Pyramid Volume Conjecture Demo

GeoGebra Commands & Parameters

1. Sequence(Mat * Element[cube, k], k, 1, 8) → cube'
2. Element(Element[AE, 3], 1) → droite
3. Sequence((Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
4. Point(listepoints) → A
5. Point(listepoints) → E
6. Point(listepoints) → C_1
7. Point(listepoints) → D
8. Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
9. Point(listepoints) → B
10. Point(listepoints) → F
11. Point(listepoints) → G
12. Point(listepoints) → H
13. Polygon(B, F, G, H) → poly2, e, f, g, h
14. Point(listepoints) → C
15. Polygon(F, C, A, B) → poly3, f_1, i, a_2, b_1
16. Element(AB, 3, 1) → avant
17. Polygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1
18. Element(AC, 3, 1) → dessus
19. Polygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2
20. Polygon(A, B, H, E) → poly6, a_3, b_2, h_2, e_2
21. Segment(E, A) → c
22. Segment(A, C) → j
23. Segment(A, B) → k
24. Segment(C, C_1) → l
25. Segment(C_1, E) → m
26. Segment(H, E) → n
27. Segment(A, B) → p
28. Segment(B, H) → q
29. Segment(H, E) → r
30. Segment(H, G) → s
31. Segment(B, F) → t
32. Segment(G, C_1) → d_1
33. Segment(F, G) → i_1
34. Segment(F, C) → j_1
35. PointIn(poly5) → J
36. Translate(J, Vector[val1 * Vector[A, B]]) → pyr1_1
37. Translate(A, Vector[val1 * Vector[A, B]]) → pyr1_2
38. Translate(B, Vector[val1 * Vector[A, B]]) → pyr1_3
39. Translate(H, Vector[val1 * Vector[A, B]]) → pyr1_4
40. Translate(E, Vector[val1 * Vector[A, B]]) → pyr1_5
41. Polygon(pyr1_1, pyr1_2, pyr1_3) → poly11, pyr1_6, pyr1_7, pyr1_8
42. Polygon(pyr1_1, pyr1_3, pyr1_4) → poly12, pyr1_9, pyr1_{10}, pyr1_{11}
43. Polygon(pyr1_5, pyr1_1, pyr1_2) → poly13, pyr1_{12}, pyr1_{13}, pyr1_{14}
44. Polygon(pyr1_5, pyr1_4, pyr1_3, pyr1_2) → poly14, pyr1_{15}, pyr1_{16}, pyr1_{17}, pyr1_{18}
45. Translate(J, Vector[val2 * Vector[A, E]]) → pyr2_1
46. Translate(E, Vector[val2 * Vector[A, E]]) → pyr2_2
47. Translate(H, Vector[val2 * Vector[A, E]]) → pyr2_3
48. Translate(C_1, Vector[val2 * Vector[A, E]]) → pyr2_4
49. Translate(G, Vector[val2 * Vector[A, E]]) → pyr2_5
50. Polygon(pyr2_1, pyr2_2, pyr2_3) → poly15, pyr2_6, pyr2_7, pyr2_8
51. Polygon(pyr2_1, pyr2_4, pyr2_5) → poly16, pyr2_9, pyr2_{10}, pyr2_{11}
52. Polygon(pyr2_1, pyr2_3, pyr2_5) → poly17, pyr2_{12}, pyr2_{13}, pyr2_{14}
53. Polygon(pyr2_4, pyr2_2, pyr2_3, pyr2_5) → poly18, pyr2_{15}, pyr2_{16}, pyr2_{17}, pyr2_{18}
54. Translate(J, Vector[val3 * Vector[D, A]]) → pyr3_1
55. Translate(F, Vector[val3 * Vector[D, A]]) → pyr3_2
56. Translate(B, Vector[val3 * Vector[D, A]]) → pyr3_3
57. Translate(G, Vector[val3 * Vector[D, A]]) → pyr3_4
58. Translate(H, Vector[val3 * Vector[D, A]]) → pyr3_5
59. Polygon(pyr3_1, pyr3_3, pyr3_2) → poly19, pyr3_6, pyr3_7, pyr3_8
60. Polygon(pyr3_2, pyr3_4, pyr3_5, pyr3_3) → poly20, pyr3_9, pyr3_{10}, pyr3_{11}, pyr3_{12}
61. Polygon(pyr3_1, pyr3_2, pyr3_4) → poly21, pyr3_{13}, pyr3_{14}, pyr3_{15}
62. Polygon(pyr3_1, pyr3_5, pyr3_4) → poly22, pyr3_{16}, pyr3_{17}, pyr3_{18}