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Square Pyramid by David Boudreaux

Square Pyramid by David Boudreaux
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2016-05-27 02:33
PolygonAngleSolid GeometryGeometric Construction
This example demonstrates the geometric construction and properties of a square pyramid. It involves core mathematical concepts such as solid geometry, polygons, angles, and vectors. The construction uses GeoGebra commands like Circle, Point, Intersect, Polygon, Midpoint, Line, Angle, Rotate, and Segment. It is suitable for high school students and mathematics enthusiasts studying solid geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Point(c) → B
  3. Circle(B, a) → d
  4. Intersect(c, d) → C, D, ,
  5. Point(d) → E
  6. Circle(E, a) → e
  7. Intersect(e, c) → F, G, ,
  8. Polygon(A, B, E, G) → poly1, a_1, b, e_1, g
  9. Midpoint(g) → H
  10. Midpoint(e_1) → I
  11. Midpoint(b) → J
  12. Midpoint(a_1) → K
  13. Line(K, I) → f
  14. Line(H, J) → h_1
  15. Intersect(h_1, f) → L
  16. Circle(L, a + h) → k
  17. Intersect(k, h_1) → M, N
  18. Intersect(k, f) → O, P
  19. Polygon(B, N, E) → poly2, e_2, b_1, n_1
  20. Polygon(G, P, E) → poly3, e_3, g_1, p
  21. Polygon(A, M, G) → poly4, g_2, a_2, m
  22. Polygon(A, O, B) → poly5, b_2, a_3, o
  23. Line(L, yAxis) → i
  24. Point(i) → Q
  25. Angle(Q, L, M) → α
  26. Angle(Q, L, O) → β
  27. Angle(P, L, Q) → γ
  28. Angle(N, L, Q) → δ
  29. Rotate(M, (-((n * α))), L) → M'
  30. Rotate(O, (-((n * β))), L) → O'
  31. Polygon(A, M', G) → poly6, g_3, a_4, m'
  32. Polygon(O', A, B) → poly7, b_3, o', a_5
  33. Angle(N, B, Q) → ε
  34. Rotate(P, (n * γ), L) → P'
  35. Polygon(G, P', E) → poly8, e_4, g_4, p'
  36. Rotate(N, (n * δ), L) → N'
  37. Polygon(E, N', B) → poly9, b_4, e_5, n'
  38. Polygon(B, E, N') → poly10, n'_1, b_5, e_6
  39. Polygon(R, S, 4) → poly11, j, l, q, r, T, U
  40. Circle(U, V) → s
  41. Circle(T, Distance[U, V]) → t
  42. Intersect(s, t, 1) → W
  43. Segment(U, W) → c_1
  44. Segment(W, T) → d_1
  45. Polygon(U, T, W) → poly12, w, u, t_1
  46. Segment(R, T) → f_1
  47. Midpoint(f_1) → Z
  48. Rotate(U, 90°, Z) → U'
  49. Rotate(T, 90°, Z) → T'
  50. Rotate(W, 90°, Z) → W'
  51. Polygon(U', T', W') → poly12', w', u', t'
  52. Rotate(U, 180°, Z) → U'_1
  53. Rotate(T, 180°, Z) → T'_1
  54. Rotate(W, 180°, Z) → W'_1
  55. Polygon(U'_1, T'_1, W'_1) → poly12'_1, w'_1, u'_1, t'_1
  56. Rotate(U, 270°, Z) → U'_2
  57. Rotate(T, 270°, Z) → T'_2
  58. Rotate(W, 270°, Z) → W'_2
  59. Polygon(U'_2, T'_2, W'_2) → poly12'_2, w'_2, u'_2, t'_2