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Pythagoras' Theorem: Euclid's Proof

Pythagoras' Theorem: Euclid's Proof
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2020-08-01 09:05
TriangleCircleGeometric Construction
This example demonstrates Euclid's geometric proof of the Pythagorean Theorem by constructing a right triangle and related shapes to illustrate the theorem's validity. Core mathematical concepts include the Pythagorean Theorem, geometric construction, area relationships, and right triangles. It uses commands/objects like Circle, Point, Polygon, Angle, Line, Intersect, and Segment in GeoGebra. Suitable for high school mathematics teaching or for math enthusiasts studying geometric proofs.

GeoGebra Commands & Parameters

  1. Circle(O, B) → circle
  2. Point(circle) → C
  3. Polygon(A, B, C) → t1, c, a, b
  4. Angle(A, C, B) → α
  5. Polygon(A, C, 4) → poly1, f, g, h, i, D, E
  6. Polygon(C, B, 4) → poly2, j, k, l, m, F, G
  7. Polygon(B, A, 4) → poly3, n, p, q, r, H, I
  8. Line(E, D) → s
  9. Line(G, F) → t
  10. Intersect(s, t) → J
  11. Segment(D, J) → Segment_{DJ}
  12. Segment(J, G) → Segment_{GJ}
  13. Circle(F, (e * Segment_{GJ})) → d_1
  14. Circle(E, (e * Segment_{DJ})) → c_1
  15. Intersect(Segment_{DJ}, Segment_{GJ}) → K
  16. Line(E, K) → d
  17. Intersect(c_1, d) → L, ParaLeftTL
  18. Line(F, K) → f_1
  19. Intersect(d_1, f_1) → M, ParaRightTopRight
  20. Circle(ParaRightTopRight, a) → e_1
  21. Intersect(e_1, f_1) → P, ParaRightTopLeft
  22. Polygon(ParaRightTopLeft, C, B, ParaRightTopRight) → q1, ParaRightLeft, c_2, ParaRightRight, ParaRightTop
  23. Circle(ParaLeftTL, b) → g_1
  24. Intersect(g_1, d) → R, ParaLeftTR
  25. Polygon(C, ParaLeftTR, ParaLeftTL, A) → q2, ParaLeftRight, ParaLeftTop, ParaLeftLeft, a_1
  26. Circle(B, (o * c)) → h_1
  27. Intersect(h_1, r) → T,
  28. Circle(C, (o * c)) → k_1
  29. Line(J, C) → i_1
  30. Intersect(k_1, i_1, 2) → U
  31. Circle(A, (o * c)) → p_1
  32. Intersect(p_1, p) → V,
  33. Circle(T, c) → r_1
  34. Intersect(r_1, ParaRightRight) → W,
  35. Circle(U, c) → t_1
  36. Intersect(t_1, i_1) → Z, A_1
  37. Intersect(ParaLeftLeft, a_1) → B_1
  38. Circle(V, c) → d_2
  39. Intersect(d_2, ParaLeftLeft) → C_1,
  40. Polygon(V, C_1, Z, W, T, U) → poly4, HexLeft, HexTopLeft, HexTopRight, HexRight, HexBottomRight, HexBottomLeft
  41. Polygon(C_1, V, U, T, W) → poly5, c_5, v_2, u_2, t_4, w_1
  42. Segment(ParaLeftTL, ParaLeftTR) → ParaLeftTopDark
  43. Segment(ParaRightTopLeft, ParaRightTopRight) → ParaRightTopDark
  44. Circle(A, (u * c)) → q_1
  45. Circle(B, (u * c)) → s_1
  46. Circle(C, (u * c)) → e_2
  47. Intersect(HexLeft, c_5) → N
  48. Intersect(HexLeft, c_5) → Q
  49. Intersect(j_1, q1) → S
  50. Intersect(q_1, j_1) → D_1, E_1
  51. Intersect(e_2, i_1) → F_1, G_1
  52. Intersect(s_1, l_1) → H_1, I_1
  53. Polygon(E_1, G_1, I_1) → t2, i_2, e_3, g_2

AI Drawing Prompt Reference

Draw a right triangle and circle the right angle vertex to intersect the hypotenuse. Connect these intersection points to the right angle vertex, forming three smaller triangles. Circle the vertices of these triangles, intersecting to create points and connecting them into hexagons and other polygons, illustrating the geometric proof of the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.