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Einstein's Proof of the Pythagorean Theorem

Einstein's Proof of the Pythagorean Theorem
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2015-11-23 09:10
TriangleTransformationGeometric Construction
This example demonstrates how Einstein proved the Pythagorean theorem. It involves key mathematical concepts such as geometric construction and transformation. Using GeoGebra commands like Polygon, Dilate, and Segment, the proof process is dynamically illustrated. Suitable for middle school and above students to learn geometric proofs.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Polygon(A, C, D, E) → poly2, a_1, c_1, d, e
  3. Dilate(A, r, F) → A'
  4. Dilate(C, r, F) → C'
  5. Dilate(D, r, F) → D'
  6. Dilate(E, r, F) → E'
  7. Polygon(A', C', D', E') → poly2', a', c', d', e'
  8. Dilate(A, r, F) → A'_1
  9. Dilate(B, r, F) → B'
  10. Dilate(C, r, F) → C'_1
  11. Polygon(A'_1, B', C'_1) → poly1', c'_1, a'_1, b'
  12. rttri(G, H) → I, poly3
  13. subright(H, I, G) → f, g, J
  14. Segment(I, G) → h
  15. Segment(G, H) → i
  16. Segment(I, H) → j
  17. Angle(I, J, G) → α
  18. Angle(H, G, I) → γ
  19. Polygon(G, J, I) → poly7, i_3, g_3, j_1
  20. Polygon(G, J, H) → poly8, h_3, g_4, j_2
  21. Angle(G, I, J) → ζ
  22. Angle(J, G, I) → η
  23. Angle(J, H, G) → θ
  24. Angle(H, G, J) → ι
  25. Polygon(I, H, 4) → poly4, k, l, m, n, K, L
  26. Polygon(G, I, 4) → poly5, p, q, s, t, M, N
  27. Polygon(H, G, 4) → poly6, b_1, d_1, e_1, f_1, O, P
  28. Polygon(H, Q, R, S, T, U, V, I) → poly9, h_1, q_1, r_1, s_1, t_1, u, v, i_1
  29. Intersect(LineBisector[Segment[H, I]], LineBisector[Segment[I, I + ((G - I) * Distance[H, I] / Distance[I, G])]]) → W
  30. Dilate(Polygon[Rotate[H, Angle[H, W, I], W], Rotate[Q, Angle[H, W, I], W], Rotate[R, Angle[H, W, I], W], Rotate[S, Angle[H, W, I], W], Rotate[T, Angle[H, W, I], W], Rotate[U, Angle[H, W, I], W], Rotate[V, Angle[H, W, I], W], Rotate[I, Angle[H, W, I], W]], Distance[G, I] / Distance[I, H], I) → poly10
  31. Intersect(LineBisector[Segment[H, I]], LineBisector[Segment[H, H + ((G - H) * Distance[H, I] / Distance[H, G])]]) → Z
  32. Dilate(Polygon[Rotate[H, Angle[I, Z, H], Z], Rotate[Q, Angle[I, Z, H], Z], Rotate[R, Angle[I, Z, H], Z], Rotate[S, Angle[I, Z, H], Z], Rotate[T, Angle[I, Z, H], Z], Rotate[U, Angle[I, Z, H], Z], Rotate[V, Angle[I, Z, H], Z], Rotate[I, Angle[I, Z, H], Z]], Distance[G, H] / Distance[I, H], H) → poly11