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Nested Pentagons

Nested Pentagons
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2018-11-09 11:06
PolygonFunctionGeometric Construction
In collections Flip & turn
This example demonstrates the construction of nested pentagons. Key mathematical concepts include polygons and geometric construction. Using GeoGebra commands such as Intersect, Point, Polygon, and Circle, a series of nested pentagons can be constructed. Suitable for middle school and above students to learn polygon properties and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 5) → poly1, a, b, c, d, e, C, D, E
  4. Circle(A, (a * k)) → f
  5. Circle(B, (a * k)) → g
  6. Intersect(f, a, 1) → F
  7. Intersect(g, b, 1) → G
  8. Polygon(F, G, 5) → poly2, h, i, j, l, m, H, I, J
  9. next(poly2, k) → poly3
  10. next(poly3, k) → poly4
  11. next(poly4, k) → poly5
  12. next(poly5, k) → poly6
  13. next(poly6, k) → poly7
  14. next(poly7, k) → poly8
  15. next(poly8, k) → poly9
  16. next(poly9, k) → poly10
  17. next(poly10, k) → poly11
  18. next(poly11, k) → poly12
  19. next(poly12, k) → poly13
  20. next(poly13, k) → poly14
  21. next(poly14, k) → poly15
  22. next(poly15, k) → poly16
  23. next(poly16, k) → poly17
  24. next(poly17, k) → poly18
  25. next(poly18, k) → poly19
  26. next(poly19, k) → poly20
  27. next(poly20, k) → poly21
  28. next(poly21, k) → poly22
  29. next(poly22, k) → poly23
  30. next(poly23, k) → poly24
  31. next(poly24, k) → poly25
  32. next(poly25, k) → poly26
  33. next(poly26, k) → poly27
  34. next(poly27, k) → poly28
  35. next(poly28, k) → poly29
  36. next(poly29, k) → poly30
  37. next(poly30, k) → poly31
  38. next(poly31, k) → poly32
  39. next(poly32, k) → poly33

AI Drawing Prompt Reference

Draw a series of nested pentagons starting from the origin, where each pentagon is tangent to the circumcircle of the previous one and scaled down proportionally, totaling 25 nested pentagons to illustrate a geometric progression from largest to smallest.
The prompt above was compiled from the original drawing commands and is for reference only.