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Icosahedron Temari Ball Construction

Icosahedron Temari Ball Construction
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2017-11-11 05:29
TrigonometrySolid GeometryCalculusDerivativeGeometric Construction
This example demonstrates the construction of an icosahedron-based temari ball using GeoGebra, showcasing geometric elements and relationships. Key math concepts include solid geometry, derivatives, median value, parallelograms, and differential equations. The construction involves commands like Point, Icosahedron, Midpoint, Sphere, OrthogonalLine, Intersect, Angle, Plane, Sequence, Rotate, Mirror, and objects such as A, B, C, a, D, E, F, G, H, I, J, K, L, faceABC, etc. Suitable for high school and advanced learners exploring complex geometric constructions and mathematical applications.

GeoGebra Commands & Parameters

  1. Point(Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]]) → C
  2. Icosahedron(A, B, C) → a, D, faceABC, faceACF, faceAFG, faceADG, faceABD, faceBDH, faceBEH, faceBCE, faceCEI, faceCFI, E, faceEHK, faceEIK, faceIKL, faceFIL, faceHJK, faceJKL, faceGJL, faceFGL, faceDHJ, faceDGJ, F, edgeAC, edgeAB, edgeBC, edgeAF, edgeCF, edgeAG, edgeFG, edgeAD, edgeDG, edgeBD, G, edgeBH, edgeDH, edgeBE, edgeEH, edgeCE, edgeCI, edgeEI, edgeFI, edgeEK, edgeHK, H, edgeIK, edgeIL, edgeKL, edgeFL, edgeJK, edgeHJ, edgeJL, edgeGL, edgeGJ, edgeDJ, I, J, K, L
  3. Midpoint(D, I) → M
  4. Sphere(M, A) → b
  5. OrthogonalLine(M, xOyPlane) → f
  6. Intersect(f, b) → N, O
  7. Angle(J, M, O) → α
  8. Plane(J, f) → c
  9. OrthogonalLine(M, c) → g
  10. Sequence(Rotate[Rotate[J, (-a), g], (6 * a), f], a, 0, α, α / 36) → L_1
  11. Rotate(L_1, (2 * π / 3), f) → L_2
  12. Sequence(CircleArc[M, Element[L_1, i], Element[L_2, i]], i, 1, Length[L_1]) → L_3
  13. Rotate(L_3, (2 * π / 3), f) → L_4
  14. Rotate(L_3, (-2 * π / 3), f) → L_5
  15. Sequence(Rotate[{L_3, L_4, L_5}, ((a * 2) * π / 5), Line[M, J]], a, 1, 4) → L_6
  16. Sequence(Rotate[{L_3, L_4, L_5}, ((a * 2) * π / 5), Line[M, K]], a, 2, 4) → L_7
  17. Mirror(L_6, M) → L_8
  18. Sequence(Rotate[{L_3, L_4, L_5}, ((a * 2) * π / 5), Line[M, L]], a, 2, 3) → L_9
  19. Mirror(L_9, M) → L_{10}
  20. Rotate({L_3, L_4, L_5}, (4 * π / 5), Line[M, J]) → L_{11}
  21. Rotate(L_{11}, (4 * π / 5), Line[M, D]) → L_{12}
  22. Rotate(L_{11}, (2 * π / 5), Line[M, D]) → L_{13}
  23. Rotate(L_{11}, (6 * π / 5), Line[M, G]) → L_{14}
  24. Rotate(L_{12}, (-2 * π / 5), Line[M, A]) → L_{15}