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Projective rational trigonometry
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Classroom Contents
Three Dimensional Geometry, ZOME, and the Elusive Tetrahedron
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- 1 Introduction
- 2 The elusive tetrahedron
- 3 The basic quantities: quadrances and spreads
- 4 Quadrance between points
- 5 Spread between lines
- 6 Laws of affine rational trigonometry
- 7 Proof of main laws: Cross law
- 8 Proofs of main laws: spread law and quadrea
- 9 Proofs of main laws: Triple spread formula
- 10 Projective rational trigonometry
- 11 A projective triangle
- 12 Projective rational trigonometry
- 13 Projective quadrea
- 14 The ZOME construction system
- 15 ZOME quadrances
- 16 ZOME and spreads
- 17 Two coloured primitive ZOME triangles
- 18 Three coloured primitive coloured ZOME triangles
- 19 A ZOME tetrahedra
- 20 Tartaglia's volume formula
- 21 The Alternate spreads formula
- 22 The trigonometry of a tetrahedron
- 23 Dihedral spreads and quadrances
- 24 Solid spreads
- 25 Solid spread law
- 26 The right tetrahedron
- 27 Dihedral spreads relation
- 28 Dihedral spreads formula
- 29 Our example tetrahedron
- 30 Circumdiameter quadrance
- 31 Some ZOME challenges
- 32 Two key examples
- 33 The right isosceles tetrahedron
- 34 The regular tetrahedron
- 35 More info
