Rhombus Dance on a Hexagonal Grid

Rhombus Dance on a Hexagonal Grid
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2020-05-28 21:56
This example demonstrates the illusion of rotating rhombuses on a hexagonal grid, where translations appear to produce rotational movement. It involves core mathematical concepts like polygons, rhombuses, geometric transformations, translation, rotation, ratios, Poisson distribution, incircle, and conic sections. The construction uses GeoGebra commands such as Polygon, Centroid, Sequence, and Rotate. It is suitable for high school and above, focusing on geometric transformations and dynamic visual effects.

GeoGebra Commands & Parameters

  1. Polygon(O, E, 6) → poly1, g, I, h, j, k, l, m, F, G, H
  2. Polygon(O, A, B, C) → q1, o, a, b, c
  3. Centroid(q1) → D
  4. Sequence(Translate[l2, Vector[((i * k) * u) + ((i * d) * u)]], k, (-n), n, 1) → l1
  5. Rotate(l1, 60°) → l1'
  6. Rotate(l1, (2 * 60°)) → l1'_1
  7. Rotate(l1, (3 * 60°)) → l1'_2
  8. Rotate(l1, (4 * 60°)) → l1'_3
  9. Rotate(l1, (5 * 60°)) → l1'_4