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勾股定理演示 by Mark Beckwith

勾股定理演示 by Mark Beckwith
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2016-07-09 04:57
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①本范例通过拖动点并使用滑块演示勾股定理，直观展示直角三角形三边关系；②涉及核心数学概念为勾股定理、直角三角形、距离计算；③作图要点运用了Point（点）、Intersect（交点）、CircleArc（圆弧）、Polygon（多边形）、If（条件）、Rotate（旋转）、Dilate（缩放）、Vector（向量）、Translate（平移）、Midpoint（中点）等GeoGebra命令与对象；④适合初中及以上学生学习和理解勾股定理的证明及应用。

GeoGebra 命令及参数

  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, 4) → poly3, j, k, l, m, J, K
  8. Intersect(b, m) → L
  9. Intersect(i, l) → M
  10. Polygon(A, G, F, L) → poly4, a_1, g_1, f_1, l_1
  11. Polygon(M, I, J) → poly5, j_1, m_1, i_1
  12. Polygon(J, C, H) → poly6, h_1, j_2, c_1
  13. Polygon(A, E, L) → poly7, l_2, a_2, e_1
  14. Polygon(E, M, J, C) → poly8, e_2, m_2, j_3, c_2
  15. If(n < 1, n, 1) → r1
  16. Rotate(A, (-(((r1 * 90))°)), A) → A'
  17. Rotate(G, (-(((r1 * 90))°)), A) → G'
  18. Rotate(F, (-(((r1 * 90))°)), A) → F'
  19. Rotate(L, (-(((r1 * 90))°)), A) → L'
  20. Polygon(A', G', F', L') → poly4', a', g', f', l'
  21. Dilate(J, If[1 ≤ n < 2, 2 - n, If[n ≥ 2, 0, 1]], C) → J'
  22. Vector(J, J') → u
  23. Translate(M, u) → M'
  24. Translate(I, u) → I'
  25. Translate(J, u) → J'_1
  26. Polygon(M', I', J'_1) → poly5', j'_1, m', i'
  27. Midpoint(A, J) → N
  28. Vector(A, L) → v
  29. Translate(C, v) → C'
  30. Vector(A, E) → w
  31. Translate(C, w) → C'_1
  32. Polygon(C, C', C'_1) → poly9, c'_1, c_3, c'
  33. Polygon(C', J, H, C'_1) → poly10, c'_2, j_4, h_2, c'_3
  34. Dilate(J, If[2 ≤ n < 3, 3 - n, If[n ≥ 3, 0, 1]], K) → J'_2
  35. Vector(J, J'_2) → p
  36. Translate(C', p) → C''
  37. Translate(J, p) → J'_3
  38. Translate(H, p) → H'
  39. Translate(C'_1, p) → O
  40. Polygon(C'', J'_3, H', O) → poly10', c'', j'_3, h', o
  41. If(3 ≤ n ≤ 4, n - 3, 0) → r2
  42. Rotate(C, (-(((r2 * 90))°)), J) → C'_2
  43. Rotate(C', (-(((r2 * 90))°)), J) → C''_1
  44. Rotate(C'_1, (-(((r2 * 90))°)), J) → P
  45. Polygon(C'_2, C''_1, P) → poly9', p_1, c'_4, c''_1