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Pythagoras Proof Shearing: Geometric Construction and Parametric Curves

Pythagoras Proof Shearing: Geometric Construction and Parametric Curves
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2015-03-06 11:46
TriangleParametric EquationGeometric Construction
This example demonstrates the Pythagorean theorem proof through geometric construction and parametric curves. Key mathematical concepts include triangles, vectors, and parametric equations. Construction involves using commands like Intersect, Segment, OrthogonalLine, and objects such as Polygon, Ray. Suitable for high school students or math enthusiasts to understand the principles of combining geometry and algebra.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Segment(A, C) → a
  3. OrthogonalLine(C, a) → b
  4. Intersect(b, xAxis) → D
  5. Polygon(A, D, 4) → poly1, a_1, d, c, e, B, E
  6. OrthogonalLine(C, a_1) → j
  7. Polygon(D, C, 4) → poly2, d_1, c_1, f, g, F, G
  8. Ray(G, F) → r
  9. Intersect(j, r) → L
  10. Segment(F, L) → m
  11. Polygon(C, A, 4) → poly3, c_2, a_2, h, i, H, I
  12. Point(m) → J
  13. Segment(I, L) → l
  14. Ray(H, I) → k
  15. Point(l) → K
  16. Vector(C, K) → v
  17. Vector(F, J) → w
  18. Translate(F, w) → F'
  19. Translate(G, w) → G'
  20. Segment(F', G') → f'
  21. Polygon(D, G', J, C) → poly4, d_2, g', j_1, c_3
  22. Vector(I, K) → u
  23. Translate(H, u) → H'
  24. Translate(I, u) → I'
  25. Segment(H', I') → h'
  26. Polygon(A, H', K, C) → poly5, a_3, h'_1, k_1, c_4
  27. Intersect(a_1, j) → M
  28. Segment(M, C) → n
  29. Point(n) → N
  30. Vector(M, N) → z
  31. Vector(C, N) → p
  32. Translate(J, p) → J'
  33. Translate(C, p) → C'
  34. Segment(J', C') → q
  35. Polygon(A, N, D, G', J', H') → poly6, a_4, n_1, d_3, g'_1, j', h'_2
  36. Polygon(A, C, D) → poly7, d_4, a_5, c_5
  37. Intersect(j, c_5) → O

AI Drawing Prompt Reference

Draw a right triangle to demonstrate the Pythagorean theorem through geometric shearing. Construct the axes and intersect to form the right angle, then create the legs and hypotenuse. Fill the legs with squares and sketch parametric curves to show the shearing transformation. The final image should include nested polygons, illustrating the integration of geometry and algebra.
The prompt above was compiled from the original drawing commands and is for reference only.