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Scaled Flower

Scaled Flower
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2018-05-01 10:40
TrigonometrySequenceTransformationGeometric Construction
This example demonstrates the generation of petal-like polygons through similarity transformations and sine functions. Core mathematical concepts include similarity transformation, trigonometry, sequence generation, and geometric construction. GeoGebra commands used in construction are Polygon, Segment, Dilate, Sequence, and Perimeter. Suitable for high school mathematics education, illustrating the application of transformations and functions in plane figure generation.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Polygon(E, F, G, H, I, J, K, L) → poly1, e, f, g, h, i, j, k, l
  3. Segment(K, A) → m
  4. Polygon(M, M + (0, 1), M + (1, 1), M + (1, 0)) → q2, m_1, n, p, q
  5. Dilate(A, lsf, N) → A'
  6. Dilate(B, lsf, N) → B'
  7. Dilate(C, lsf, N) → C'
  8. Dilate(D, lsf, N) → D'
  9. Polygon(A', B', C', D') → q1', a', b', c', d'
  10. Dilate(K, lsf, N) → K'
  11. Dilate(A, lsf, N) → A'_1
  12. Segment(K', A'_1) → m'
  13. Dilate(E, lsf, N) → E'
  14. Dilate(F, lsf, N) → F'
  15. Dilate(G, lsf, N) → G'
  16. Dilate(H, lsf, N) → H'
  17. Dilate(I, lsf, N) → I'
  18. Dilate(J, lsf, N) → J'
  19. Dilate(K, lsf, N) → K'_1
  20. Dilate(L, lsf, N) → L'
  21. Polygon(E', F', G', H', I', J', K'_1, L') → poly1', e', f', g', h', i', j', k'_1, l'
  22. Dilate(q2, lsf, N) → q2'
  23. Dilate(M, lsf, N) → M'
  24. Sequence(Segment[M' + (i, 0), M' + (i, lsf)], i, 1, floor(lsf)) → vlns
  25. Sequence(Segment[M' + (0, i), M' + (lsf, i)], i, 1, floor(lsf)) → hlns
  26. Perimeter(poly1) → s