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GoGeometry 动态演示113

GoGeometry 动态演示113
几何画板及绘图内容加载中，请稍等……
2017-12-21 09:41
圆函数几何作图
这是一个动态可修改的几何问题演示，由 Antonio Gutierrez 在 Twitter 上提出。该范例展示了内切圆、中线值、函数图像、菱形等核心数学概念。通过旋转、角度、线段、射线、点、交点、正交线、圆、距离等 GeoGebra 命令进行构造。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Segment(B, A) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Segment(B, C) → h
  7. Segment(C, A) → i
  8. Angle(C, A, B) → β
  9. Rotate(C, β / 2, A) → C'
  10. Angle(C, A, C') → γ
  11. Ray(A, C') → j
  12. Rotate(A, α / 2, B) → A'_1
  13. Angle(A, B, A'_1) → δ
  14. Ray(B, A'_1) → k
  15. Intersect(j, k) → D
  16. OrthogonalLine(D, f) → l
  17. Intersect(l, f) → E
  18. Circle(D, E) → c
  19. Segment(B, D) → m
  20. Segment(D, A) → n
  21. Segment(C, D) → p
  22. Intersect(c, m, 1) → F
  23. Intersect(c, p, 1) → G
  24. Intersect(c, n, 1) → H
  25. OrthogonalLine(F, m) → q
  26. OrthogonalLine(G, p) → r
  27. OrthogonalLine(H, n) → s
  28. Intersect(q, f) → I
  29. Angle(F, I, B) → ε
  30. Rotate(F, ε / 2, I) → F'
  31. Angle(F, I, F') → ζ
  32. Ray(I, F') → t
  33. Intersect(m, t) → J
  34. OrthogonalLine(J, f) → b
  35. Intersect(b, f) → K
  36. Circle(J, K) → d
  37. Intersect(q, h) → L
  38. Segment(I, L) → e
  39. Intersect(f, s) → M
  40. Angle(A, M, H) → η
  41. Rotate(A, η / 2, M) → A'_2
  42. Angle(A, M, A'_2) → θ
  43. Ray(M, A'_2) → f_1
  44. Intersect(n, f_1) → N
  45. OrthogonalLine(N, f) → g_1
  46. Intersect(g_1, f) → O
  47. Circle(N, O) → c_1
  48. Intersect(s, i) → P
  49. Segment(M, P) → h_1
  50. Intersect(r, i) → Q
  51. Intersect(r, h) → R
  52. Angle(C, Q, G) → κ
  53. Rotate(C, κ / 2, Q) → C'_1
  54. Angle(C, Q, C'_1) → ι
  55. Ray(Q, C'_1) → i_1
  56. Intersect(p, i_1) → S
  57. OrthogonalLine(S, i) → j_1
  58. Intersect(j_1, i) → T
  59. Circle(S, T) → d_1
  60. Segment(R, Q) → k_1
  61. OrthogonalLine(N, i) → l_1
  62. Intersect(l_1, i) → U
  63. OrthogonalLine(S, h) → m_1
  64. Intersect(h, m_1) → V
  65. Segment(S, V) → n_1
  66. Segment(J, K) → p_1
  67. Segment(N, U) → q_1
  68. OrthogonalLine(D, f) → r_1
  69. Intersect(f, r_1) → W
  70. Circle(D, o) → e_1
  71. Intersect(e_1, r_1, 1) → Z
  72. Circle(Z, u) → s_1
  73. Intersect(s_1, r_1, 1) → A_1
  74. Distance(A_1, W) → distanceA1W
  75. Circle(B, p_1) → t_1
  76. Circle(C, n_1) → d_2
  77. Circle(A, q_1) → k_2
  78. Segment(B, C) → a_1
  79. Segment(C, A) → b_1
  80. Segment(B, A) → f_2
  81. Max({p_1 + n_1, n_1 + q_1, q_1 + p_1}) → w_1
  82. OrthogonalLine(B, f_2) → g_2
  83. OrthogonalLine(A, f_2) → h_2
  84. Circle(B, w_1 + 0.3) → c_2
  85. Circle(A, w_1 + 0.3) → e_2
  86. Intersect(c_2, g_2, 1) → B_1
  87. Intersect(e_2, h_2, 1) → C_1
  88. Line(B_1, C_1) → i_2
  89. Circle(B_1, p_1) → p_2
  90. Intersect(p_2, i_2, 2) → D_1
  91. Circle(D_1, n_1) → q_2
  92. Intersect(q_2, i_2, 2) → E_1
  93. Circle(E_1, n_1) → r_2
  94. Intersect(r_2, i_2, 2) → F_1
  95. Circle(F_1, q_1) → s_2
  96. Intersect(s_2, i_2) → G_1, H_1
  97. Circle(H_1, q_1) → t_2
  98. Intersect(t_2, i_2, 2) → I_1
  99. Circle(I_1, p_1) → c_3
  100. Intersect(c_3, i_2) → J_1, K_1
  101. Semicircle(B_1, E_1) → d_3
  102. Semicircle(E_1, H_1) → e_3
  103. Semicircle(H_1, K_1) → f_3
  104. OrthogonalLine(D_1, i_2) → j_2
  105. OrthogonalLine(F_1, i_2) → l_2
  106. OrthogonalLine(I_1, i_2) → m_2
  107. Intersect(d_3, j_2, 1) → L_1
  108. Intersect(e_3, l_2, 1) → M_1
  109. Intersect(f_3, m_2, 1) → N_1
  110. Angle(L_1, D_1, B_1) → λ
  111. Angle(M_1, F_1, E_1) → μ
  112. Angle(N_1, I_1, H_1) → ν
  113. Polygon(B, A, C) → t1, c_4, b_2, a_2
  114. Segment(D, W) → n_2
  115. Segment(B_1, D_1) → i_3
  116. Segment(D_1, E_1) → j_3
  117. Segment(E_1, F_1) → l_3
  118. Segment(F_1, H_1) → m_3
  119. Segment(H_1, I_1) → n_3
  120. Segment(I_1, K_1) → q_3
  121. Segment(K_1, C_1) → r_3
  122. Angle(I, F, D) → ξ
  123. Angle(P, H, D) → ο
  124. Angle(R, G, D) → ρ
  125. Dilate(K, If[0 < w ≤ 1, 1 - w, 0], B_1) → K'
  126. Vector(K, K') → u_1
  127. Translate(J, u_1) → J'
  128. Translate(K, u_1) → K'_1
  129. Segment(J', K'_1) → s_3
  130. Rotate(J', If[1 < w ≤ 2, ((-(w - 1)) * π / 2), ((-π)) / 2], B_1) → J''
  131. Rotate(K'_1, If[1 < w ≤ 2, ((-(w - 1)) * π / 2), ((-π)) / 2], B_1) → O_1
  132. Segment(J'', O_1) → t_3
  133. Line(V, r_3) → a_3
  134. Point(a_3) → P_1
  135. Angle(S, V, P_1) → σ
  136. Dilate(V, If[2 < w ≤ 3, 3 - w, 0], D_1) → V'
  137. Vector(V, V') → v_1
  138. Translate(S, v_1) → S'
  139. Translate(V, v_1) → V'_1
  140. Segment(S', V'_1) → b_3
  141. Rotate(S', If[3 < w ≤ 4, ((w - 3) * σ), σ], D_1) → S''
  142. Rotate(V'_1, If[3 < w ≤ 4, ((w - 3) * δ), δ], D_1) → Q_1
  143. Segment(S'', Q_1) → f_4
  144. Rotate(S'', If[4 < w ≤ 5, ((w - 4) * π), π], E_1) → S'''
  145. Rotate(Q_1, If[4 < w ≤ 5, ((w - 4) * π), π], E_1) → R_1
  146. Segment(S''', R_1) → g_4
  147. Dilate(N, If[5 < w ≤ 6, 6 - w, 0], F_1) → N'
  148. Vector(N, N') → u_2
  149. Translate(N, u_2) → N'_1
  150. Translate(U, u_2) → U'
  151. Segment(N'_1, U') → h_4
  152. Line(N, r_3) → i_4
  153. Intersect(i_4, b_1) → S_1
  154. Angle(S_1, N, U) → τ
  155. Rotate(N'_1, If[6 < w ≤ 7, ((-(w - 6)) * τ), (-τ)], F_1) → T_1
  156. Rotate(U', If[6 < w ≤ 7, ((-(w - 6)) * τ), (-τ)], F_1) → U''
  157. Segment(T_1, U'') → j_4
  158. Rotate(T_1, If[7 < w ≤ 8, ((-(w - 7)) * π), (-π)], H_1) → U_1
  159. Rotate(U'', If[7 < w ≤ 8, ((-(w - 7)) * π), (-π)], H_1) → U'''
  160. Segment(U_1, U''') → k_4
  161. Dilate(K, If[8 < w ≤ 9, 9 - w, 0], I_1) → K'_2
  162. Vector(K, K'_2) → v_2
  163. Translate(J, v_2) → J'_1
  164. Translate(K, v_2) → K'_3
  165. Segment(J'_1, K'_3) → l_4
  166. Rotate(J'_1, If[9 < w ≤ 10, ((-(w - 9)) * π / 2), ((-π)) / 2], I_1) → V_1
  167. Rotate(K'_3, If[9 < w ≤ 10, ((-(w - 9)) * π / 2), ((-π)) / 2], I_1) → W_1
  168. Segment(V_1, W_1) → m_4
  169. Midpoint(B_1, E_1) → Z_1
  170. Midpoint(E_1, H_1) → A_2
  171. Midpoint(H_1, K_1) → B_2
  172. Rotate(E_1, If[10 < w ≤ 11, ((w - 10) * π), π], Z_1) → C_2
  173. CircleArc(Z_1, E_1, C_2) → d_4
  174. Rotate(H_1, If[11 < w ≤ 12, ((w - 11) * π), π], A_2) → D_2
  175. CircleArc(A_2, H_1, D_2) → e_4
  176. Rotate(K_1, If[12 < w ≤ 13, ((w - 12) * π), π], B_2) → E_2
  177. CircleArc(B_2, K_1, E_2) → p_4
  178. Dilate(L_1, If[13 < w ≤ 14, 14 - w, 0], D_1) → F_2
  179. Dilate(M_1, If[13 < w ≤ 14, 14 - w, 0], F_1) → G_2
  180. Dilate(N_1, If[13 < w ≤ 14, 14 - w, 0], I_1) → H_2
  181. Segment(L_1, F_2) → n_4
  182. Segment(M_1, G_2) → q_4
  183. Segment(N_1, H_2) → r_4
  184. Dilate(D, If[14 < w ≤ 15, 15 - w, 0], Z) → D'
  185. Dilate(Z, If[15 < w ≤ 16, 16 - w, 0], A_1) → Z'
  186. Dilate(A_1, If[16 < w ≤ 17, 17 - w, 0], W) → I_2
  187. Segment(D, D') → s_4
  188. Segment(Z, Z') → t_4
  189. Segment(A_1, I_2) → a_4
  190. Angle(D, W, B) → υ
  191. Dilate(L_1, If[17 < w ≤ 18, 18 - w, 0], D) → J_2
  192. Dilate(M_1, If[18 < w ≤ 19, 19 - w, 0], Z) → K_2
  193. Dilate(N_1, If[19 < w ≤ 20, 20 - w, 0], A_1) → L_2
  194. Vector(L_1, J_2) → w_2
  195. Translate(L_1, w_2) → O_2
  196. Translate(F_2, w_2) → P_2
  197. Segment(O_2, P_2) → b_4
  198. Vector(M_1, K_2) → u_3
  199. Translate(M_1, u_3) → M_2
  200. Translate(G_2, u_3) → N_2
  201. Segment(M_2, N_2) → f_5
  202. Vector(N_1, L_2) → v_3
  203. Translate(N_1, v_3) → Q_2
  204. Translate(H_2, v_3) → R_2
  205. Segment(Q_2, R_2) → g_5