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Temari Ball 3: Rotating Equilateral Triangles on a Sphere

Temari Ball 3: Rotating Equilateral Triangles on a Sphere
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2020-09-02 21:29
TriangleSequenceSolid GeometryTransformationGeometric Construction
① This example demonstrates the creation of a decorative temari‑ball pattern by rotating equilateral triangles on a spherical surface. ② Core mathematical concepts include solid geometry (sphere, cylinder), properties of equilateral triangles, rotation transformations, and discrete sampling of a stochastic process. ③ Construction highlights: the Sequence command generates ordered lists, Sphere creates the base sphere, and objects a, r, b, k, f, O, R, motif, m, ff, liste1‑liste6, c, A, B, image1 control triangle placement and rotation. ④ Suitable for high‑school solid geometry, university geometric modeling courses, and advanced GeoGebra animation practice.

GeoGebra Commands & Parameters

  1. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), z(O) + (R * sin(i - (π / ((2 * motif)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / motif) → liste1
  2. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), z(O) - (R * sin(i - (π / ((2 * motif)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / motif) → liste2
  3. Sequence(CurveCartesian[x(O) + (R * sin(i - (π / ((2 * motif)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), z(O) + ((R * cos(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / motif) → liste3
  4. Sequence(CurveCartesian[x(O) - (R * sin(i - (π / ((2 * motif)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), z(O) + ((R * cos(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / motif) → liste4
  5. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), y(O) + (R * sin(i - (π / ((2 * motif)) * ff((m * t))))), z(O) + ((R * sin(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / motif) → liste5
  6. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), y(O) - (R * sin(i - (π / ((2 * motif)) * ff((m * t))))), z(O) + ((R * sin(t)) * cos(i - (π / ((2 * motif)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / motif) → liste6
  7. Sphere(O, R - 0.005) → c

AI Drawing Prompt Reference

Draw a decorative temari‑ball pattern on a sphere by arranging six families of rotating equilateral triangles. Start with a sphere of radius R centered at O. Distribute the triangle vertices uniformly in latitude and longitude according to a motif parameter, then let each triangle rotate continuously as a function ff(m·t) while its three edges trace space curves on the sphere surface. Generate six sets of curves corresponding to the three edges on both the front and back hemispheres, and finally add a slightly smaller concentric sphere for reference. The result is a symmetric, animated lattice of equilateral triangles covering the sphere.
The prompt above was compiled from the original drawing commands and is for reference only.