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Regular Star Polygons by Denis

Regular Star Polygons by Denis
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2013-11-25 12:57
PolygonSequenceGeometric Construction
This example demonstrates the construction of regular star polygons, a special type of polygon formed by connecting vertices of a regular polygon. Key mathematical concepts include polygons, geometric construction, and sequences. It uses commands like Join, Sequence, PolyLine, etc., in GeoGebra. Suitable for middle school and above students to learn about polygons and geometric construction.

GeoGebra Commands & Parameters

  1. Join({Sequence[Rotate[(0, 1), θ], θ, 0, 6.28319, 2 * π / n], {(0, 1)}}) → points
  2. Sequence(k, k, 1, max) → numbs
  3. KeepIf(IsInteger[n / k], k, numbs) → divisors
  4. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 1]) → tmp1
  5. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 2]) → tmp2
  6. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 4]) → tmp4
  7. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 5]) → tmp5
  8. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 10]) → tmp10
  9. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 8]) → tmp8
  10. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 3]) → tmp3
  11. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 11]) → tmp11
  12. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 7]) → tmp7
  13. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 6]) → tmp6
  14. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 9]) → tmp9
  15. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 14]) → tmp14
  16. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 13]) → tmp13
  17. PolyLine(Sequence[Element[points, j], j, 1, n + 1, 12]) → tmp12
  18. GCD(n, step) → gcd
  19. If(step ∈ divisors, Element[prefixes, n - 2] + "gram", Element[prefixes, n / gcd - 2] + "gram") → name
  20. Sequence(Rotate[tmp14, a], a, 0, 28 * π / n, 2 * π / n) → obj14
  21. PolyLine(Sequence[Element[points, If[Mod[j, n] ≟ 0, n, Mod[j, n]]], j, 1, 13 * (n + 1), 13]) → obj13
  22. Sequence(Rotate[tmp12, a], a, 0, 24 * π / n, 2 * π / n) → obj12
  23. Sequence(Rotate[tmp11, a], a, 0, 22 * π / n, 2 * π / n) → obj11
  24. Sequence(Rotate[tmp10, a], a, 0, 20 * π / n, 2 * π / n) → obj10
  25. Sequence(Rotate[tmp1, a], a, 0, 2 * π / n, 2 * π / n) → obj1
  26. Sequence(Rotate[tmp2, a], a, 0, 4 * π / n, 2 * π / n) → obj2
  27. Sequence(Rotate[tmp3, a], a, 0, 6 * π / n, 2 * π / n) → obj3
  28. PolyLine(Sequence[Element[points, If[Mod[j, n] ≟ 0, n, Mod[j, n]]], j, 1, 4 * (n + 1), 4]) → obj4
  29. PolyLine(Sequence[Element[points, If[Mod[j, n] ≟ 0, n, Mod[j, n]]], j, 1, 5 * (n + 1), 5]) → obj5
  30. Sequence(Rotate[tmp6, a], a, 0, 12 * π / n, 2 * π / n) → obj6
  31. PolyLine(Sequence[Element[points, If[Mod[j, n] ≟ 0, n, Mod[j, n]]], j, 1, 7 * (n + 1), 7]) → obj7
  32. PolyLine(Sequence[Element[points, If[Mod[j, n] ≟ 0, n, Mod[j, n]]], j, 1, 8 * (n + 1), 8]) → obj8
  33. Sequence(Rotate[tmp9, a], a, 0, 18 * π / n, 2 * π / n) → obj9

AI Drawing Prompt Reference

Draw regular polygons and connect their vertices to form star polygons, showing star patterns with different step lengths like 3/2, 5/2, 7/2, and rotate these patterns to display dynamic changes, finally presenting a series of rotating star polygons, emphasizing geometric construction and sequence relationships.
The prompt above was compiled from the original drawing commands and is for reference only.