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Intro to Rational Trigonometry
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Classroom Contents
Towards a More Computational Mathematics - Rational Trigonometry and New Foundations for Geometry
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- 1 Intro to Rational Trigonometry
- 2 Two key examples
- 3 Outline of talk
- 4 Quadrance between points
- 5 Pythagoras and Triple quad formula
- 6 Spread between lines
- 7 Spread as a normalized squared determinant
- 8 Paul Miller's spread protractor
- 9 Laws of affine rational trigonometry
- 10 Thales' theorem
- 11 The ZOME construction system
- 12 ZOME and spreads
- 13 Two coloured primitive ZOME triangles
- 14 Three coloured primitive ZOME triangles
- 15 Proofs of main laws: Cross law
- 16 Proofs of spread law, and quadrea
- 17 Proof of Triple spread formula
- 18 Equal spreads and the logistic map
- 19 Spread polynomials
- 20 Formulas for spread polynomials
- 21 Examples of spread polynomials
- 22 Factorization of spread polynomials
- 23 Quadruple quad formula
- 24 Quadruple spread formula
- 25 Cyclic quadrilaterals
- 26 Application to a right tetrahedron
- 27 Projective Pythagoras theorem
- 28 Projective rational trigonometry
- 29 A projective triangle
- 30 Projective rational trigonometry
- 31 Projective quadrea
- 32 Solid geometry and tetrahedra
- 33 The regular tetrahedron
