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Temari Ball Construction

Temari Ball Construction
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2019-10-06 19:40
FunctionTrigonometrySolid GeometryCalculusGeometric Construction
This example demonstrates the construction of a Temari ball model by rotating an octahedron. It involves core mathematical concepts such as spheres, cylinders, differential equations, definite integrals, prisms, and exponential functions. The construction utilizes GeoGebra commands and objects like points, rotations, octahedra, midpoints, spheres, intersections, points on curves, circular arcs, sequences, and mirrors. It is suitable for high school and above students to explore the integration of spatial geometry and calculus.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Rotate(A, (2 * π / 3)) → A'
  3. Point(Circle[Midpoint[A, A'], (Distance[A, A'] * sqrt(3) / 2), Segment[A, A']]) → B
  4. Octahedron(A, A', B) → a, C, faceBDE, faceCDE, edgeAB, edgeAA', edgeA'B, edgeAE, edgeBE, edgeAC, edgeCE, edgeA'C, D, edgeA'D, edgeCD, edgeBD, edgeDE, E, faceAA'B, faceABE, faceACE, faceAA'C, faceA'CD, faceA'BD
  5. Midpoint(A, D) → F
  6. Sphere(F, A) → b
  7. Intersect(zAxis, b, 2) → G
  8. PointIn(b) → H
  9. PointIn(b) → I
  10. PointIn(b) → J
  11. CircumcircleArc(C, H, I) → c
  12. CircumcircleArc(I, J, E) → d
  13. Sequence(Rotate[{c, d}, w, zAxis], w, π / 18, (2 * π), π / 18) → l1
  14. Rotate(l1, π / 2, Line[F, C]) → l1'
  15. Rotate(l1, π / 2, Line[F, D]) → l1'_1
  16. Rotate(l1, π / 2, Line[F, E]) → l1'_2
  17. Rotate(l1', π / 2, Line[F, A]) → l1''
  18. Rotate(l1'_1, π / 2, Line[F, A']) → l2
  19. Rotate(l1'_2, π / 2, Line[F, B]) → l3
  20. Mirror(l1, F) → l1'_3