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Mixed Coordinate System Demo

Mixed Coordinate System Demo
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2019-09-20 00:47
VectorTrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the mixed coordinate system of Common space-time & Natural space-time, featuring axes for common time (Z), common space (X), and private time (Y). Core math concepts include coordinate systems, cones, coordinate geometry, trigonometric functions, and vectors. Construction highlights from the summary involve commands like Vector, Angle, InfiniteCone, Segment, Circle, Tangent, Line, and Text. Suitable for high school students and math enthusiasts exploring spatial geometry and coordinate applications.

GeoGebra Commands & Parameters

  1. Vector(O, Pτst) → vτst
  2. Vector(O, Pt) → vt
  3. Vector(O, Pτs) → vτs
  4. Angle(vt, vτst) → a45
  5. InfiniteCone(O, vt, a45) → plLightCone
  6. Segment(Pτst, Pτs) → sPτs
  7. Segment(Pτst, Pst) → sPst
  8. Segment(Pτst, Ptτ) → sPtτ
  9. Segment(Pτst, Pt) → sPt
  10. Segment(Pτs, Pτ) → sτsτ
  11. Segment(Pτs, Ps) → sτss
  12. Segment(Pst, Pt) → sstt
  13. Segment(Pst, Ps) → ssts
  14. Segment(Ptτ, Pt) → stτt
  15. Segment(Ptτ, Pτ) → stττ
  16. Vector(O, Pst) → vst
  17. Angle(vst, Vector[Pt]) → θ
  18. Angle(vτs, Vector[(0, 1, 0)]) → ϕ
  19. Circle(O, tm) → cir
  20. Circle(Pt, tm, xOyPlane) → seccir
  21. Vector(Pti, Psγt) → vsγ
  22. Segment(O, Psγt) → sPsγt
  23. Tangent(Pτs, cir) → lsγ,
  24. Vector(Ptγ, Pτs) → vsγτ
  25. Line(O, lsγ) → lsγAxis
  26. Vector(O, Psγ) → vPsγ
  27. Segment(Ps, Psγ) → sPsγ
  28. Angle(vPsγ, Vector[(1, 0, 0)]) → ϕi
  29. Angle(vPsγ, vτs) → ar1
  30. Text("Natural (Angular) Space-time", (4.5, 2.5)) → txtNat
  31. Text(RotateText["Common Space-time", 20°], (5, 0, 7), true, true) → txtCom
  32. Angle(Vector[Pτs, O], Vector[Pτs, Ps]) → ϕa

AI Drawing Prompt Reference

Draw a mixed coordinate system showing common time (Z), common space (X), and private time (Y) axes. Include two cones representing light cones and private time cones. Add segments connecting key points, with text labels for common and private space-time. Use circles and tangents to highlight geometric relationships, and label angles.
The prompt above was compiled from the original drawing commands and is for reference only.