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Pythagorean Theorem Animation

Pythagorean Theorem Animation
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2014-07-10 23:26
TriangleCirclePolygonGeometric Construction
This example demonstrates the Pythagorean Theorem through an animated visualization, clearly illustrating the relationship between the sides of a right triangle. Key mathematical concepts include the Pythagorean Theorem, circles, polygons, rotation, symmetry, and more. The construction utilizes GeoGebra commands such as Semicircle, Intersect, CircleArc, Point, Segment, Mirror, Polygon, OrthogonalLine, Rotate, Midpoint, and If. It is suitable for middle school students and above, as well as for educational purposes in mathematics classes.

GeoGebra Commands & Parameters

  1. Semicircle(A4, A5) → c
  2. Intersect(c, LineBisector[A4, A5]) → A,
  3. CircleArc(Midpoint[A4, A5], A, A4) → r_1
  4. Point(r_1) → A6
  5. Segment(A6, A5) → b
  6. Mirror(A4, b) → A12
  7. Polygon(A6, A5, 4) → poly2, c_2, b_1, g, h, A9, A10
  8. OrthogonalLine(A12, h) → m
  9. Segment(A10, A5) → j
  10. Intersect(m, j) → A11
  11. Rotate(A6, 90*°, A5) → B8
  12. Segment(A4, A6) → a
  13. Segment(A5, A4) → d
  14. Polygon(A4, A6, 4) → poly1, a_1, c_1, e, f, A7, A8
  15. Segment(A4, A7) → i
  16. Mirror(A12, j) → A13
  17. Segment(A5, A12) → k_1
  18. Segment(A5, A13) → l
  19. Segment(A11, A13) → n
  20. Segment(A11, A12) → p
  21. Polygon(A5, A4, 4) → poly4, b_2, a_2, k, q, B12, B6
  22. Rotate(A11, 90*°, A5) → B7
  23. Midpoint(A4, B6) → O
  24. Rotate(B8, 90*°, O) → B10
  25. Rotate(B10, 90*°, O) → B11
  26. Rotate(B11, 90*°, O) → B13
  27. Rotate(B7, 180*°, O) → B9
  28. Segment(B13, B8) → r
  29. Segment(B8, B10) → s
  30. Segment(B11, B13) → d_1
  31. Segment(B11, A4) → e_1
  32. Segment(B13, B12) → f_1
  33. Segment(B8, B6) → g_1
  34. Segment(B10, A5) → h_1
  35. Segment(B7, A5) → j_1
  36. Segment(B9, B12) → p_1
  37. Segment(B10, B11) → q_1
  38. Polygon(C4, C5, C6, C7) → poly3, c2, c3, c4, c5
  39. Polygon(D4, D5, D6) → poly5, d4, d2, d3
  40. Polygon(E4, E5, E6) → poly6, e4, e2, e3
  41. Polygon(F4, F5, F6) → poly7, f4, f2, f3
  42. Polygon(G4, G5, G6) → poly8, g4, g2, g3
  43. Polygon(H4, H5, H6) → poly9, h4, h2, h3
  44. Polygon(I4, I5, I6) → poly10, i4, i2, i3
  45. If(time < C$2, C4, If[(C$2 ≤ time) ∧ (time < C$3), C4 - (time - C$2) * (C4 - C9) / (C$3 - C$2), C9]) → J4
  46. If(time < C$2, C5, If[(C$2 ≤ time) ∧ (time < C$3), C5 - (time - C$2) * (C5 - C10) / (C$3 - C$2), C10]) → J5
  47. If(time < C$2, C6, If[(C$2 ≤ time) ∧ (time < C$3), C6 - (time - C$2) * (C6 - C11) / (C$3 - C$2), C11]) → J6
  48. If(time < C$2, C7, If[(C$2 ≤ time) ∧ (time < C$3), C7 - (time - C$2) * (C7 - C12) / (C$3 - C$2), C12]) → J7
  49. If(time < D$2, D4, If[(D$2 ≤ time) ∧ (time < D$3), D4 - (time - D$2) * (D4 - D9) / (D$3 - D$2), D9]) → K4
  50. If(time < D$2, D5, If[(D$2 ≤ time) ∧ (time < D$3), D5 - (time - D$2) * (D5 - D10) / (D$3 - D$2), D10]) → K5
  51. If(time < D$2, D6, If[(D$2 ≤ time) ∧ (time < D$3), D6 - (time - D$2) * (D6 - D11) / (D$3 - D$2), D11]) → K6
  52. If(time < E$2, E4, If[(E$2 ≤ time) ∧ (time < E$3), E4 - (time - E$2) * (E4 - E9) / (E$3 - E$2), E9]) → L4
  53. If(time < E$2, E5, If[(E$2 ≤ time) ∧ (time < E$3), E5 - (time - E$2) * (E5 - E10) / (E$3 - E$2), E10]) → L5
  54. If(time < E$2, E6, If[(E$2 ≤ time) ∧ (time < E$3), E6 - (time - E$2) * (E6 - E11) / (E$3 - E$2), E11]) → L6
  55. If(time < F$2, F4, If[(F$2 ≤ time) ∧ (time < F$3), F4 - (time - F$2) * (F4 - F9) / (F$3 - F$2), F9]) → M4
  56. If(time < F$2, F5, If[(F$2 ≤ time) ∧ (time < F$3), F5 - (time - F$2) * (F5 - F10) / (F$3 - F$2), F10]) → M5
  57. If(time < F$2, F6, If[(F$2 ≤ time) ∧ (time < F$3), F6 - (time - F$2) * (F6 - F11) / (F$3 - F$2), F11]) → M6
  58. If(time < G$2, G4, If[(G$2 ≤ time) ∧ (time < G$3), G4 - (time - G$2) * (G4 - G9) / (G$3 - G$2), G9]) → N4
  59. If(time < G$2, G5, If[(G$2 ≤ time) ∧ (time < G$3), G5 - (time - G$2) * (G5 - G10) / (G$3 - G$2), G10]) → N5
  60. If(time < G$2, G6, If[(G$2 ≤ time) ∧ (time < G$3), G6 - (time - G$2) * (G6 - G11) / (G$3 - G$2), G11]) → N6
  61. If(time < H$2, H4, If[(H$2 ≤ time) ∧ (time < H$3), H4 - (time - H$2) * (H4 - H9) / (H$3 - H$2), H9]) → O4
  62. If(time < H$2, H5, If[(H$2 ≤ time) ∧ (time < H$3), H5 - (time - H$2) * (H5 - H10) / (H$3 - H$2), H10]) → O5
  63. If(time < H$2, H6, If[(H$2 ≤ time) ∧ (time < H$3), H6 - (time - H$2) * (H6 - H11) / (H$3 - H$2), H11]) → O6
  64. If(time < I$2, I4, If[(I$2 ≤ time) ∧ (time < I$3), I4 - (time - I$2) * (I4 - I9) / (I$3 - I$2), I9]) → P4
  65. If(time < I$2, I5, If[(I$2 ≤ time) ∧ (time < I$3), I5 - (time - I$2) * (I5 - I10) / (I$3 - I$2), I10]) → P5
  66. If(time < I$2, I6, If[(I$2 ≤ time) ∧ (time < I$3), I6 - (time - I$2) * (I6 - I11) / (I$3 - I$2), I11]) → P6
  67. Polygon(J4, J5, J6, J7) → poly11, j4, j5, j6, j7
  68. Polygon(K4, K5, K6) → poly12, k6, k4, k5
  69. Polygon(L4, L5, L6) → poly13, l6, l4, l5
  70. Polygon(M4, M5, M6) → poly14, m6, m4, m5
  71. Polygon(N4, N5, N6) → poly15, n6, n4, n5
  72. Polygon(O4, O5, O6) → poly16, o6, o4, o5
  73. Polygon(P4, P5, P6) → poly17, p6, p4, p5
  74. Polygon(C9, C10, C11, C12) → poly18, c9, c10, c11, c12
  75. Polygon(D9, D10, D11) → poly19, d11, d9, d10
  76. Polygon(E9, E10, E11) → poly20, e11, e9, e10
  77. Polygon(F9, F10, F11) → poly21, f11, f9, f10
  78. Polygon(G9, G10, G11) → poly22, g11, g9, g10
  79. Polygon(H9, H10, H11) → poly23, h11, h9, h10
  80. Polygon(I9, I10, I11) → poly24, i11, i9, i10

AI Drawing Prompt Reference

Draw an animated visualization of the Pythagorean theorem, featuring a right triangle with three semicircles and multiple squares. One square's side equals the sum of the triangle's legs, while the other equals the hypotenuse. Show rotation and mirror operations to illustrate the theorem, with dynamic changes in semicircles and squares during the animation, clearly demonstrating the geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.