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Triangle Rotation Tessellation Step 4 Apply Design

Triangle Rotation Tessellation Step 4 Apply Design
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2014-04-07 07:51
TriangleGeometric Construction
In collections Real Triangle Rotation Tessellation Math 206 by Marie Towne
This example demonstrates how to create a tessellation pattern by rotating triangles, specifically showing the step of applying the design to the next side. Core math concepts include rotation, geometric construction, symmetry, and potential fractal geometry ideas. Construction highlights the use of GeoGebra commands/objects like Point, Segment, and Rotate. Suitable for high school students or math enthusiasts learning geometric transformations and pattern design.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 3]) → B
  2. Segment(A, B) → a
  3. Point(Circle[B, 3]) → C
  4. Segment(B, C) → b
  5. Point(Circle[C, 3]) → D
  6. Segment(C, D) → c
  7. Rotate(A, -120*°, B) → A'
  8. Rotate(B, -120*°, B) → B'
  9. Segment(A', B') → a'
  10. Rotate(C, 120*°, C) → C'
  11. Rotate(D, 120*°, C) → D'
  12. Segment(C', D') → c'
  13. Segment(A', E) → d
  14. Segment(E, F) → e
  15. Segment(F, G) → f
  16. Segment(G, H) → g
  17. Segment(H, B) → h
  18. Rotate(A', -60*°, B) → A''
  19. Rotate(E, -60*°, B) → E'
  20. Segment(A'', E') → d'
  21. Rotate(E, -60*°, B) → E'_1
  22. Rotate(F, -60*°, B) → F'
  23. Segment(E'_1, F') → e'
  24. Rotate(F, -60*°, B) → F'_1
  25. Rotate(G, -60*°, B) → G'
  26. Segment(F'_1, G') → f'
  27. Rotate(G, -60*°, B) → G'_1
  28. Rotate(H, -60*°, B) → H'
  29. Segment(G'_1, H') → g'
  30. Rotate(H, -60*°, B) → H'_1
  31. Rotate(B, -60*°, B) → B'_1
  32. Segment(H'_1, B'_1) → h'
  33. Rotate(B', -60*°, B) → B''
  34. Rotate(D', -60*°, B) → D''

AI Drawing Prompt Reference

Create a hexagonal tessellation pattern made of rotated triangles. Start by drawing a circle and selecting three points A, B, and C on it, then connect them to form a triangle. Rotate A, B, and C around B by -120 degrees to get A', B', and C', and connect A'B'. Next, rotate D around C by 120 degrees to get D', and connect CD'. Then, rotate A', E, F, G, and H around B by -60 degrees to get a series of new points, and connect them to form the tessellation pattern.
The prompt above was compiled from the original drawing commands and is for reference only.