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Rhombic Rosette

Rhombic Rosette
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2020-07-07 04:30
PolygonAngle
This example demonstrates the construction of a rhombic rosette. It involves key mathematical concepts such as polygons, angles, and isosceles triangles. Using GeoGebra commands like Sequence and Intersect, a dynamic construction of the rhombic rosette is achieved. Suitable for high school geometry education and learning.

GeoGebra Commands & Parameters

  1. Sequence((1 / n; i), i, 0, 6.283185307179586, (2 * π / n)) → P_1
  2. Intersect(xAxis, yAxis) → O
  3. Sequence(Mirror[O, Line[Element[P_1, i], Element[P_1, i + 1]]], i, 1, n) → P_2
  4. Sequence(Polygon[{O, Element[P_1, i], Element[P_2, i], Element[P_1, i + 1]}], i, 1, n) → L_1
  5. Sequence(Mirror[Element[P_1, i + 1], Line[Element[P_2, i], Element[P_2, i + 1 - (n * floor(i / n))]]], i, 1, n) → P_3
  6. Sequence(Polygon[{Element[P_1, i + 1], Element[P_2, i], Element[P_3, i], Element[P_2, i + 1 - (n * floor(i / n))]}], i, 1, n) → L_2
  7. Sequence(Mirror[Element[P_2, i + 1 - (n * floor(i / n))], Line[Element[P_3, i], Element[P_3, i + 1 - (n * floor(i / n))]]], i, 1, n) → P_4
  8. Sequence(Mirror[Element[P_3, i + 1 - (n * floor(i / n))], Line[Element[P_4, i], Element[P_4, i + 1 - (n * floor(i / n))]]], i, 1, n) → P_5
  9. Sequence(Polygon[{Element[P_2, i + 1 - (n * floor(i / n))], Element[P_3, i], Element[P_4, i], Element[P_3, i + 1 - (n * floor(i / n))]}], i, 1, n) → L_3
  10. Sequence(Polygon[{Element[P_3, i + 1 - (n * floor(i / n))], Element[P_4, i], Element[P_5, i], Element[P_4, i + 1 - (n * floor(i / n))]}], i, 1, n) → L_4
  11. Sequence(Mirror[Element[P_4, i + 1 - (n * floor(i / n))], Line[Element[P_5, i], Element[P_5, i + 1 - (n * floor(i / n))]]], i, 1, n) → P_6
  12. Sequence(Mirror[Element[P_5, i + 1 - (n * floor(i / n))], Line[Element[P_6, i], Element[P_6, i + 1 - (n * floor(i / n))]]], i, 1, n) → P_7
  13. Sequence(Mirror[Element[P_6, i + 1 - (n * floor(i / n))], Line[Element[P_7, i], Element[P_7, i + 1 - (n * floor(i / n))]]], i, 1, n) → P_8
  14. Sequence(Polygon[{Element[P_4, i + 1 - (n * floor(i / n))], Element[P_5, i], Element[P_6, i], Element[P_5, i + 1 - (n * floor(i / n))]}], i, 1, n) → L_5
  15. Sequence(Polygon[{Element[P_5, i + 1 - (n * floor(i / n))], Element[P_6, i], Element[P_7, i], Element[P_6, i + 1 - (n * floor(i / n))]}], i, 1, n) → L_6
  16. Sequence(Polygon[{Element[P_6, i + 1 - (n * floor(i / n))], Element[P_7, i], Element[P_8, i], Element[P_7, i + 1 - (n * floor(i / n))]}], i, 1, n) → L_7
  17. Sequence(Mirror[Element[P_7, i + 1 - (n * floor(i / n))], Line[Element[P_8, i], Element[P_8, i + 1 - (n * floor(i / n))]]], i, 1, n) → P_9
  18. Sequence(Mirror[Element[P_8, i + 1 - (n * floor(i / n))], Line[Element[P_9, i], Element[P_9, i + 1 - (n * floor(i / n))]]], i, 1, n) → P_{10}
  19. Sequence(Polygon[{Element[P_7, i + 1 - (n * floor(i / n))], Element[P_8, i], Element[P_9, i], Element[P_8, i + 1 - (n * floor(i / n))]}], i, 1, n) → L_8
  20. Sequence(Polygon[{Element[P_8, i + 1 - (n * floor(i / n))], Element[P_9, i], Element[P_{10}, i], Element[P_9, i + 1 - (n * floor(i / n))]}], i, 1, n) → L_9
  21. Sequence(B + ((2 / n * cos(i)), (2 / n * sin(i)), 2 / n), i, 0, (2 * π), (2 * π / n)) → l1
  22. Sequence(Mirror[O, Line[Element[l1, i], Element[l1, i + 1]]], i, 1, n) → l2
  23. Sequence(Mirror[Element[l1, i + 1], Line[Element[l2, i], Element[l2, i + 1 - (n * floor(i / n))]]], i, 1, n) → l3
  24. Sequence(Mirror[Element[l2, i + 1 - (n * floor(i / n))], Line[Element[l3, i], Element[l3, i + 1 - (n * floor(i / n))]]], i, 1, n) → l4
  25. Sequence(Mirror[Element[l3, i + 1 - (n * floor(i / n))], Line[Element[l4, i], Element[l4, i + 1 - (n * floor(i / n))]]], i, 1, n) → l5
  26. Sequence(Mirror[Element[l4, i + 1 - (n * floor(i / n))], Line[Element[l5, i], Element[l5, i + 1 - (n * floor(i / n))]]], i, 1, n) → l6
  27. Sequence(Mirror[Element[l5, i + 1 - (n * floor(i / n))], Line[Element[l6, i], Element[l6, i + 1 - (n * floor(i / n))]]], i, 1, n) → l7
  28. Sequence(Mirror[Element[l6, i + 1 - (n * floor(i / n))], Line[Element[l7, i], Element[l7, i + 1 - (n * floor(i / n))]]], i, 1, n) → l8
  29. Sequence(Mirror[Element[l7, i + 1 - (n * floor(i / n))], Line[Element[l8, i], Element[l8, i + 1 - (n * floor(i / n))]]], i, 1, n) → l9
  30. Sequence(Polygon[{O, Element[l1, i], Element[l2, i], Element[l1, i + 1]}], i, 1, n) → LL1
  31. Sequence(Polygon[{Element[l1, i + 1], Element[l2, i], Element[l3, i], Element[l2, i + 1 - (n * floor(i / n))]}], i, 1, n) → LL2
  32. Sequence(Polygon[{Element[l2, i + 1 - (n * floor(i / n))], Element[l3, i], Element[l4, i], Element[l3, i + 1 - (n * floor(i / n))]}], i, 1, n) → LL3
  33. Sequence(Polygon[{Element[l3, i + 1 - (n * floor(i / n))], Element[l4, i], Element[l5, i], Element[l4, i + 1 - (n * floor(i / n))]}], i, 1, n) → LL4
  34. Sequence(Polygon[{Element[l4, i + 1 - (n * floor(i / n))], Element[l5, i], Element[l6, i], Element[l5, i + 1 - (n * floor(i / n))]}], i, 1, n) → LL5
  35. Sequence(Polygon[{Element[l5, i + 1 - (n * floor(i / n))], Element[l6, i], Element[l7, i], Element[l6, i + 1 - (n * floor(i / n))]}], i, 1, n) → LL6
  36. Sequence(Polygon[{Element[l6, i + 1 - (n * floor(i / n))], Element[l7, i], Element[l8, i], Element[l7, i + 1 - (n * floor(i / n))]}], i, 1, n) → LL7
  37. Sequence(Mirror[Element[l8, i + 1 - (n * floor(i / n))], Line[Element[l9, i], Element[l9, i + 1 - (n * floor(i / n))]]], i, 1, n) → l10
  38. Sequence(Polygon[{Element[l7, i + 1 - (n * floor(i / n))], Element[l8, i], Element[l9, i], Element[l8, i + 1 - (n * floor(i / n))]}], i, 1, n) → LL8
  39. Sequence(Polygon[{Element[l8, i + 1 - (n * floor(i / n))], Element[l9, i], Element[l10, i], Element[l9, i + 1 - (n * floor(i / n))]}], i, 1, n) → LL9

AI Drawing Prompt Reference

Draw a rhombic rosette. Start by drawing a center point O and a circle with a radius of 2. Then place 8 points evenly on the circle's circumference. Use reflection and rotation to generate points P2 to P10. Finally, construct multiple rhombuses using these points to form a complex rhombic rosette pattern.
The prompt above was compiled from the original drawing commands and is for reference only.