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Dynamic Cone and Pyramid

Dynamic Cone and Pyramid
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2020-10-29 03:44
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the dynamic construction of a cone and a pyramid. Key mathematical concepts include cones, pyramids, vectors, and coordinate geometry. Using GeoGebra commands such as Line, OrthogonalLine, Point, Tangent, Intersect, etc., the intersection points, ellipses, and vectors are dynamically displayed. Suitable for high school mathematics education, particularly in solid and coordinate geometry.

GeoGebra Commands & Parameters

  1. Line(B, A) → f
  2. OrthogonalLine(E, f) → g
  3. Point(g) → F
  4. Tangent(F, c) → h, i
  5. Intersect(c, h, 1) → C
  6. Intersect(c, i, 1) → D
  7. Segment(F, C) → j
  8. Segment(F, D) → k
  9. Line(F, f) → l
  10. Segment(F, E) → r
  11. Point(r) → K
  12. OrthogonalLine(K, r) → t
  13. Segment(K, E) → e
  14. Line(G, H) → m
  15. Line(I, G) → n
  16. Line(H, n) → p
  17. Line(I, m) → q
  18. Circle(G, I) → d
  19. Intersect(d, n, 2) → J
  20. Line(J, m) → s
  21. Intersect(p, q) → L
  22. Intersect(p, s) → M
  23. LineBisector(H, G) → f_1
  24. Intersect(m, f_1) → N
  25. Intersect(l, f_1) → O
  26. Segment(I, J) → g_1
  27. Segment(J, M) → h_1
  28. Segment(M, L) → i_1
  29. Segment(L, I) → j_1
  30. Segment(I, O) → k_1
  31. Segment(J, O) → l_1
  32. Segment(M, O) → m_1
  33. Segment(L, O) → n_1
  34. Polygon(I, J, M, L) → poly1, i_2, j_2, m_2, l_2
  35. Segment(O, N) → p_1
  36. Intersect(t, p_1) → P
  37. Intersect(t, k_1) → Q
  38. Intersect(t, n_1) → R
  39. Line(Q, g_1) → q_1
  40. Line(R, i_1) → r_1
  41. Intersect(q_1, l_1) → S
  42. Intersect(r_1, m_1) → T
  43. Segment(S, T) → s_1
  44. Segment(T, R) → t_1
  45. Segment(R, Q) → a_1
  46. Segment(Q, S) → b_1

AI Drawing Prompt Reference

Draw a dynamic solid-geometry style figure in the plane. Start with a base line determined by two given points, then construct a line perpendicular to it through a chosen point. Using that point as the main reference, build tangency-related directions and create a circle from an appropriate center point pair. Intersect the circle with two tangent lines to obtain two key points, then connect them to the reference point with segments to form the cone-like side edges. Next, construct additional lines from intersections to determine four vertices and connect them into a polygonal face. Use a vertical auxiliary line to intersect several constructed segments, and draw the connecting segments between these intersection points so the final figure shows coupled cone and pyramid-like geometry.
The prompt above was compiled from the original drawing commands and is for reference only.