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非相似圆的勾股定理新发现

非相似圆的勾股定理新发现
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2019-08-03 01:39
圆变换几何作图
本范例展示了非相似圆中的新勾股定理。它涉及的核心数学概念包括几何均值和几何变换。通过使用GeoGebra中的Circle, Point, Line, Segment, Midpoint, Circumference, PointIn, Area等命令，可以构造出这一有趣的几何现象。适合高中几何学习者和数学爱好者探索。

GeoGebra 命令及参数

  1. Circle(A, a) → c
  2. Point(c) → C
  3. Point(c) → B
  4. Line(C, B) → f
  5. Point(c) → D
  6. Segment(D, C) → g
  7. Segment(D, B) → h
  8. Midpoint(C, D) → E
  9. Midpoint(D, B) → F
  10. Circle(E, D) → d
  11. Circle(F, D) → e
  12. Point(d) → G
  13. Segment(G, C) → i
  14. Segment(G, D) → j
  15. Point(e) → H
  16. Segment(D, H) → k
  17. Segment(H, B) → l
  18. Midpoint(G, C) → I
  19. Midpoint(G, D) → J
  20. Midpoint(D, H) → K
  21. Midpoint(H, B) → L
  22. Circle(I, G) → p
  23. Circle(J, G) → q
  24. Circle(K, D) → r
  25. Circle(L, H) → s
  26. Circumference(p) → cep
  27. PointIn(p) → Pointp_1
  28. Circumference(q) → ceq
  29. PointIn(q) → Pointq_1
  30. Circumference(r) → cer
  31. PointIn(r) → Pointr_1
  32. Circumference(s) → ces
  33. PointIn(s) → Points_1
  34. Circumference(c) → downbig
  35. PointIn(c) → Pointc_1
  36. Circumference(c) → circumferencec
  37. PointIn(c) → Pointc_2
  38. Area(p) → b
  39. PointIn(p) → Pointp
  40. Area(q) → m
  41. PointIn(q) → Pointq
  42. Area(r) → n
  43. PointIn(r) → Pointr
  44. Area(s) → o
  45. PointIn(s) → Points
  46. Area(c) → t
  47. PointIn(c) → Pointc