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课堂旋转器：参数曲线与几何变换的探索

课堂旋转器：参数曲线与几何变换的探索
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2020-10-02 23:35
立体几何概率统计参数方程
本范例通过参数方程和旋转操作，展示锥体与圆锥的几何关系。核心数学概念包括参数曲线、旋转变换和几何作图。作图要点涉及使用GeoGebra命令如Rotate、CircleSector和Parametric Curves来构造图形。适合高中生或数学爱好者用于理解几何变换与参数方程的应用。

GeoGebra 命令及参数

  1. If(B2 > 0, B2, 0) → D2
  2. If(B3 > 0, B3, 0) → D3
  3. If(B4 > 0, B4, 0) → D4
  4. If(B5 > 0, B5, 0) → D5
  5. If(B6 > 0, B6, 0) → D6
  6. If(B7 > 0, B7, 0) → D7
  7. If(B8 > 0, B8, 0) → D8
  8. If(B9 > 0, B9, 0) → D9
  9. If(B10 > 0, B10, 0) → D10
  10. If(B11 > 0, B11, 0) → D11
  11. If(B12 > 0, B12, 0) → D12
  12. If(B13 > 0, B13, 0) → D13
  13. If(B14 > 0, B14, 0) → D14
  14. If(B15 > 0, B15, 0) → D15
  15. If(B16 > 0, B16, 0) → D16
  16. If(B17 > 0, B17, 0) → D17
  17. If(B18 > 0, B18, 0) → D18
  18. If(B19 > 0, B19, 0) → D19
  19. If(B20 > 0, B20, 0) → D20
  20. If(B21 > 0, B21, 0) → D21
  21. If(B22 > 0, B22, 0) → D22
  22. If(B23 > 0, B23, 0) → D23
  23. If(B24 > 0, B24, 0) → D24
  24. If(B25 > 0, B25, 0) → D25
  25. If(B26 > 0, B26, 0) → D26
  26. If(B27 > 0, B27, 0) → D27
  27. If(B28 > 0, B28, 0) → D28
  28. If(B29 > 0, B29, 0) → D29
  29. If(B30 > 0, B30, 0) → D30
  30. If(B31 > 0, B31, 0) → D31
  31. If(B32 > 0, B32, 0) → D32
  32. If(B33 > 0, B33, 0) → D33
  33. If(B34 > 0, B34, 0) → D34
  34. If(B35 > 0, B35, 0) → D35
  35. Sum(D2:D35) → D37
  36. Sum(E2:E35) → E37
  37. Sum(F2:F35) → F37
  38. Point(eq1) → driver
  39. Sum(F$2:F2) → G2
  40. Sum(F$2:F3) → G3
  41. Sum(F$2:F4) → G4
  42. Sum(F$2:F5) → G5
  43. Sum(F$2:F6) → G6
  44. Sum(F$2:F7) → G7
  45. Sum(F$2:F8) → G8
  46. Sum(F$2:F9) → G9
  47. Sum(F$2:F10) → G10
  48. Sum(F$2:F11) → G11
  49. Sum(F$2:F12) → G12
  50. Sum(F$2:F13) → G13
  51. Sum(F$2:F14) → G14
  52. Sum(F$2:F15) → G15
  53. Sum(F$2:F16) → G16
  54. Sum(F$2:F17) → G17
  55. Sum(F$2:F18) → G18
  56. Sum(F$2:F19) → G19
  57. Sum(F$2:F20) → G20
  58. Sum(F$2:F21) → G21
  59. Sum(F$2:F22) → G22
  60. Sum(F$2:F23) → G23
  61. Sum(F$2:F24) → G24
  62. Sum(F$2:F25) → G25
  63. Sum(F$2:F26) → G26
  64. Sum(F$2:F27) → G27
  65. Sum(F$2:F28) → G28
  66. Sum(F$2:F29) → G29
  67. Sum(F$2:F30) → G30
  68. Sum(F$2:F31) → G31
  69. Sum(F$2:F32) → G32
  70. Sum(F$2:F33) → G33
  71. Sum(F$2:F34) → G34
  72. Sum(F$2:F35) → G35
  73. Rotate(driver, G2, (0, 0)) → H2
  74. Rotate(driver, G3, (0, 0)) → H3
  75. Rotate(driver, G4, (0, 0)) → H4
  76. Rotate(driver, G5, (0, 0)) → H5
  77. Rotate(driver, G6, (0, 0)) → H6
  78. Rotate(driver, G7, (0, 0)) → H7
  79. Rotate(driver, G8, (0, 0)) → H8
  80. Rotate(driver, G9, (0, 0)) → H9
  81. Rotate(driver, G10, (0, 0)) → H10
  82. Rotate(driver, G11, (0, 0)) → H11
  83. Rotate(driver, G12, (0, 0)) → H12
  84. Rotate(driver, G13, (0, 0)) → H13
  85. Rotate(driver, G14, (0, 0)) → H14
  86. Rotate(driver, G15, (0, 0)) → H15
  87. Rotate(driver, G16, (0, 0)) → H16
  88. Rotate(driver, G17, (0, 0)) → H17
  89. Rotate(driver, G18, (0, 0)) → H18
  90. Rotate(driver, G19, (0, 0)) → H19
  91. Rotate(driver, G20, (0, 0)) → H20
  92. Rotate(driver, G21, (0, 0)) → H21
  93. Rotate(driver, G22, (0, 0)) → H22
  94. Rotate(driver, G23, (0, 0)) → H23
  95. Rotate(driver, G24, (0, 0)) → H24
  96. Rotate(driver, G25, (0, 0)) → H25
  97. Rotate(driver, G26, (0, 0)) → H26
  98. Rotate(driver, G27, (0, 0)) → H27
  99. Rotate(driver, G28, (0, 0)) → H28
  100. Rotate(driver, G29, (0, 0)) → H29
  101. Rotate(driver, G30, (0, 0)) → H30
  102. Rotate(driver, G31, (0, 0)) → H31
  103. Rotate(driver, G32, (0, 0)) → H32
  104. Rotate(driver, G33, (0, 0)) → H33
  105. Rotate(driver, G34, (0, 0)) → H34
  106. Rotate(driver, G35, (0, 0)) → H35
  107. CircleSector((0, 0), driver, H2) → I2
  108. CircleSector((0, 0), H2, H3) → I3
  109. CircleSector((0, 0), H3, H4) → I4
  110. CircleSector((0, 0), H4, H5) → I5
  111. CircleSector((0, 0), H5, H6) → I6
  112. CircleSector((0, 0), H6, H7) → I7
  113. CircleSector((0, 0), H7, H8) → I8
  114. CircleSector((0, 0), H8, H9) → I9
  115. CircleSector((0, 0), H9, H10) → I10
  116. CircleSector((0, 0), H10, H11) → I11
  117. CircleSector((0, 0), H11, H12) → I12
  118. CircleSector((0, 0), H12, H13) → I13
  119. CircleSector((0, 0), H13, H14) → I14
  120. CircleSector((0, 0), H14, H15) → I15
  121. CircleSector((0, 0), H15, H16) → I16
  122. CircleSector((0, 0), H16, H17) → I17
  123. CircleSector((0, 0), H17, H18) → I18
  124. CircleSector((0, 0), H18, H19) → I19
  125. CircleSector((0, 0), H19, H20) → I20
  126. CircleSector((0, 0), H20, H21) → I21
  127. CircleSector((0, 0), H21, H22) → I22
  128. CircleSector((0, 0), H22, H23) → I23
  129. CircleSector((0, 0), H23, H24) → I24
  130. CircleSector((0, 0), H24, H25) → I25
  131. CircleSector((0, 0), H25, H26) → I26
  132. CircleSector((0, 0), H26, H27) → I27
  133. CircleSector((0, 0), H27, H28) → I28
  134. CircleSector((0, 0), H28, H29) → I29
  135. CircleSector((0, 0), H29, H30) → I30
  136. CircleSector((0, 0), H30, H31) → I31
  137. CircleSector((0, 0), H31, H32) → I32
  138. CircleSector((0, 0), H32, H33) → I33
  139. CircleSector((0, 0), H33, H34) → I34
  140. CircleSector((0, 0), H34, H35) → I35
  141. Segment((0, 0), H2) → J2
  142. Segment((0, 0), H3) → J3
  143. Segment((0, 0), H4) → J4
  144. Segment((0, 0), H5) → J5
  145. Segment((0, 0), H6) → J6
  146. Segment((0, 0), H7) → J7
  147. Segment((0, 0), H8) → J8
  148. Segment((0, 0), H9) → J9
  149. Segment((0, 0), H10) → J10
  150. Segment((0, 0), H11) → J11
  151. Segment((0, 0), H12) → J12
  152. Segment((0, 0), H13) → J13
  153. Segment((0, 0), H14) → J14
  154. Segment((0, 0), H15) → J15
  155. Segment((0, 0), H16) → J16
  156. Segment((0, 0), H17) → J17
  157. Segment((0, 0), H18) → J18
  158. Segment((0, 0), H19) → J19
  159. Segment((0, 0), H20) → J20
  160. Segment((0, 0), H21) → J21
  161. Segment((0, 0), H22) → J22
  162. Segment((0, 0), H23) → J23
  163. Segment((0, 0), H24) → J24
  164. Segment((0, 0), H25) → J25
  165. Segment((0, 0), H26) → J26
  166. Segment((0, 0), H27) → J27
  167. Segment((0, 0), H28) → J28
  168. Segment((0, 0), H29) → J29
  169. Segment((0, 0), H30) → J30
  170. Segment((0, 0), H31) → J31
  171. Segment((0, 0), H32) → J32
  172. Segment((0, 0), H33) → J33
  173. Segment((0, 0), H34) → J34
  174. Segment((0, 0), H35) → J35
  175. Rotate(H2, ((-F2)) / 2) → K2
  176. Rotate(H3, ((-F3)) / 2) → K3
  177. Rotate(H4, ((-F4)) / 2) → K4
  178. Rotate(H5, ((-F5)) / 2) → K5
  179. Rotate(H6, ((-F6)) / 2) → K6
  180. Rotate(H7, ((-F7)) / 2) → K7
  181. Rotate(H8, ((-F8)) / 2) → K8
  182. Rotate(H9, ((-F9)) / 2) → K9
  183. Rotate(H10, ((-F10)) / 2) → K10
  184. Rotate(H11, ((-F11)) / 2) → K11
  185. Rotate(H12, ((-F12)) / 2) → K12
  186. Segment((0, 0), K2) → L2
  187. Segment((0, 0), K3) → L3
  188. Segment((0, 0), K4) → L4
  189. Segment((0, 0), K5) → L5
  190. Segment((0, 0), K6) → L6
  191. Rotate(H13, ((-F13)) / 2) → K13
  192. Rotate(H14, ((-F14)) / 2) → K14
  193. Rotate(H15, ((-F15)) / 2) → K15
  194. Rotate(H16, ((-F16)) / 2) → K16
  195. Rotate(H17, ((-F17)) / 2) → K17
  196. Rotate(H18, ((-F18)) / 2) → K18
  197. Rotate(H19, ((-F19)) / 2) → K19
  198. Rotate(H20, ((-F20)) / 2) → K20
  199. Rotate(H21, ((-F21)) / 2) → K21
  200. Rotate(H22, ((-F22)) / 2) → K22
  201. Rotate(H23, ((-F23)) / 2) → K23
  202. Rotate(H24, ((-F24)) / 2) → K24
  203. Rotate(H25, ((-F25)) / 2) → K25
  204. Rotate(H26, ((-F26)) / 2) → K26
  205. Rotate(H27, ((-F27)) / 2) → K27
  206. Rotate(H28, ((-F28)) / 2) → K28
  207. Rotate(H29, ((-F29)) / 2) → K29
  208. Rotate(H30, ((-F30)) / 2) → K30
  209. Rotate(H31, ((-F31)) / 2) → K31
  210. Rotate(H32, ((-F32)) / 2) → K32
  211. Rotate(H33, ((-F33)) / 2) → K33
  212. Rotate(H34, ((-F34)) / 2) → K34
  213. Rotate(H35, ((-F35)) / 2) → K35
  214. Segment((0, 0), K7) → L7
  215. Segment((0, 0), K8) → L8
  216. Segment((0, 0), K9) → L9
  217. Segment((0, 0), K10) → L10
  218. Segment((0, 0), K11) → L11
  219. Segment((0, 0), K12) → L12
  220. Segment((0, 0), K13) → L13
  221. Segment((0, 0), K14) → L14
  222. Segment((0, 0), K15) → L15
  223. Segment((0, 0), K16) → L16
  224. Segment((0, 0), K17) → L17
  225. Segment((0, 0), K18) → L18
  226. Segment((0, 0), K19) → L19
  227. Segment((0, 0), K20) → L20
  228. Segment((0, 0), K21) → L21
  229. Segment((0, 0), K22) → L22
  230. Segment((0, 0), K23) → L23
  231. Segment((0, 0), K24) → L24
  232. Segment((0, 0), K25) → L25
  233. Segment((0, 0), K26) → L26
  234. Segment((0, 0), K27) → L27
  235. Segment((0, 0), K28) → L28
  236. Segment((0, 0), K29) → L29
  237. Segment((0, 0), K30) → L30
  238. Segment((0, 0), K31) → L31
  239. Segment((0, 0), K32) → L32
  240. Segment((0, 0), K33) → L33
  241. Segment((0, 0), K34) → L34
  242. Segment((0, 0), K35) → L35
  243. Intersect(eq2, L2) → M2,
  244. Intersect(eq2, L3) → M3,
  245. Intersect(eq2, L4) → M4,
  246. Intersect(eq2, L5) → M5,
  247. Intersect(eq2, L6) → M6,
  248. Intersect(eq2, L7) → M7,
  249. Intersect(eq2, L8) → M8,
  250. Intersect(eq2, L9) → M9,
  251. Intersect(eq2, L10) → M10,
  252. Intersect(eq2, L11) → M11,
  253. Intersect(eq2, L12) → M12,
  254. Intersect(eq2, L13) → M13,
  255. Intersect(eq2, L14) → M14,
  256. Intersect(eq2, L15) → M15,
  257. Intersect(eq2, L16) → M16,
  258. Intersect(eq2, L17) → M17,
  259. Intersect(eq2, L18) → M18,
  260. Intersect(eq2, L19) → M19,
  261. Intersect(eq2, L20) → M20,
  262. Intersect(eq2, L21) → M21,
  263. Intersect(eq2, L22) → M22,
  264. Intersect(eq2, L23) → M23,
  265. Intersect(eq2, L24) → M24,
  266. Intersect(eq2, L25) → M25,
  267. Intersect(eq2, L26) → M26,
  268. Intersect(eq2, L27) → M27,
  269. Intersect(eq2, L28) → M28,
  270. Intersect(eq2, L29) → M29,
  271. Intersect(eq2, L30) → M30,
  272. Intersect(eq2, L31) → M31,
  273. Intersect(eq2, L32) → M32,
  274. Intersect(eq2, L33) → M33,
  275. Intersect(eq2, L34) → M34,
  276. Intersect(eq2, L35) → M35,
  277. Line((0, 0), (0, 1)) → f
  278. Point(f) → choice
  279. Point(f) → B
  280. OrthogonalLine(B, f) → g
  281. Point(g) → C
  282. Mirror(C, f) → C'
  283. Polygon(C, choice, C') → t1, c', c, a
  284. Point(a) → D
  285. Mirror(D, f) → D'
  286. OrthogonalLine(D, g) → h
  287. Point(h) → E
  288. Mirror(E, f) → E'
  289. Polygon(E, D, D', E') → q1, e, d, d', e'
  290. IsInRegion(choice, I2) → N2
  291. IsInRegion(choice, I3) → N3
  292. IsInRegion(choice, I4) → N4
  293. IsInRegion(choice, I5) → N5
  294. IsInRegion(choice, I6) → N6
  295. IsInRegion(choice, I7) → N7
  296. IsInRegion(choice, I8) → N8
  297. IsInRegion(choice, I9) → N9
  298. IsInRegion(choice, I10) → N10
  299. IsInRegion(choice, I11) → N11
  300. IsInRegion(choice, I12) → N12
  301. IsInRegion(choice, I13) → N13
  302. IsInRegion(choice, I14) → N14
  303. IsInRegion(choice, I15) → N15
  304. IsInRegion(choice, I16) → N16
  305. IsInRegion(choice, I17) → N17
  306. IsInRegion(choice, I18) → N18
  307. IsInRegion(choice, I19) → N19
  308. IsInRegion(choice, I20) → N20
  309. IsInRegion(choice, I21) → N21
  310. IsInRegion(choice, I22) → N22
  311. IsInRegion(choice, I23) → N23
  312. IsInRegion(choice, I24) → N24
  313. IsInRegion(choice, I25) → N25
  314. IsInRegion(choice, I26) → N26
  315. IsInRegion(choice, I27) → N27
  316. IsInRegion(choice, I28) → N28
  317. IsInRegion(choice, I29) → N29
  318. IsInRegion(choice, I30) → N30
  319. IsInRegion(choice, I31) → N31
  320. IsInRegion(choice, I32) → N32
  321. IsInRegion(choice, I33) → N33
  322. IsInRegion(choice, I34) → N34
  323. IsInRegion(choice, I35) → N35

AI 绘图提示语参考

绘制一个概率转盘教学演示，包含参数曲线绘制的锥形螺旋面和圆形扇区。创建若干扇形区域表示不同概率区间，通过参数方程定义驱动点，使其沿圆形路径旋转演示。展示圆锥与圆的参数化关系，体现几何变换过程，适合高中数学课堂概率与几何教学使用。
以上提示语为根据原始绘图命令整理而来，仅供参考。