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Proof Without Words by Steve Phelps (10)

Proof Without Words by Steve Phelps (10)
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2015-02-08 09:54
TriangleCirclePolygonInequalityGeometric Construction
In collections Proofs Without Words Proofs Without Words
This example demonstrates the Pythagorean Theorem geometrically by dragging points and a slider. It involves core concepts like the Pythagorean Theorem, inequalities, triangles, squares, fractal geometry, and ratios. Constructed using commands such as Point, Intersect, CircleArc, Polygon, Line, OrthogonalLine, Midpoint, Rotate. Suitable for high school mathematics teaching and geometric exploration.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. CircleArc(B, D, A) → c
  4. Point(c) → E
  5. Polygon(A, E, 4) → poly1, a, b, d, e, F, G
  6. Polygon(E, C, 4) → poly2, f, g, h, i, H, I
  7. Polygon(A, C, E) → poly3, e_1, a_1, c_1
  8. Polygon(C, A, 4) → poly4, j, k, l, m, J, K
  9. Line(G, F) → n
  10. Line(I, H) → p
  11. Intersect(n, p) → L
  12. Polygon(F, L, E) → poly5, e_2, f_1, l_1
  13. Polygon(L, I, E) → poly6, e_3, l_2, i_1
  14. Line(E, A) → q
  15. Line(E, C) → r
  16. OrthogonalLine(J, q) → s
  17. OrthogonalLine(K, r) → t
  18. Intersect(q, s) → M
  19. Intersect(s, t) → N
  20. Intersect(r, t) → O
  21. Polygon(M, A, J) → poly7, j_1, m_1, a_2
  22. Polygon(J, K, N) → poly8, n_1, j_2, k_1
  23. Polygon(K, C, O) → poly9, o, k_2, c_2
  24. Midpoint(e_1) → P
  25. Rotate(M, rrr, P) → M'
  26. Rotate(A, rrr, P) → A'
  27. Rotate(J, rrr, P) → J'
  28. Polygon(M', A', J') → poly7', j', m', a'
  29. Rotate(poly4, rrr, P) → poly4'
  30. Rotate(K, rrr, P) → K'
  31. Rotate(C, rrr, P) → C'
  32. Rotate(O, rrr, P) → O'
  33. Polygon(K', C', O') → poly9', o', k', c'
  34. Rotate(J, rrr, P) → J'_1
  35. Rotate(K, rrr, P) → K'_1
  36. Rotate(N, rrr, P) → N'
  37. Polygon(J'_1, K'_1, N') → poly8', n', j'_1, k'_1

AI Drawing Prompt Reference

This is a geometric proof of the Pythagorean Theorem. The figure includes points such as A, B, C, D, E, J, K, L, M, N, O. There are triangles and squares formed by connecting these points. Lines and perpendicular lines are also present to establish geometric relationships. By dragging points and a slider, the figure can be explored. The figure illustrates concepts like triangles, circles, polygons, inequalities, and geometric construction, suitable for mathematics teaching and geometric exploration.
The prompt above was compiled from the original drawing commands and is for reference only.