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Pythagorean Dissection Demonstration

Pythagorean Dissection Demonstration
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2013-09-18 22:28
TriangleVectorSolid GeometryGeometric Construction
In collections Pythagorean Theorem
This example demonstrates a 3D dissection proof of the Pythagorean Theorem, visually illustrating the relationship between the sides of a right triangle. It involves core mathematical concepts such as the Pythagorean Theorem, solid geometry, and vector operations. The construction utilizes GeoGebra commands and objects like Line, Point, Midpoint, OrthogonalLine, Circle, Intersect, Polygon, Angle, Rotate, Vector, Translate, and Segment to build geometric shapes and dynamic effects. Suitable for high school students and math enthusiasts to understand spatial geometry and theorem proof intuitively.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Point(a) → C
  3. Midpoint(A, C) → D
  4. Midpoint(C, B) → E
  5. OrthogonalLine(D, a) → b
  6. OrthogonalLine(E, a) → c
  7. Circle(D, C) → d
  8. Circle(E, C) → e
  9. Intersect(d, b, 1) → F
  10. Intersect(d, b, 2) → G
  11. Polygon(F, C, G, A) → poly1, f, c_1, g, a_1
  12. Intersect(e, c, 2) → H
  13. Intersect(e, c, 1) → I
  14. Polygon(C, H, B, I) → poly2, c_2, h, b_1, i
  15. Polygon(C'', G'', A'') → poly3, a'', c'', g''
  16. Polygon(C', H', B') → poly4, b', c', h'
  17. Polygon(C, B, I) → poly5, i_1, c_3, b_2
  18. Polygon(A, C, F) → poly6, f_1, a_2, c_4
  19. Polygon(A, J, K, L, B, I, C, F) → poly7, a_3, j_1, k, l, b_3, i_2, c_5, f_2
  20. Polygon(J, F, A) → poly8, a_4, j_2, f_3
  21. Polygon(I, B, L) → poly9, l_1, i_3, b_4
  22. Angle(B, L, K) → α
  23. Angle(A, F, C) → β
  24. Rotate(I, (j - 3) * α, L) → I'
  25. Rotate(B, (j - 3) * α, L) → B'_1
  26. Rotate(L, (j - 3) * α, L) → L'
  27. Polygon(I', B'_1, L') → poly9', l', i', b'_1
  28. Rotate(J, (j - 3) * β, F) → J'
  29. Rotate(F, (j - 3) * β, F) → F'
  30. Rotate(A, (j - 3) * β, F) → A'
  31. Polygon(J', F', A') → poly8', a', j', f'
  32. Polygon(F, C, I, L, K, J) → poly10, f_4, c_6, i_4, l_2, k_1, j_3
  33. Polygon(F, I, L, J) → poly11, f_5, i_5, l_3, j_4
  34. Vector(L, I) → v
  35. Translate(F, Vector[(j - 5) * v]) → F'_1
  36. Translate(I, Vector[(j - 5) * v]) → I'_1
  37. Translate(L, Vector[(j - 5) * v]) → L'_1
  38. Translate(J, Vector[(j - 5) * v]) → J'_1
  39. Polygon(F'_1, I'_1, L'_1, J'_1) → poly11', f'_1, i'_1, l'_1, j'_1
  40. Translate(F, v) → F'_2
  41. Translate(I, v) → I'_2
  42. Translate(L, v) → L'_2
  43. Translate(J, v) → J'_2
  44. Polygon(F'_2, I'_2, L'_2, J'_2) → poly11'_1, f'_2, i'_2, l'_2, j'_2
  45. Segment(J'_2, L'_2) → m
  46. Segment(L'_2, C) → n
  47. Segment(C, J'_2) → p

AI Drawing Prompt Reference

Draw a 3D dissection proof of the Pythagorean Theorem to visually illustrate the relationship between the sides of a right triangle. Include a right triangle and two squares on its legs. Demonstrate the theorem by rotating and translating the squares, showing how they fit together to form a larger square, proving the area relationship.
The prompt above was compiled from the original drawing commands and is for reference only.