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Rotating Green by IM 6 - 8 Math

Rotating Green by IM 6 - 8 Math
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2016-06-24 21:56
VectorFunctionTrigonometrySequenceGeometric Construction
This example demonstrates the rotation of green shapes. It involves concepts such as ratios, real numbers, probability, arithmetic mean, tangent function, and centroid. Using commands like Ellipse, Point, If, Segment, Vector, Translate, Polygon, Sequence, and Ray, dynamic rotating shapes can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Ellipse((1, 0), (2.5, 0), 1.5) → e
  2. Point(e) → F
  3. If(yellow + blue ≟ 0, 1, If[ratio ≤ 1, 0, (0.79 * ratio2^(2)) - (1.72 * ratio2) + 0.99]) → a
  4. If(yellow + blue ≟ 0, 1, If[ratio ≥ 1, 1, (-0.85 * ratio^(2)) + (1.78 * ratio)]) → b
  5. If(yellow + blue ≟ 0, 1, If[ratio ≥ 1, 0, (0.79 * ratio^(2)) - (1.72 * ratio) + 0.99]) → c
  6. Point(e) → E
  7. Segment(F, (x(F), ht)) → f
  8. Vector(F, G) → u
  9. Translate(e, u) → e'
  10. Polygon(G, F, E, H) → poly2, g, f_1, e_1, h
  11. Segment(I, F) → i
  12. Segment(E, J) → j
  13. Vector(F, I) → v
  14. Ellipse((1, ht), (2.5, ht), 1.5) → p
  15. Ellipse((1, 0), (2.5, 0), 1.5) → q
  16. Segment(H, E) → l
  17. Ellipse((1, top), (2.5, top), 1.5) → k
  18. Segment(C, A) → m
  19. Segment(B, D) → n
  20. Vector(A, C) → w
  21. Vector(A, K) → r
  22. Translate(B, r) → B'
  23. Polygon(K, A, B, B') → poly1, k_1, a_1, b_1, b'
  24. If(yellow2 + blue2 ≟ 0, 1, If[ratiox ≤ 1, 0, (0.79 * (1 / ratiox)^(2)) - (1.72 * 1 / ratiox) + 0.99]) → a2
  25. If(yellow2 + blue2 ≟ 0, 1, If[ratiox ≥ 1, 1, (-0.85 * ratiox^(2)) + (1.78 * ratiox)]) → b2
  26. If(yellow2 + blue2 ≟ 0, 1, If[ratiox ≥ 1, 0, (0.79 * ratiox^(2)) - (1.72 * ratiox) + 0.99]) → c2
  27. Vector(F, A) → d
  28. Translate(q, d) → q'
  29. Translate(q, d) → q'_1
  30. Translate(q'_1, r) → s
  31. Translate(q'_1, r) → t
  32. Segment(B', B) → g_1
  33. Segment(K, A) → h_1
  34. Sequence(Ellipse[(1, k), (2.5, k), 1.5], k, 10, 90, 10) → list1
  35. Translate(list1, d) → list1'
  36. Ray((8.5, 0), (8.5, 1)) → i_1
  37. Sequence((8.5, n), n, 0, 100, 10) → list2
  38. Point(i_1) → L
  39. Sequence(Text[m + "ml", (8.65, m - 1.5)], m, 0, 100, 10) → list3
  40. Polygon(M, N, O, P) → poly3, m_1, n_1, o, p_1