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Pythagoras in a Box

Pythagoras in a Box
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2017-11-09 00:11
VectorSolid GeometryGeometric Construction
This example demonstrates geometric relationships constructed through three sections of a cube: midpoints of parallel edges, base diagonals, and side diagonals. Core math concepts include solid geometry, Pythagorean theorem, and vector operations. It uses GeoGebra commands like Midpoint, Odcinek_3D, If, Segment, and Angle. Suitable for high school geometry teaching to understand spatial geometric relationships and the extension of the Pythagorean theorem.

GeoGebra Commands & Parameters

  1. Midpoint(D7, D8) → G
  2. Midpoint(D5, D6) → F
  3. Midpoint(D3, D4) → E
  4. Midpoint(D1, D2) → D
  5. Odcinek_3D(D8, D4, D7, D6) → c, d
  6. Odcinek_3D(D8, D6, D4, D7) → e, f
  7. Odcinek_3D(D8, D7, D6, D4) → g, h
  8. Odcinek_3D(D7, D3, D5, D8) → i, j
  9. Odcinek_3D(D7, D5, D8, D3) → k, l
  10. Odcinek_3D(D5, D1, D6, D7) → m, n_1
  11. Odcinek_3D(D5, D6, D7, D1) → p, q
  12. Odcinek_3D(D6, D2, D8, D5) → s, t
  13. Odcinek_3D(D2, D1, D4, D6) → a_1, b_1
  14. Odcinek_3D(D2, D4, D6, D1) → c_1, d_1
  15. Odcinek_3D(D1, D3, D2, D5) → e_1, f_1
  16. Odcinek_3D(D3, D4, D1, D7) → g_1, h_1
  17. If(n ≟ 1 ∧ p_1, Polygon[D, E, G, F]) → wielokąt1
  18. If(n ≟ 2 ∧ p_1, Polygon[D1, D4, D8, D5]) → wielokąt2
  19. If(n ≟ 3 ∧ p_1, Polygon[D1, D2, D8, D7]) → wielokąt3
  20. Segment(D, F) → i_1
  21. Segment(E, G) → j_1
  22. Segment(D, E) → k_1
  23. Segment(F, G) → l_1
  24. Segment(F, E) → m_1
  25. Angle(G, F, E) → γ
  26. Angle(F, E, G) → δ
  27. Midpoint(D1, D4) → B
  28. Midpoint(D5, D8) → C
  29. Segment(B, C) → s_1
  30. Segment(D1, D4) → t_1
  31. Segment(D5, D8) → a_2
  32. Segment(D5, D4) → b_2
  33. Angle(D8, D5, D4) → ε
  34. Angle(D5, D4, D8) → ζ
  35. Segment(D1, D8) → c_2
  36. Segment(D2, D8) → e_2
  37. Segment(D1, D7) → f_2
  38. Angle(D2, D8, D6) → η
  39. Angle(D6, D2, D8) → θ
  40. Angle(D7, D8, D1) → ι
  41. Angle(D7, D1, D8) → κ