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Pythagorean Theorem Proof Without Words by Camilo Sua Flórez

Pythagorean Theorem Proof Without Words by Camilo Sua Flórez
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2020-05-20 03:39
TriangleCirclePolygonOptimizationGeometric Construction
This example demonstrates the Pythagorean Theorem through dynamic geometry, eliminating the need for text. It involves core concepts like area, Pythagorean theorem, squares, linear programming, orthocenter, subtraction, surface area, and isosceles triangles. The construction uses GeoGebra commands such as Polygon, Point, Circle, Intersect, and Rotate. Ideal for high school mathematics teaching or exploration by math enthusiasts for intuitive geometric proofs.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Point(i) → E
  3. Circle(D, Segment[A, E]) → c
  4. Circle(C, Segment[E, A]) → d
  5. Circle(B, Segment[E, A]) → e
  6. Intersect(c, h, 1) → F
  7. Intersect(d, g, 1) → G
  8. Intersect(e, f, 1) → H
  9. Polygon(F, D, 4) → poly2, j, k, l, m, I, J
  10. Polygon(A, H, 4) → poly3, n, p, q, r, K, L
  11. Polygon(E, H, A) → t1, a, e_1, h_1
  12. Polygon(E, F, D) → t2, d_1, e_2, f_1
  13. Polygon(F, G, C) → t3, c_1, f_2, g_1
  14. Polygon(G, B, H) → t4, h_2, g_2, b
  15. Rotate(E, β, F) → E'
  16. Rotate(F, β, F) → F'
  17. Rotate(D, β, F) → D'
  18. Polygon(E', F', D') → t2', d', e', f'
  19. Rotate(E, (-β), H) → E'_1
  20. Rotate(H, (-β), H) → H'
  21. Rotate(A, (-β), H) → A'
  22. Polygon(E'_1, H', A') → t1', a', e'_1, h'
  23. Polygon(E, F, G, H) → q1, e_3, f_3, g_3, h_3
  24. Polygon(I, A', H, A) → q2, i_1, s, h_4, a_1
  25. Polygon(I, D', F, D) → q3, i_2, t, f_4, d_2