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Cross Sections of a Square Based Pyramid by nandrews

Cross Sections of a Square Based Pyramid by nandrews
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2016-05-10 21:37
VectorSolid GeometryCalculusGeometric ConstructionSlider Animation
This example demonstrates the changing cross-sectional shapes of a square-based pyramid as different planes intersect it. Core mathematical concepts include solid geometry, cross-section geometry, 3D vectors, and calculus. The construction utilizes GeoGebra commands/objects such as Intersect, Point, Polygon, Pyramid, Line, OrthogonalLine, OrthogonalPlane, IntersectPath, Plane, and Segment. It is suitable for high school and above students studying solid geometry, calculus, and 3D vectors, helping to develop spatial reasoning skills and understanding of cross-sectional geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  4. Pyramid(poly1, 6) → e, E, faceABE, faceBCE, faceCDE, faceADE, edgeAE, edgeBE, edgeCE, edgeDE
  5. Point(edgeBE) → F
  6. Line(F, b) → f
  7. Intersect(f, edgeCE) → G
  8. OrthogonalLine(F, a, space) → g
  9. OrthogonalLine(G, c, space) → h
  10. Intersect(a, g) → H
  11. Intersect(c, h) → I
  12. Point(edgeBE) → J
  13. OrthogonalPlane(J, edgeBE) → k
  14. IntersectPath(k, e) → poly3, K, q, L, M, N, O, l, m, n, p
  15. Point(edgeCE) → P
  16. Line(P, b) → i
  17. Intersect(i, edgeBE) → Q
  18. Line(P, c) → r
  19. Intersect(edgeDE, r) → R
  20. Plane(Q, P, R) → s
  21. IntersectPath(s, e) → poly2, S, T, U, V, t, a_1, b_1, c_1
  22. OrthogonalLine(F, poly1) → d_1
  23. Intersect(edgeBE, b) → W
  24. Intersect(edgeDE, c) → Z
  25. Segment(W, Z) → e_1
  26. Intersect(e_1, d_1) → A_1
  27. OrthogonalLine(F, e_1, space) → f_1
  28. OrthogonalPlane(F, e_1) → v
  29. IntersectPath(v, e) → poly4, B_1, C_1, D_1, g_1, h_1, i_1
  30. Point(edgeBE) → E_1
  31. Line(E_1, b) → j_1
  32. Intersect(edgeCE, j_1) → F_1
  33. OrthogonalLine(F_1, poly1) → k_1
  34. Point(k_1) → G_1
  35. Plane(E_1, F_1, G_1) → w
  36. IntersectPath(w, e) → poly5, H_1, I_1, J_1, K_1, l_1, m_1, n_1, p_1