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几句话证明度量关系

几句话证明度量关系
几何画板及绘图内容加载中，请稍等……
2020-01-23 21:27
多边形向量三角函数解析几何几何作图
①本范例通过动态演示矩形、三角形等图形的度量关系，揭示几何图形内在的数学规律；②涉及的核心数学概念包括解析几何、三角函数、向量运算、几何变换等；③作图要点运用了Line（线）、Point（点）、Circle（圆）、Segment（线段）、Intersect（交点）、OrthogonalLine（垂线）、Polygon（多边形）、Vector（向量）、Translate（平移）、Midpoint（中点）、Angle（角度）等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解几何证明与动态几何的关联。

GeoGebra 命令及参数

  1. Line(O, xAxis) → b
  2. Point(b) → E
  3. Circle(O, a) → c
  4. Point(c) → A
  5. Segment(A, E) → d2
  6. Circle(A, If[t < d2, t, d2]) → e2
  7. Intersect(c, b) → C, B
  8. Segment(A, C) → e
  9. OrthogonalLine(E, b) → i
  10. Circle(E, e) → k
  11. Intersect(k, i) → G, I
  12. Segment(C, I) → b2
  13. Circle(C, If[t < b2, t, b2]) → c2
  14. Segment(A, E) → t1
  15. Line(A, E) → h1
  16. Segment(A, E) → f1
  17. Circle(A, If[t < f1, t, f1]) → g1
  18. Intersect(g1, h1) → U, V
  19. Line(C, I) → n
  20. Segment(C, I) → d1
  21. Circle(C, If[t < t1, t, t1]) → p
  22. Segment(A, B) → f
  23. Circle(E, f) → h
  24. Intersect(h, b) → D, F
  25. Segment(B, F) → i1
  26. Circle(B, If[t < i1, t, i1]) → k1
  27. OrthogonalLine(A, b) → d
  28. Intersect(d, b) → H
  29. Segment(A, H) → g
  30. Segment(I, F) → j
  31. Segment(I, E) → l
  32. Segment(E, F) → m
  33. Line(A, b) → q
  34. Intersect(q, i) → L
  35. Segment(H, B) → r
  36. Circle(E, r) → s
  37. Intersect(s, b) → M, N
  38. Segment(L, N) → a1
  39. Circle(E, g) → c1
  40. Intersect(c1, b) → J, K
  41. Segment(C, H) → b1
  42. Circle(E, b1) → e1
  43. Intersect(e1, i) → P, Q
  44. Polygon(I, E, F) → poly1, f_1, i_1, e_1
  45. Polygon(A, C, B) → poly2, b_1, a_1, c_1
  46. Polygon(A, H, B) → poly3, b_2, a_2, h_1
  47. Polygon(L, E, N) → poly4, n_1, l_1, e_2
  48. Polygon(A, C, H) → poly5, h_2, a_3, c_2
  49. Polygon(Q, E, K) → poly6, k_1, q_1, e_3
  50. Intersect(f1, h1) → T
  51. Intersect(k1, t1) → Z, H1
  52. Segment(A, L) → j1_1
  53. Circle(A, If[t < j1_1, t, j1_1]) → p1
  54. Intersect(p1, j1_1) → A1, B1
  55. Vector(A, A1) → u
  56. Translate(A, u) → A'
  57. Translate(H, u) → H'
  58. Translate(B, u) → B'
  59. Polygon(A', H', B') → poly3', b', a', h'
  60. Segment(A, K) → m1_2
  61. Circle(A, If[t < m1_2, t, m1_2]) → q1
  62. Intersect(q1, m1_2) → C1, D1
  63. Segment(C, Q) → l1_2
  64. Circle(C, If[t < l1_2, t, l1_2]) → r1
  65. Intersect(r1, l1_2, 1) → E1
  66. Segment(H, E) → n1
  67. Circle(H, If[t < n1, t, n1]) → s1
  68. Intersect(s1, b) → F1, G1
  69. Polygon(C1, E1, G1) → poly8, g1_1, c1_1, e1_1
  70. Segment(B, F) → j1
  71. Intersect(k1, j1) → I1, J1
  72. Intersect(c2, b2) → S, R
  73. Intersect(e2, d2) → W, K1
  74. Segment(S, W) → l1
  75. Segment(W, I1) → m1
  76. Segment(I1, S) → a2
  77. Polygon(S, W, I1) → poly7, i1_1, s_1, w
  78. Circle(H, a / 10) → f2
  79. Intersect(f2, r) → L1,
  80. Intersect(f2, b1) → M1,
  81. Intersect(f2, g) → N1,
  82. Circle(A, a / 10) → g2
  83. Intersect(g2, f) → O1,
  84. Intersect(g2, e) → P1,
  85. Line(O1, e) → h2
  86. Line(P1, f) → i2
  87. Intersect(i2, h2) → Q1
  88. Segment(O1, Q1) → j2
  89. Segment(Q1, P1) → k2
  90. Line(M1, g) → l2
  91. Line(L1, g) → m2
  92. Line(N1, r) → n2
  93. Intersect(l2, n2) → R1
  94. Intersect(m2, n2) → S1
  95. Polygon(R1, M1, H, N1) → poly9, r1_1, m1_1, h_3, n1_1
  96. Polygon(N1, S1, L1, H) → poly10, n1_2, s1_1, l1_1, h_4
  97. Circle(E, a / 10) → p2
  98. Intersect(p2, c1_1) → U1,
  99. Line(U1, r) → r2
  100. Intersect(p2, e1_1) → V1,
  101. Line(V1, g) → q2
  102. Line(U1, r) → s2
  103. Intersect(s2, q2) → W1
  104. Polygon(U1, W1, V1, E) → poly11, u1, w1, v1, e_4
  105. Midpoint(w) → Z1
  106. Midpoint(h') → A2
  107. Midpoint(g1_1) → B2
  108. Polygon(C2, D2, E2, F2) → poly12, c2_1, d2_1, e2_1, f2_1
  109. Polygon(G2, H2, I2, J2) → poly13, g2_1, h2_1, i2_1, j2_1
  110. Vector(K2, L2) → v
  111. Vector(M2, N2) → z
  112. Vector(O2, P2) → z1
  113. Polygon(Q2, R2, S2, U2) → poly14, q2_1, r2_1, s2_1, u2
  114. Vector(E, A_1) → u_1
  115. Vector(E, B_1) → v_1
  116. Vector(H, C_1) → w_1
  117. Translate(W, Vector[(t / 10 * w_1)]) → W'
  118. Translate(A, Vector[(t / 10 * u_1)]) → A'_1
  119. Translate(H, Vector[(t / 10 * u_1)]) → H'_1
  120. Translate(B, Vector[(t / 10 * u_1)]) → B'_1
  121. Polygon(A'_1, H'_1, B'_1) → poly3'_1, b'_1, a'_1, h'_1
  122. Translate(A, Vector[(t / 10 * v_1)]) → A'_2
  123. Translate(C, Vector[(t / 10 * v_1)]) → C'
  124. Translate(H, Vector[(t / 10 * v_1)]) → H'_2
  125. Polygon(A'_2, C', H'_2) → poly5', h'_2, a'_2, c'
  126. Translate(A, Vector[(t / 10 * w_1)]) → A'_3
  127. Translate(C, Vector[(t / 10 * w_1)]) → C'_1
  128. Translate(B, Vector[(t / 10 * w_1)]) → B'_2
  129. Polygon(A'_3, C'_1, B'_2) → poly2', b'_2, a'_3, c'_1
  130. Segment(C'_1, B'_2) → d_1
  131. Angle(C'_1, A'_3, B'_2) → α
  132. Angle(A'_2, H'_2, C') → β
  133. Angle(B'_1, H'_1, A'_1) → γ
  134. Segment(C'_1, B'_2) → g_1
  135. Segment(A'_2, C') → j_1
  136. Segment(A'_1, B'_1) → m_1
  137. Segment(A'_1, H'_1) → p_1
  138. Segment(H'_1, B'_1) → r_1
  139. Segment(A'_3, B'_2) → t_1
  140. Segment(A'_3, C'_1) → d_2
  141. Segment(A'_2, H'_2) → f_2
  142. Segment(C', H'_2) → g_2
  143. Angle(A'_2, H'_2, C') → δ
  144. Angle(B'_1, H'_1, A'_1) → ε

AI 绘图提示语参考

画一个动态几何图形，展示矩形和三角形中的度量关系。包含坐标轴、圆、线段和点，通过交点和垂线构造几何形状。用向量操作和几何变换揭示内在数学原理，最终形成多个多边形，展示动态几何与几何证明的联系。
以上提示语为根据原始绘图命令整理而来，仅供参考。