqrt(2)?
– Tung Ken Lam

2.

Folding strips of paper

  • 1. LMOrigami08 Trisect Length Iterative Thirds Fujim…

2.1.

LMOrigami08 Trisect Length Iterative Thirds Fujim…

– Tung Ken Lam

3.

Exploring angles

  • 1. LMOrigami12 Trisect Acute Angle Abe Method
  • 2. LMOrigami12 Triangle Angles Sum to 180 degrees an…
  • 3. LMOrigami13 Trisect Right Angle Iterative Strip

3.1.

LMOrigami12 Trisect Acute Angle Abe Method

– Tung Ken Lam

3.2.

–

3.3.

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4.

Polygons

  • 1. LMOrigami18 A Paper Series Spiral
  • 2. LMOrigami18 Cairo Tessellation
  • 3. LMOrigami18 Tessellation Hexagon and Triangle wit…
  • 4. LMOrigami18 Cairo Tessellation Variable Animation
  • 5. LMOrigami18 Equilateral triangles, squares and regular hexagons Tessellation Variable Animation

4.1.

LMOrigami18 A Paper Series Spiral

– Tung Ken Lam

4.2.

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4.3.

–

4.4.

–

4.5.

–

5.

Modular origami

  • 1. LMOrigami20 Robert Neale Pinwheel-Ring-Pinwheel a…
  • 2. LMOrigami22 Belt Cube
  • 3. LMOrigami23 Skeletal Cuboctahedron variable to tr…
  • 4. LMOrigami23 Skeletal Octahedron Eversion
  • 5. LMOrigami23 Skeletal Octahedron variable to Rhombicuboctahedron and Cube
  • 6. LMOrigami20 Robert Neale Pinwheel-Ring-Pinwheel aka Magic Star

5.1.

LMOrigami20 Robert Neale Pinwheel-Ring-Pinwheel a…

– Tung Ken Lam

5.2.

–

5.3.

–

5.4.

–

5.5.

–

5.6.

–

6.

Modular poyhedra

  • 1. LMOrigami24 Sonobe 03 piece Jewel Hexahedron
  • 2. LMOrigami24 Sonobe 12 piece Octahedral with variable pyramids
  • 3. LMOrigami25 Sonobe 30 piece Icosohedral with vari…

6.1.

LMOrigami24 Sonobe 03 piece Jewel Hexahedron

Page 24 of “Learning Mathematics with Origami” by Tung Ken Lam and Sue Pope published by the Association of Teachers of Mathematics
Interaction
None, but as with all 3D constructions, you can rotate and scale the view.
– Tung Ken Lam

6.2.

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6.3.

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Information