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Geometric Proof of Pythagorean Theorem by Steve Phelps (2)

Geometric Proof of Pythagorean Theorem by Steve Phelps (2)
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2019-06-03 06:06
CirclePolygonGeometric Construction
This example demonstrates the Pythagorean Theorem using regular polygons and semicircles. It involves core math concepts like polygons, circles, the Pythagorean Theorem, functions, linear regression, and more. Constructed with GeoGebra commands such as Point, Semicircle, Polygon, Centroid, Mirror, OrthogonalLine, Line, Intersect, Sequence, and Midpoint. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(yAxis) → B
  3. Semicircle(A, B) → c
  4. Point(c) → C
  5. Polygon(A, C, n) → poly1, f, G, J, M, P, S, g, h, q, t, d, g_1, j_1, D
  6. Polygon(C, B, n) → poly2, i, H, K, N, Q, T, j, k, r, a, e, h_1, k_1, E
  7. Polygon(B, A, n) → poly3, l, I, L, O, R, U, m, p, s, b, f_1, i_1, l_1, F
  8. Centroid(poly3) → V
  9. Centroid(poly2) → W
  10. Centroid(poly1) → Z
  11. Mirror(A, i) → A'
  12. OrthogonalLine(W, i) → m_1
  13. Line(B, A') → n_1
  14. Intersect(m_1, n_1) → A_1
  15. Sequence(Rotate[A_1, ((w * 2) * π / n), W], w, 0, 7) → l1
  16. Intersect(m_1, i) → B_1
  17. Sequence(Rotate[B_1, ((w * 2) * π / n), W], w, 1, 8) → l2
  18. Sequence(Rotate[B, ((w * 2) * π / n), W], w, 0, 7) → l3
  19. Sequence(Polygon[W, l1(w), l3(w), l2(w)], w, 1, n) → l4
  20. Sequence(Rotate[Mirror[l4(1), Segment[B, C]], ((w * 2) * π / n), V], w, 1, n) → l5
  21. Sequence(Rotate[Mirror[W, Segment[B, C]], ((w * 2) * π / n), V], w, 1, n) → l6
  22. Sequence(Rotate[Mirror[A_1, Segment[B, C]], ((w * 2) * π / n), V], w, 1, n) → l7
  23. Midpoint(l) → C_1
  24. Sequence(Rotate[Mirror[B_1, C_1], ((w * 2) * π / n), V], w, 1, n) → l8
  25. Polygon(l6) → poly4
  26. Polygon(C_1, l8(n), A) → t1, a_1, c_1, p_1
  27. Sequence(Rotate[t1, ((w * 2) * π / n), V], w, 1, n) → l9
  28. Sequence(Polygon[Rotate[A_1, ((w * 2) * π / n), W], Rotate[B_1, ((w * 2) * π / n), W], Rotate[B, ((w * 2) * π / n), W]], w, 1, n) → l10
  29. Polygon(A, C, n) → poly5, q_1, E_1, F_1, G_1, H_1, I_1, r_1, s_1, t_1, b_1, d_1, e_1, f_2, D_1

AI Drawing Prompt Reference

Draw a geometric proof of the Pythagorean theorem. Include three semicircles and a square, with the diameters of the semicircles being the sides of the square. Connect each vertex of the square to the corresponding semicircle, forming three triangles. The diagonals of the square intersect the lines connecting the centers of the semicircles at a single point, demonstrating the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.