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Origami Mathematics: Folding Techniques, Geometric Reasoning, and Polyhedra

Explore the mathematical principles behind origami, including surds, coordinate geometry, conic sections, angle rules, and folding techniques. Discover the area, diagonals ratio, perimeter, and side ratio of kites, as well as folding angles and patterns for various shapes and polyhedra.

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Origami Mathematics: Folding Techniques, Geometric Reasoning, and Polyhedra

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Presentation Transcript

  1. The Mathematics of Origami James Hurring

  2. Surds and A4 paper • What is the area of the kite? • What is the ratio of the diagonals of the kite? • What is the perimeter of the kite? • What is the ratio of the sides of the small rectangle?

  3. Folding paper into Thirds and Fifths (Coordinate Geometry)

  4. Folding a Hyperbolic Paraboloid (Complex roots of quadratics)

  5. Folding Conic Sections

  6. Folding Conic Sections

  7. Angle Rules with a Triangle (Geometric Reasoning)

  8. The Axioms of Folding

  9. Folding a 60o Angle

  10. Trisecting an Angle

  11. Making a simple protractor

  12. Doubling a cube Start by folding into thirds

  13. Folding Pentagons (Geometric Reasoning)

  14. 3-D Right-angled Triangles

  15. Analysing the Crease pattern for Great Icosahedron (Non-right-angled Trigonometry)

  16. Hamiltonian Graphs • Edge models of Polyhedra • (Colouring the edges)

  17. Experimental Probability

  18. Graphs & Patterns

  19. Polyhedra Euler’s Rule Vertex Deficiency and 720o

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