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Pythagorean Theorem Animation by hheinrich

Pythagorean Theorem Animation by hheinrich
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2014-03-14 19:50
TriangleCircleGeometric Construction
This example demonstrates the Pythagorean Theorem through animation, illustrating that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Key math concepts include right triangles, Pythagorean Theorem, circles, semicircles, rotation, symmetry, etc. The construction involves commands and objects like Semicircle, Intersect, CircleArc, Point, Segment, Mirror, Polygon, OrthogonalLine, Rotate, Midpoint, and If from GeoGebra. Suitable for middle school students and above for learning geometric theorems and for classroom demonstrations.

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 a right triangle with two semicircles representing the squares of the legs and a third semicircle for the hypotenuse, demonstrating the Pythagorean theorem through animation. Include rotation and symmetry elements.
The prompt above was compiled from the original drawing commands and is for reference only.