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Sphere and Pyramid Construction: Solid Geometry Visualization

Sphere and Pyramid Construction: Solid Geometry Visualization
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2018-09-04 00:05
Solid GeometryGeometric Construction
This example demonstrates how to construct a sphere and pyramid combination in GeoGebra, highlighting spatial relationships in solid geometry. Key mathematical concepts include sphere, pyramid, intersecting lines, rotation, and sequences. Construction involves commands like Sphere, IntersectPath, Intersect, Line, Rotate, and objects such as r, n, A. Suitable for middle school students or teachers for geometry teaching and classroom demonstrations.

GeoGebra Commands & Parameters

  1. Sphere(A, r) → a
  2. IntersectPath(b, a) → c
  3. Intersect(yAxis, a) → B, C
  4. Intersect(xAxis, a) → D, E
  5. Line(D, E) → f
  6. Line(B, C) → g
  7. Rotate(c, 90°, f) → c'
  8. Intersect(c, c') → G, H, ,
  9. Sequence(Rotate[c, ((i * 360) * ° / n), g], i, 1, n) → L_1
  10. Point(L_1) → I
  11. Segment(E, I) → h
  12. Segment(I, C) → i
  13. Segment(C, E) → j
  14. OrthogonalLine(C, h, space) → k
  15. Intersect(k, h) → J
  16. Segment(J, C) → l
  17. Segment(I, E) → dx
  18. Segment(C, J) → dy
  19. Polygon(A, K, L) → t1, l_1, a_1, k_1
  20. Pyramid(t1, dy) → d, M, faceAKM, faceKLM, faceALM, edgeAM, edgeKM, edgeLM
  21. CircleSector(L, A, K) → e
  22. Sequence(CircleSector[((((2 * i) - 1) * dx / 2), dy, 0), (((i - 1) * dx), 0, 0), ((i * dx), 0, 0), xOyPlane], i, 1, (2 * n)) → L_2
  23. Sequence(Pyramid[Polygon[(((i - 1) * dx), 0, 0), ((i * dx), 0, 0), ((((2 * i) - 1) * dx / 2), dy, 0)], r], i, 1, (2 * n)) → L_3