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Pyramid in a Cube by Nicolas ERDRICH

Pyramid in a Cube by Nicolas ERDRICH
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2013-12-21 01:20
TrigonometrySolid GeometryGeometric Construction
This example demonstrates constructing a pyramid inside a cube, involving core concepts in solid geometry such as centroids, orthogonal lines, and angle calculations. It utilizes commands like OrthogonalLine, Point, Sequence, Element, Polygon, Segment, and PointIn. Suitable for high school geometry education, helping students understand spatial constructions and properties.

GeoGebra Commands & Parameters

  1. OrthogonalLine(I, xAxis) → l_1
  2. OrthogonalLine(I, l_1) → m_1
  3. Point(m_1) → K
  4. Point(l_1) → P
  5. Sequence(Mat * Element[cube, k], k, 1, 8) → cube'
  6. Element(Element[AE, 3], 1) → droite
  7. Sequence((Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
  8. Point(listepoints) → A
  9. Point(listepoints) → E
  10. Point(listepoints) → C_1
  11. Point(listepoints) → D
  12. Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
  13. Point(listepoints) → B
  14. Point(listepoints) → F
  15. Point(listepoints) → G
  16. Point(listepoints) → H
  17. Polygon(B, F, G, H) → poly2, e, f, g, h
  18. Point(listepoints) → C
  19. Polygon(F, C, A, B) → poly3, f_1, i, a_2, b_1
  20. Element(AB, 3, 1) → avant
  21. Polygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1
  22. Element(AC, 3, 1) → dessus
  23. Polygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2
  24. Polygon(A, B, H, E) → poly6, a_3, b_2, h_2, e_2
  25. Segment(E, A) → c
  26. Segment(A, C) → j
  27. Segment(A, B) → k
  28. Segment(C, C_1) → l
  29. Segment(C_1, E) → m
  30. Segment(H, E) → n
  31. Segment(A, B) → p
  32. Segment(B, H) → q
  33. Segment(H, E) → r
  34. Segment(H, G) → s
  35. Segment(B, F) → t
  36. Segment(G, C_1) → d_1
  37. Segment(F, G) → i_1
  38. Segment(F, C) → j_1
  39. PointIn(poly5) → J
  40. Segment(J, E) → k_1
  41. Polygon(J, E, H) → poly7, h_3, j_2, e_3
  42. Polygon(J, H, B) → poly8, b_3, j_3, h_4
  43. Polygon(J, E, A) → poly9, a_4, j_4, e_4
  44. Polygon(J, A, B) → poly10, b_4, j_5, a_5
  45. Angle(Line[A, E], Line[A, J]) → ang1
  46. Angle(Line[E, H], Line[E, J]) → ang2
  47. Angle(Line[H, B], Line[H, J]) → ang3
  48. Angle(Line[B, A], Line[B, J]) → ang4
  49. Polygon(A, B, H, E) → poly11, a_6, b_5, h_5, e_5
  50. Angle(Line[B, H], Line[B, A]) → ang5

AI Drawing Prompt Reference

Draw a pyramid inside a cube with its apex at the center of the cube's diagonal and base on one of its faces. Start by constructing the cube's diagonal and finding its midpoint. Use this midpoint to form the pyramid's sides, ensuring they are perpendicular to the base. The base of the pyramid should be a quadrilateral formed by four cube vertices and one midpoint. Connect the base vertices to the apex to complete the pyramid. Label all edges and vertices, and indicate the angles between the pyramid's sides and base.
The prompt above was compiled from the original drawing commands and is for reference only.