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Spiky Ball Model

Spiky Ball Model
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2019-02-01 23:18
PolygonCoordinate GeometrySolid Geometry
This example demonstrates a spiky ball model, involving the construction of polyhedra in solid geometry. Using commands such as Point, Polygon, Prism, Sphere, and IntersectPath, it shows how to construct a three-dimensional ball with spikes. The model uses objects like points, polygons, prisms, spheres, path intersections, planes, and line segments. Suitable for high school or university solid geometry courses, it helps students understand geometric constructions in three-dimensional space.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → D
  3. Polygon(A, B, C, D) → q1, a, b, c, d
  4. Prism(q1, -4) → e, G, edgeAG, edgeBH, edgeCI, edgeDJ, edgeGH, edgeHI, edgeIJ, edgeGJ, H, I, J, faceABHG, faceBCIH, faceCDJI, faceADJG, faceGHIJ
  5. Sphere(C1, 1) → f
  6. Sphere(C2, 1) → g
  7. Sphere(C3, 1) → h
  8. Sphere(C4, 1) → i
  9. Sphere(C5, 1) → j
  10. Sphere(C6, 1) → k
  11. Sphere(C7, 1) → l
  12. Sphere(C8, 1) → m
  13. Polygon(A, D, I, H) → q2, a_1, d_1, i_1, h_1
  14. IntersectPath(xOyPlane, q2) → n
  15. Intersect(xOyPlane, q2) → E, F
  16. Plane(q2) → o
  17. IntersectPath(o, f) → q
  18. IntersectPath(o, g) → r
  19. IntersectPath(o, h) → s
  20. IntersectPath(o, i) → t
  21. IntersectPath(o, j) → c_1
  22. IntersectPath(o, k) → e_1
  23. IntersectPath(o, l) → f_1
  24. IntersectPath(o, m) → g_1
  25. Segment(A, I) → p
  26. Segment(H, D) → j_1
  27. Intersect(p, j_1) → K
  28. Segment(G, C) → k_1
  29. Intersect(k_1, j) → L, M
  30. Sphere(K, M) → u
  31. IntersectPath(o, u) → p_1