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小矮人策略
几何画板及绘图内容加载中，请稍等……
2023-03-22 02:55
测试改名0函数解析几何最值优化几何作图
所属专题 Realidades de GeoGebra
该范例展示了如何利用几何作图工具解决优化问题。核心数学概念包括三角形、中线、角平分线、双曲线等。通过使用Midpoint、Line、AngularBisector等GeoGebra命令，可以构造出优化问题的几何模型。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Midpoint(C, B) → M1
  2. Line(A, M1) → mediana1
  3. AngularBisector(C, A, B) → bisectrizV1
  4. Mirror(mediana1, bisectrizV1) → simediana1
  5. OrthogonalLine(A, bisectrizV1) → j
  6. AngularBisector(A, C, B) → bisectrizV2
  7. Intersect(bisectrizV1, bisectrizV2) → I
  8. OrthogonalLine(C, bisectrizV2) → i
  9. Intersect(i, j) → I3
  10. Intersect(bisectrizV1, i) → I1
  11. Polygon(A, C, B) → isleta, v3, v1, v2
  12. LineBisector(v2) → mediatriz1
  13. LineBisector(v1) → mediatriz2
  14. Intersect(mediatriz2, mediatriz1) → O
  15. Midpoint(A, B) → M2
  16. Line(C, M2) → mediana2
  17. Mirror(mediana2, bisectrizV2) → simediana2
  18. Intersect(simediana1, simediana2) → Lemoine
  19. Conic(Lemoine, I, I3, I1, O) → h1
  20. Focus(h1) → Foco2, Foco1
  21. FirstAxisLength(h1) → semieje
  22. Hyperbola(Foco1, Foco2, semieje) → h
  23. Segment(O, B) → R
  24. OrthogonalLine(I, v1) → ortoI
  25. Intersect(v1, ortoI) → Ibase
  26. Segment(I, Ibase) → r
  27. Axes(h1) → eje2, eje1
  28. Slope(eje2) → m
  29. Center(h1) → X110
  30. OrthogonalLine(G, v3) → g3
  31. Intersect(v3, g3) → G3
  32. Vector(G, G3) → u3
  33. Ray(P, R312) → s312
  34. Intersect(v3, s312) → S312
  35. Circle(P, d) → circuloP
  36. Intersect(circuloP, v3, 1) → P31
  37. Intersect(circuloP, v3, 2) → P32
  38. Midpoint(P31, P32) → PM3
  39. Ray(P, PM3) → sM3
  40. Intersect(circuloP, sM3) → PCM3,
  41. CircumcircleSector(P31, PCM3, P32) → sector2cE
  42. Polygon(P, P31, P32) → tri2c, z2c2, z2c3, z2c1
  43. Area(A, C, B) → areai
  44. Intersect(circuloP, v1, 1) → P11
  45. If(P11 ≟ P11, true, false) → p11
  46. Intersect(circuloP, v1, 2) → P12
  47. If(P12 ≟ P12, true, false) → p12
  48. Midpoint(P11, P12) → PM1
  49. Ray(P, PM1) → sM1
  50. Intersect(circuloP, sM1) → PCM1,
  51. CircumcircleSector(P11, PCM1, P12) → sector2aE
  52. Polygon(P, P11, P12) → tri2a, z2a2, z2a3, z2a1
  53. OrthogonalLine(G, v1) → g1
  54. Intersect(v1, g1) → G1
  55. Vector(G, G1) → u1
  56. Ray(P, R112) → s112
  57. Intersect(circuloP, s112) → P112, Cir1
  58. CircumcircleSector(P11, P112, P12) → sector2a
  59. Intersect(v1, s112) → S112
  60. If(S112 ≟ S112, sector2a - tri2a, sector2a + tri2a) → area2a
  61. Intersect(circuloP, v2, 1) → P22
  62. If(P22 ≟ P22, true, false) → p22
  63. Intersect(circuloP, v2, 2) → P21
  64. If(P21 ≟ P21, true, false) → p21
  65. Midpoint(P21, P22) → PM2
  66. Ray(P, PM2) → sM2
  67. Intersect(circuloP, sM2) → PCM2, Cir2
  68. CircumcircleSector(P21, PCM2, P22) → sector2bE
  69. Polygon(P, P21, P22) → tri2b, z2b2, z2b3, z2b1
  70. OrthogonalLine(G, v2) → g2
  71. Intersect(v2, g2) → G2
  72. Vector(G, G2) → u2
  73. Ray(P, R212) → s212
  74. Intersect(circuloP, s212) → P212, Cir3
  75. CircumcircleSector(P21, P212, P22) → sector2b
  76. Intersect(v2, s212) → S212
  77. If(S212 ≟ S212, sector2b - tri2b, sector2b + tri2b) → area2b
  78. If(P32 ≟ P32, true, false) → p32
  79. If(P31 ≟ P31, true, false) → p31
  80. If(p11 ∧ p12 ∧ p21 ∧ p22 ∧ p31 ∧ p32, true, false) → pos2E
  81. Intersect(circuloP, s312) → P312, Cir4
  82. CircumcircleSector(P31, P312, P32) → sector2c
  83. If(S312 ≟ S312, sector2c - tri2c, sector2c + tri2c) → area2c
  84. If(pos2E, aread - area2aE - area2bE - area2cE, area2) → area2E
  85. Segment(P, A) → dV1
  86. Segment(P, C) → dV2
  87. Midpoint(A, C) → M3
  88. Ray(P, M3) → fuera3
  89. Segment(P, B) → dV3
  90. If(dV1 ≤ d ∧ dV2 ≤ d ∧ dV3 ≤ d, true, false) → pos5
  91. If(pos5, areai, 0) → area5
  92. If(area5 < areai, area5, areai) → area5T
  93. Intersect(v2, fuera3) → Corte32
  94. Intersect(v1, fuera3) → Corte31
  95. If(p12 ∧ (¬p11), P12, P11) → P1
  96. If(P1 ≟ P1, true, false) → p1
  97. If(Distance[P21, P1] > Distance[P22, P1], P22, P21) → P21'
  98. Polygon(P, P1, P21') → tri621, ztri621c, ztri621b, ztri621a
  99. If(Distance[P21, P1] > Distance[P22, P1], P21, P22) → P22'
  100. If(p22 ∧ (¬p21), P22, P21) → P2
  101. Midpoint(P2, P1) → V3b
  102. Ray(P, V3b) → sV3
  103. Intersect(circuloP, sV3, 1) → V3c
  104. CircumcircleSector(P2, V3c, P1) → sector1c
  105. Polygon(B, P1, P2) → tri1c, z1c2, z1c3, z1c1
  106. Polygon(P, P1, P2) → tri01c, z01c2, z01c3, z01c1
  107. If(Distance[V3b, B] < dV3 ∧ Distance[A, P] < d, aread - sector1c + tri1c + tri01c, tri1c + sector1c - tri01c) → area1c
  108. Polygon(C, A, P2, P1) → cuadri3, zcuadri3a, zcuadri3b, zcuadri3c, zcuadri3d
  109. If(Distance[P11, P2] > Distance[P12, P2], P12, P11) → P11'
  110. Polygon(P, P2, P11') → tri611, ztri611b, ztri611a, ztri611c
  111. If(Distance[P11, P2] > Distance[P12, P2], P11, P12) → P12'
  112. If(P2 ≟ P2, true, false) → p2
  113. If(Distance[P31, P2] > Distance[P32, P2], P32, P31) → P31'
  114. Polygon(P, P2, P31') → tri632, ztri632a, ztri632c, ztri632b
  115. If(Distance[P31, P2] > Distance[P32, P2], P31, P32) → P32'
  116. Polygon(B, P1, P32', P31', P2) → penta3, zpenta3e, zpenta3d, zpenta3c, zpenta3b, zpenta3a
  117. Polygon(P, P1, P32') → tri631, ztri631b, ztri631c, ztri631a
  118. If(p31 ∧ p32 ∧ p1 ∧ p2 ∧ ((¬p11) ∨ (¬p12)) ∧ ((¬p21) ∨ (¬p22)), true, false) → pos6c
  119. If(p11 ∧ p12 ∧ p21 ∧ p22 ∨ p11 ∧ p12 ∧ p31 ∧ p32 ∨ p21 ∧ p22 ∧ p31 ∧ p32, true, false) → pos2
  120. If(p32 ∧ (¬p31), P32, P31) → P3
  121. Polygon(C, P1, P21', P22', P3) → penta2, zpenta2c, zpenta2b, zpenta2a, zpenta2e, zpenta2d
  122. Polygon(P, P3, P22') → tri622, ztri622c, ztri622a, ztri622b
  123. Midpoint(P1, P3) → V2b
  124. Ray(P, V2b) → sV2
  125. Intersect(circuloP, sV2, 1) → V2c
  126. CircumcircleSector(P1, V2c, P3) → sector1b
  127. Polygon(C, P1, P3) → tri1b, z1b2, z1b3, z1b1
  128. Polygon(P, P1, P3) → tri01b, z01b2, z01b3, z01b1
  129. If(Distance[V2b, C] < dV2 ∧ Distance[A, P] < d, aread - sector1b + tri1b + tri01b, tri1b + sector1b - tri01b) → area1b
  130. Polygon(A, B, P1, P3) → cuadri2, zcuadri2a, zcuadri2b, zcuadri2c, zcuadri2d
  131. Polygon(A, P2, P11', P12', P3) → penta1, zpenta1a, zpenta1b, zpenta1c, zpenta1d, zpenta1e
  132. Polygon(P, P3, P12') → tri612, ztri612c, ztri612b, ztri612a
  133. Midpoint(P2, P3) → V1b
  134. Ray(P, V1b) → sV1
  135. Intersect(circuloP, sV1, 1) → V1c
  136. CircumcircleSector(P2, V1c, P3) → sector1a
  137. Polygon(P, P2, P3) → tri01a, z01a2, z01a3, z01a1
  138. Polygon(A, P2, P3) → tri1a, z1a2, tri1a3, z1a1
  139. If(Distance[V1b, A] < dV1 ∧ Distance[B, P] < d, aread - sector1a + tri1a + tri01a, tri1a + sector1a - tri01a) → area1a
  140. If(area1a ≟ area1a, area1a, If[area1b ≟ area1b, area1b, area1c]) → area1
  141. If(area1 < areai, area1, areai) → area1T
  142. Polygon(C, B, P2, P3) → cuadri1, zcuadri1a, zcuadri1b, zcuadri1c, zcuadri1d
  143. If(area4 < areai, area4, areai) → area4T
  144. If(P3 ≟ P3, true, false) → p3
  145. If(p21 ∧ p22 ∧ p1 ∧ p3 ∧ ((¬p11) ∨ (¬p12)) ∧ ((¬p31) ∨ (¬p32)), true, false) → pos6b
  146. If((¬p3) ∧ p1 ∧ ((¬p11) ∨ (¬p12)) ∧ p2 ∧ ((¬p21) ∨ (¬p22)), true, false) → pos1c
  147. If((¬p2) ∧ p1 ∧ ((¬p11) ∨ (¬p12)) ∧ p3 ∧ ((¬p31) ∨ (¬p32)), true, false) → pos1b
  148. If((¬p1) ∧ p2 ∧ ((¬p21) ∨ (¬p22)) ∧ p3 ∧ ((¬p31) ∨ (¬p32)), true, false) → pos1a
  149. If(pos1a ∨ pos1b ∨ pos1c, true, false) → pos1
  150. If(pos1 ∧ dV2 ≤ d ∧ dV3 ≤ d, true, false) → pos4c
  151. If(pos1 ∧ dV1 ≤ d ∧ dV3 ≤ d, true, false) → pos4b
  152. If(pos1 ∧ dV1 ≤ d ∧ dV2 ≤ d, true, false) → pos4a
  153. If(pos4a ∨ pos4b ∨ pos4c, true, false) → pos4
  154. If(p1 ∧ (¬p2) ∧ (¬p3) ∨ (¬p1) ∧ p2 ∧ (¬p3) ∨ (¬p1) ∧ (¬p2) ∧ p3, true, false) → pos3
  155. If(p11 ∧ p12 ∧ p2 ∧ p3 ∧ ((¬p21) ∨ (¬p22)) ∧ ((¬p31) ∨ (¬p32)), true, false) → pos6a
  156. If(pos6a ∨ pos6b ∨ pos6c, true, false) → pos6
  157. CircumcircleSector(P2, P312, P1) → sector6c
  158. If(pos6c, penta3 + sector6c - sector2c - tri631 - tri632, 0) → area6c
  159. CircumcircleSector(P1, P212, P3) → sector6b
  160. If(pos6b, penta2 + sector6b - sector2b - tri621 - tri622, 0) → area6b
  161. CircumcircleSector(P2, P112, P3) → sector6a
  162. If(pos6a, penta1 + sector6a - sector2a - tri611 - tri612, 0) → area6a
  163. If(area2E < areai, area2E, areai) → area2T
  164. If(area6 < areai, area6, areai) → area6T
  165. Ray(P, M2) → fuera2
  166. Intersect(v1, fuera2) → Corte21
  167. Intersect(v3, fuera2) → Corte23
  168. Ray(P, M1) → fuera1
  169. Intersect(v3, fuera1) → Corte13
  170. Intersect(v2, fuera1) → Corte12
  171. Line(B, Lemoine) → simediana3
  172. Angle(B, A, C) → α
  173. Angle(A, C, B) → β
  174. Angle(C, B, A) → γ
  175. If(δ ≟ α, M1, If[δ ≟ β, M2, M3]) → M
  176. Line(M, Lemoine) → e
  177. If(sector2c > aread / 2, sector2c + tri2c, sector2c) → sector2C
  178. If(areaT > 0 ∨ Corte12 ≟ Corte12 ∨ Corte13 ≟ Corte13 ∨ Corte21 ≟ Corte21 ∨ Corte23 ≟ Corte23 ∨ Corte31 ≟ Corte31 ∨ Corte32 ≟ Corte32, areaT, aread) → area
  179. Angle(isleta) → ε, ζ, η
  180. Line(B, M3) → mediana3
  181. Intersect(bisectrizV2, j) → I2
  182. Circle(O, R) → circunscrita
  183. Line(G, O) → euler
  184. Mirror(euler, v2) → euler2
  185. Mirror(euler, v1) → euler1
  186. Intersect(h1, e, 2) → H
  187. Intersect(h1, euler, 1) → J
  188. Segment(J, I) → a
  189. Intersect(euler, euler1) → EE
  190. Segment(O, B) → b
  191. Circle(I, Ibase) → f
  192. Line(O, I) → c
  193. Circle(O, P59, I) → g

AI 绘图提示语参考

请绘制一个由三角形、椭圆和圆组成的几何图形。图形中包含一个三角形，其重心、角平分线和垂线被标记。三角形与椭圆通过交点相连，椭圆的焦点和轴被标出。圆与椭圆相交，形成一个扇形区域。整个图形展示了三角形与椭圆之间的优化关系，适合数学教育使用。
以上提示语为根据原始绘图命令整理而来，仅供参考。