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# MathsConf33: Origami and Mathematics with Sue Pope and Tung Ken Lam

Updated versions of these notes are at https://www.foldworks.net/mathsconf33

Session description: Folding paper is an accessible entry to many aspects of mathematics. In this practical workshop, we’ll explore fractions, angles, symmetry and proof.

Here are some of the ideas that we might explore:

• Proof of the angle sum of a triangle by folding
• and the area of a triangle

• Folding an angle of 60 degrees
• Fractions 4. Dividing lengths into equal parts

• Proofs of Pythagoras Theorem (including fractions, perpendicular bisector and rotational symmetry)
• Tilted square

Pythagorean tiling

• The Platonic Solids
• Reverse engineering
• Cube
• Skeletal Octahedron
• 1:sqrt(2) paper (ISO A standard paper)
• Golden rectangle by folding
• Exact https://www.geogebra.org/material/show/id/bc9rmbqe
• Excellent approximation using A4 paper: trim a long strip that is 1/8 of the short edge. 7(√2)/8 is √5 – 1 with 0.1/% error.
• Rarely used in origami, but two models using golden rectangles are
• Skeletal Icosahedron (Kasahara and others)

• Great Dodecahedron (Shapcott and others)

• Lesson plans, presentations and origami instructions for KS2 and KS3 at https://www.japansociety.org.uk/resource?resource=105
• Other ideas are in the ATM publication Learning Mathematics with Origami. Some sample materials is in Mathematics Teaching 254.