Three Dimensional Geometry, ZOME, and the Elusive Tetrahedron

Three Dimensional Geometry, ZOME, and the Elusive Tetrahedron

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Some ZOME challenges

31 of 35

31 of 35

Some ZOME challenges

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Classroom Contents

Three Dimensional Geometry, ZOME, and the Elusive Tetrahedron

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

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