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Isosceles Trapezoid Dilation Tessellation

Isosceles Trapezoid Dilation Tessellation
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2016-04-11 02:00
PolygonSequenceTransformationGeometric Construction
In collections Transformations
This example demonstrates a plane tessellation pattern generated by dilating isosceles trapezoids. Core concepts involve dilation transformations, polygon tiling, and geometric symmetry. Construction utilizes GeoGebra commands like Rotate, Dilate, and Sequence alongside Point and Polygon objects. It is suitable for middle school geometry education or for math enthusiasts exploring transformation patterns.

GeoGebra Commands & Parameters

  1. Rotate(B, (360 * ° / N), A) → B'
  2. Point(Ray[B, (2 * B) - A]) → C
  3. Rotate(C, (360 * ° / N), A) → D'
  4. Polygon(B, (3 * C) - (2 * B), (3 * D') - (2 * B'), B') → poly1, a, b, c, d
  5. PointIn(poly1) → I
  6. Circle((B + C) / 2, B) → e
  7. PointIn(e) → D
  8. PointIn(e) → E
  9. PointIn(poly1) → H
  10. PointIn(poly1) → G
  11. PointIn(poly1) → F
  12. Dilate(F, 1 / r, A) → F'
  13. Dilate(G, 1 / r, A) → G'
  14. Dilate(H, 1 / r, A) → H'
  15. Dilate(I, 1 / r, A) → I'
  16. Rotate(E, (360 * ° / N), A) → C'
  17. Rotate(D, (360 * ° / N), A) → E'
  18. Polygon(B, D, E', B', I', H', G', F', E, C, F, G, H, I, D', C') → poly2, b_1, c', e', b', i', h', g', f', e_1, c_1, d_1, f, g, h, i, d'
  19. Sequence(Polygon[Rotate[B, ((i * 360) * ° / N), A], Rotate[D, ((i * 360) * ° / N), A], Rotate[E, ((i * 360) * ° / N), A], Rotate[C, ((i * 360) * ° / N), A], Rotate[F, ((i * 360) * ° / N), A], Rotate[G, ((i * 360) * ° / N), A], Rotate[H, ((i * 360) * ° / N), A], Rotate[I, ((i * 360) * ° / N), A], Rotate[D', ((i * 360) * ° / N), A], Rotate[C', ((i * 360) * ° / N), A], Rotate[E', ((i * 360) * ° / N), A], Rotate[B', ((i * 360) * ° / N), A], Rotate[I', ((i * 360) * ° / N), A], Rotate[H', ((i * 360) * ° / N), A], Rotate[G', ((i * 360) * ° / N), A], Rotate[F', ((i * 360) * ° / N), A]], i, 1, N) → list1
  20. Sequence(Dilate[list1, r^(i), A], i, 1, M) → list3
  21. Sequence(Dilate[list1, (1 / r)^(i), A], i, 1, m) → list2