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Conjecture for the Volume of a Pyramid (Copy) by 박정숙

Conjecture for the Volume of a Pyramid (Copy) by 박정숙
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2017-08-30 13:42
PolygonSequenceSolid GeometryGeometric ConstructionSlider Animation
① This dynamic geometry example demonstrates the relationship between the volume of a pyramid, its base area, and height, guiding users to conjecture the formula V = (1/3)Sh. ② Core mathematical concepts include solid geometry (pyramid volume), proportional reasoning, and limit ideas, with scatter plots used to visualize data patterns. ③ Construction highlights: GeoGebra commands such as Sequence, Element, Point, Polygon, Segment, PointIn, and Translate are used to build the pyramid and its cross-sections; sliders adjust parameters; objects include z, w, v, a, O, P, β, sinβ, cosβ, α, sinα, cosα, X, Y, Z, echelle, R_x, R_y, cube, texte1, texte2, Mat, cube', AE, droite, listepoints, A, E, C_1, D, poly1, a_1, b, c_1, d, B, F, G, H, poly2, with translations and point sequences generating volume measurement data. ④ Suitable for upper secondary students (e.g., geometry enrichment or introductory solid geometry) to explore the pyramid volume formula, and for math lab activities or teacher demonstrations, helping learners move from hands-on manipulation to formal derivation.

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}

AI Drawing Prompt Reference

Draw a pyramid to demonstrate the relationship between its volume, base area, and height, using scatter plots to visualize data patterns. The pyramid consists of multiple polygons forming its base and sides, with sliders adjusting parameters. Show cross-sections of the pyramid and use dynamic graphics to display volume measurement data, guiding users to conjecture the volume formula V = (1/3)Sh.
The prompt above was compiled from the original drawing commands and is for reference only.