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Animated Demonstration of Pythagoras

Animated Demonstration of Pythagoras
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2015-08-20 03:44
TriangleCircleCoordinate GeometryGeometric ConstructionSlider Animation
This example animates the Pythagorean Theorem, showing that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Key mathematical concepts include right triangles, Pythagorean Theorem, and circles. It uses commands such as Semicircle, Intersect, CircleArc, Point, Segment, Mirror, Polygon, OrthogonalLine, Rotate, Midpoint, If. Suitable for middle school and above students learning geometry and algebra.

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