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可调节角度与倾斜的线段

可调节角度与倾斜的线段
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2020-03-08 01:31
角变换几何作图
该范例演示了如何通过旋转和倾斜来调整线段的角度。涉及的核心数学概念包括角度、旋转和平移变换。通过使用GeoGebra命令如Rotate、Ray、Intersect等，可以动态地改变线段的方向和位置。适合初中及以上学生学习几何变换和角度相关问题。

GeoGebra 命令及参数

  1. Line(P0, A) → rt0
  2. Rotate(A, θ, P0) → A1
  3. Line(P0, A1) → rt1
  4. Rotate(B1, α, P1) → C1
  5. Ray(P1, C1) → sr1
  6. Intersect(rt1, sr1) → F1
  7. Circle(P0, F1) → c1
  8. If(x(F1) < x(P0), 1, 2) → SnDx1
  9. Intersect(c1, rt0, SnDx1) → P2
  10. Rotate(B2, α + γ, P2) → C2
  11. Ray(P2, C2) → sr2
  12. Intersect(rt1, sr2) → F2
  13. Rotate(F2, θ, P0) → W2
  14. If(x(F2) < x(P0), 1, 2) → SnDx2
  15. Circle(P0, F2) → c2
  16. Intersect(c2, rt0, SnDx2) → P3
  17. Rotate(B3, α + (2 * γ), P3) → C3
  18. Ray(P3, C3) → sr3
  19. Intersect(rt1, sr3) → F3
  20. Rotate(F3, (2 * θ), P0) → W3
  21. Circle(P0, F3) → c3
  22. If(x(F3) < x(P0), 1, 2) → SnDx3
  23. Intersect(c3, rt0, SnDx3) → P4
  24. Rotate(B4, α + (3 * γ), P4) → C4
  25. Ray(P4, C4) → sr4
  26. Intersect(rt1, sr4) → F4
  27. Rotate(F4, (3 * θ), P0) → W4
  28. If(x(F4) < x(P0), 1, 2) → SnDx4
  29. Circle(P0, F4) → c4
  30. Intersect(c4, rt0, SnDx4) → P5
  31. Rotate(B5, α + (4 * γ), P5) → C5
  32. Ray(P5, C5) → sr5
  33. Intersect(rt1, sr5) → F5
  34. Rotate(F5, (4 * θ), P0) → W5
  35. Circle(P0, F5) → c5
  36. If(x(F5) < x(P0), 1, 2) → SnDx5
  37. Intersect(c5, rt0, SnDx5) → P6
  38. Rotate(B6, α + (5 * γ), P6) → C6
  39. Ray(P6, C6) → sr6
  40. Intersect(rt1, sr6) → F6
  41. Rotate(F6, (5 * θ), P0) → W6
  42. If(x(F6) < x(P0), 1, 2) → SnDx6
  43. Circle(P0, F6) → c6
  44. Intersect(c6, rt0, SnDx6) → P7
  45. Rotate(B7, α + (6 * γ), P7) → C7
  46. Ray(P7, C7) → sr7
  47. Intersect(rt1, sr7) → F7
  48. Rotate(F7, (6 * θ), P0) → W7
  49. Circle(P0, F7) → c7
  50. If(x(F7) < x(P0), 1, 2) → SnDx7
  51. Intersect(c7, rt0, SnDx7) → P8
  52. Rotate(B8, α + (7 * γ), P8) → C8
  53. Ray(P8, C8) → sr8
  54. Intersect(rt1, sr8) → F8
  55. Rotate(F8, (7 * θ), P0) → W8
  56. If(x(F8) < x(P0), 1, 2) → SnDx8
  57. Circle(P0, F8) → c8
  58. Intersect(c8, rt0, SnDx8) → P9
  59. Rotate(B9, α + (8 * γ), P9) → C9
  60. Ray(P9, C9) → sr9
  61. Intersect(rt1, sr9) → F9
  62. Rotate(F9, (8 * θ), P0) → W9
  63. Circle(P0, F9) → c9
  64. If(x(F9) < x(P0), 1, 2) → SnDx9
  65. Intersect(c9, rt0, SnDx9) → P10
  66. Rotate(B10, α + (9 * γ), P10) → C10
  67. Ray(P10, C10) → sr10
  68. Intersect(rt1, sr10) → F10
  69. Rotate(F10, (9 * θ), P0) → W10
  70. If(x(F10) < x(P0), 1, 2) → SnDx10
  71. Circle(P0, F10) → c10
  72. Intersect(c10, rt0, SnDx10) → P11
  73. Rotate(B11, α + (10 * γ), P11) → C11
  74. Ray(P11, C11) → sr11
  75. Intersect(rt1, sr11) → F11
  76. Rotate(F11, (10 * θ), P0) → W11
  77. Circle(P0, F11) → c11
  78. If(x(F11) < x(P0), 1, 2) → SnDx11
  79. Intersect(c11, rt0, SnDx11) → P12
  80. Rotate(B12, α + (11 * γ), P12) → C12
  81. Ray(P12, C12) → sr12
  82. Intersect(rt1, sr12) → F12
  83. Rotate(F12, (11 * θ), P0) → W12
  84. If(x(F12) < x(P0), 1, 2) → SnDx12
  85. Circle(P0, F12) → c12
  86. Intersect(c12, rt0, SnDx12) → P13
  87. Rotate(B13, α + (12 * γ), P13) → C13
  88. Ray(P13, C13) → sr13
  89. Intersect(rt1, sr13) → F13
  90. Rotate(F13, (12 * θ), P0) → W13
  91. Circle(P0, F13) → c13
  92. If(x(F13) < x(P0), 1, 2) → SnDx13
  93. Intersect(c13, rt0, SnDx13) → P14
  94. Rotate(B14, α + (13 * γ), P14) → C14
  95. Ray(P14, C14) → sr14
  96. Intersect(rt1, sr14) → F14
  97. Rotate(F14, (13 * θ), P0) → W14
  98. If(x(F14) < x(P0), 1, 2) → SnDx14
  99. Circle(P0, F14) → c14
  100. Intersect(c14, rt0, SnDx14) → P15
  101. Rotate(B15, α + (14 * γ), P15) → C15
  102. Ray(P15, C15) → sr15
  103. Intersect(rt1, sr15) → F15
  104. Rotate(F15, (14 * θ), P0) → W15
  105. Circle(P0, F15) → c15
  106. If(x(F15) < x(P0), 1, 2) → SnDx15
  107. Intersect(c15, rt0, SnDx15) → P16
  108. Rotate(B16, α + (15 * γ), P16) → C16
  109. Ray(P16, C16) → sr16
  110. Intersect(rt1, sr16) → F16
  111. Rotate(F16, (15 * θ), P0) → W16
  112. If(x(F16) < x(P0), 1, 2) → SnDx16
  113. Circle(P0, F16) → c16
  114. Intersect(c16, rt0, SnDx16) → P17
  115. Rotate(B17, α + (16 * γ), P17) → C17
  116. Ray(P17, C17) → sr17
  117. Intersect(rt1, sr17) → F17
  118. Rotate(F17, (16 * θ), P0) → W17
  119. Circle(P0, F17) → c17
  120. If(x(F17) < x(P0), 1, 2) → SnDx17
  121. Intersect(c17, rt0, SnDx17) → P18
  122. Rotate(B18, α + (17 * γ), P18) → C18
  123. Ray(P18, C18) → sr18
  124. Intersect(rt1, sr18) → F18
  125. Rotate(F18, (17 * θ), P0) → W18
  126. If(x(F18) < x(P0), 1, 2) → SnDx18
  127. Circle(P0, F18) → c18
  128. Intersect(c18, rt0, SnDx18) → P19
  129. Rotate(B19, α + (18 * γ), P19) → C19
  130. Ray(P19, C19) → sr19
  131. Intersect(rt1, sr19) → F19
  132. Rotate(F19, (18 * θ), P0) → W19
  133. Circle(P0, F19) → c19
  134. If(x(F19) < x(P0), 1, 2) → SnDx19
  135. Intersect(c19, rt0, SnDx19) → P20
  136. Rotate(B20, α + (19 * γ), P20) → C20
  137. Ray(P20, C20) → sr20
  138. Intersect(rt1, sr20) → F20
  139. Rotate(F20, (19 * θ), P0) → W20
  140. If(x(F20) < x(P0), 1, 2) → SnDx20
  141. Circle(P0, F20) → c20
  142. Intersect(c20, rt0, SnDx20) → P21
  143. Rotate(B21, α + (20 * γ), P21) → C21
  144. Ray(P21, C21) → sr21
  145. Intersect(rt1, sr21) → F21
  146. Rotate(F21, (20 * θ), P0) → W21
  147. Circle(P0, F21) → c21
  148. If(x(F21) < x(P0), 1, 2) → SnDx21
  149. Intersect(c21, rt0, SnDx21) → P22
  150. Rotate(B22, α + (21 * γ), P22) → C22
  151. Ray(P22, C22) → sr22
  152. Intersect(rt1, sr22) → F22
  153. Rotate(F22, (21 * θ), P0) → W22
  154. If(x(F22) < x(P0), 1, 2) → SnDx22
  155. Circle(P0, F22) → c22
  156. Intersect(c22, rt0, SnDx22) → P23
  157. Rotate(B23, α + (22 * γ), P23) → C23
  158. Ray(P23, C23) → sr23
  159. Intersect(rt1, sr23) → F23
  160. Rotate(F23, (22 * θ), P0) → W23
  161. Circle(P0, F23) → c23
  162. If(x(F23) < x(P0), 1, 2) → SnDx23
  163. Intersect(c23, rt0, SnDx23) → P24
  164. Rotate(B24, α + (23 * γ), P24) → C24
  165. Ray(P24, C24) → sr24
  166. Intersect(rt1, sr24) → F24
  167. Rotate(F24, (23 * θ), P0) → W24
  168. If(x(F24) < x(P0), 1, 2) → SnDx24
  169. Circle(P0, F24) → c24
  170. Intersect(c24, rt0, SnDx24) → P25
  171. Rotate(B25, α + (24 * γ), P25) → C25
  172. Ray(P25, C25) → sr25
  173. Intersect(rt1, sr25) → F25
  174. Rotate(F25, (24 * θ), P0) → W25
  175. Circle(P0, F25) → c25
  176. If(x(F25) < x(P0), 1, 2) → SnDx25
  177. Intersect(c25, rt0, SnDx25) → P26
  178. Rotate(B26, α + (25 * γ), P26) → C26
  179. Ray(P26, C26) → sr26
  180. Intersect(rt1, sr26) → F26
  181. Rotate(F26, (25 * θ), P0) → W26
  182. If(x(F26) < x(P0), 1, 2) → SnDx26
  183. Circle(P0, F26) → c26
  184. Intersect(c26, rt0, SnDx26) → P27
  185. Rotate(B27, α + (26 * γ), P27) → C27
  186. Ray(P27, C27) → sr27
  187. Intersect(rt1, sr27) → F27
  188. Rotate(F27, (26 * θ), P0) → W27
  189. Circle(P0, F27) → c27
  190. If(x(F27) < x(P0), 1, 2) → SnDx27
  191. Intersect(c27, rt0, SnDx27) → P28
  192. Rotate(B28, α + (27 * γ), P28) → C28
  193. Ray(P28, C28) → sr28
  194. Intersect(rt1, sr28) → F28
  195. Rotate(F28, (27 * θ), P0) → W28
  196. If(x(F28) < x(P0), 1, 2) → SnDx28
  197. Circle(P0, F28) → c28
  198. Intersect(c28, rt0, SnDx28) → P29
  199. Rotate(B29, α + (28 * γ), P29) → C29
  200. Ray(P29, C29) → sr29
  201. Intersect(rt1, sr29) → F29
  202. Rotate(F29, (28 * θ), P0) → W29
  203. Circle(P0, F29) → c29
  204. If(x(F29) < x(P0), 1, 2) → SnDx29
  205. Intersect(c29, rt0, SnDx29) → P30
  206. Rotate(B30, α + (29 * γ), P30) → C30
  207. Ray(P30, C30) → sr30
  208. Intersect(rt1, sr30) → F30
  209. Rotate(F30, (29 * θ), P0) → W30
  210. If(x(F30) < x(P0), 1, 2) → SnDx30
  211. Circle(P0, F30) → c30
  212. Intersect(c30, rt0, SnDx30) → P31
  213. Rotate(B31, α + (30 * γ), P31) → C31
  214. Ray(P31, C31) → sr31
  215. Intersect(rt1, sr31) → F31
  216. Rotate(F31, (30 * θ), P0) → W31
  217. Circle(P0, F31) → c31
  218. If(x(F31) < x(P0), 1, 2) → SnDx31
  219. Intersect(c31, rt0, SnDx31) → P32
  220. Rotate(B32, α + (31 * γ), P32) → C32
  221. Ray(P32, C32) → sr32
  222. Intersect(rt1, sr32) → F32
  223. Rotate(F32, (31 * θ), P0) → W32
  224. If(x(F32) < x(P0), 1, 2) → SnDx32
  225. Circle(P0, F32) → c32
  226. Intersect(c32, rt0, SnDx32) → P33
  227. Rotate(B33, α + (32 * γ), P33) → C33
  228. Ray(P33, C33) → sr33
  229. Intersect(rt1, sr33) → F33
  230. Rotate(F33, (32 * θ), P0) → W33
  231. Circle(P0, F33) → c33
  232. If(x(F33) < x(P0), 1, 2) → SnDx33
  233. Intersect(c33, rt0, SnDx33) → P34
  234. Rotate(B34, α + (33 * γ), P34) → C34
  235. Ray(P34, C34) → sr34
  236. Intersect(rt1, sr34) → F34
  237. Rotate(F34, (33 * θ), P0) → W34
  238. If(x(F34) < x(P0), 1, 2) → SnDx34
  239. Circle(P0, F34) → c34
  240. Intersect(c34, rt0, SnDx34) → P35
  241. Rotate(B35, α + (34 * γ), P35) → C35
  242. Ray(P35, C35) → sr35
  243. Intersect(rt1, sr35) → F35
  244. Rotate(F35, (34 * θ), P0) → W35
  245. Circle(P0, F35) → c35
  246. If(x(F35) < x(P0), 1, 2) → SnDx35
  247. Intersect(c35, rt0, SnDx35) → P36
  248. Rotate(B36, α + (35 * γ), P36) → C36
  249. Ray(P36, C36) → sr36
  250. Intersect(rt1, sr36) → F36
  251. Rotate(F36, (35 * θ), P0) → W36
  252. Circle(P0, F36) → c36
  253. If(x(F36) < x(P0), 1, 2) → SnDx36
  254. Intersect(c36, rt0, SnDx36) → P37
  255. Max(RemoveUndefined[{MxP1, MxP2, MxP3, MxP4, MxP5, MxP6, MxP7, MxP8, MxP9, MxP10, MxP11, MxP12, MxP13, MxP14, MxP15, MxP16, MxP17, MxP18, MxP19, MxP20, MxP21, MxP22, MxP23, MxP24, MxP25, MxP26, MxP27, MxP28, MxP29, MxP30, MxP31, MxP32, MxP33, MxP34, MxP35, MxP36, MxP37}]) → QuadMaxX
  256. Segment(P1, F1) → sp1
  257. Segment(P2, F2) → g_2
  258. Segment(P3, F3) → i_2
  259. Segment(P4, F4) → k_2
  260. Circle(P0, P1) → c0
  261. Segment(P5, F5) → m_2
  262. Segment(P6, F6) → r_2
  263. Segment(P7, F7) → a_2
  264. Segment(P8, F8) → f_3
  265. Segment(P9, F9) → h_3
  266. Segment(P10, F10) → j_3
  267. Segment(P11, F11) → m_3
  268. Segment(P12, F12) → q_3
  269. Segment(P13, F13) → t_3
  270. Segment(P14, F14) → b_3
  271. Segment(P15, F15) → g_4
  272. Segment(P16, F16) → i_4
  273. Segment(P17, F17) → l_4
  274. Segment(P18, F18) → n_4
  275. Segment(P19, F19) → s_4
  276. Segment(P20, F20) → b_4
  277. Segment(P21, F21) → g_5
  278. Segment(P22, F22) → i_5
  279. Segment(P23, F23) → k_5
  280. Segment(P24, F24) → m_5
  281. Segment(P25, F25) → r_5
  282. Segment(P26, F26) → a_5
  283. Segment(P27, F27) → f_6
  284. Segment(P28, F28) → h_6
  285. Segment(P29, F29) → j_6
  286. Segment(P30, F30) → m_6
  287. Segment(P31, F31) → q_6
  288. Segment(P32, F32) → t_6
  289. Segment(P33, F33) → b_6
  290. Segment(P34, F34) → g_7
  291. Segment(P35, F35) → i_7
  292. Segment(P36, F36) → l_7
  293. Segment(P1, F1) → m_7
  294. Segment(F1, W2) → sp2
  295. Segment(W2, W3) → sp3
  296. Segment(W3, W4) → sp4
  297. Segment(W4, W5) → sp5
  298. Segment(W5, W6) → sp6
  299. Segment(W6, W7) → sp7
  300. Segment(W7, W8) → sp8
  301. Segment(W8, W9) → sp9
  302. Segment(W9, W10) → sp10
  303. Segment(W10, W11) → sp11
  304. Segment(W11, W12) → sp12
  305. Segment(W12, W13) → sp13
  306. Segment(W13, W14) → sp14
  307. Segment(W14, W15) → sp15
  308. Segment(W15, W16) → sp16
  309. Segment(W16, W17) → sp17
  310. Segment(W17, W18) → sp18
  311. Segment(W18, W19) → sp19
  312. Segment(W19, W20) → sp20
  313. Segment(W20, W21) → sp21
  314. Segment(W21, W22) → sp22
  315. Segment(W22, W23) → sp23
  316. Segment(W23, W24) → sp24
  317. Segment(W24, W25) → sp25
  318. Segment(W25, W26) → sp26
  319. Segment(W26, W27) → sp27
  320. Segment(W27, W28) → sp28
  321. Segment(W28, W29) → sp29
  322. Segment(W29, W30) → sp30
  323. Segment(W30, W31) → sp31
  324. Segment(W31, W32) → sp32
  325. Segment(W32, W33) → sp33
  326. Segment(W33, W34) → sp34
  327. Segment(W34, W35) → sp35
  328. Segment(W35, W36) → sp36
  329. Segment(P0, W2) → sg2
  330. Segment(P0, W3) → sg3
  331. Segment(P0, W4) → sg4
  332. Segment(P0, W5) → sg5
  333. Segment(P0, W6) → sg6
  334. Segment(P0, W7) → sg7
  335. Segment(P0, W8) → sg8
  336. Segment(P0, W9) → sg9
  337. Segment(P0, W10) → sg10
  338. Segment(P0, W11) → sg11
  339. Segment(P0, W12) → sg12
  340. Segment(P0, W13) → sg13
  341. Segment(P0, W14) → sg14
  342. Segment(P0, W15) → sg15
  343. Segment(P0, W16) → sg16
  344. Segment(P0, W17) → sg17
  345. Segment(P0, W18) → sg18
  346. Segment(P0, W19) → sg19
  347. Segment(P0, W20) → sg20
  348. Segment(P0, W21) → sg21
  349. Segment(P0, W22) → sg22
  350. Segment(P0, W23) → sg23
  351. Segment(P0, W24) → sg24
  352. Segment(P0, W25) → sg25
  353. Segment(P0, W26) → sg26
  354. Segment(P0, W27) → sg27
  355. Segment(P0, W28) → sg28
  356. Segment(P0, W29) → sg29
  357. Segment(P0, W30) → sg30
  358. Segment(P0, W31) → sg31
  359. Segment(P0, W32) → sg32
  360. Segment(P0, W33) → sg33
  361. Segment(P0, W34) → sg34
  362. Segment(P0, W35) → sg35
  363. Segment(P0, W36) → sg36
  364. Textfield(CN) → CampoInserimento1
  365. Segment(PS, PD) → sg0
  366. Rotate(PS, θ) → AS
  367. Rotate(PD, θ) → AD
  368. Segment(AS, AD) → sg1
  369. Last(RemoveUndefined[{W1, W2, W3, W4, W5, W6, W7, W8, W9, W10, W11, W12, W13, W14, W15, W16, W17, W18, W19, W20, W21, W22, W23, W24, W25, W26, W27, W28, W29, W30, W31, W32, W33, W34, W35, W36}]) → AAA
  370. Midpoint(sp1) → Pm1
  371. Midpoint(sp2) → Pm2
  372. OrthogonalLine(Pm1, sp1) → perp1
  373. OrthogonalLine(Pm2, sp2) → perp2
  374. Intersect(perp1, perp2) → CeCe
  375. Circle(CeCe, P1) → cerchietto

AI 绘图提示语参考

绘制一个可调整角度和倾斜度的线段。首先，通过点P0和点A画一条线段rt0。然后，围绕P0旋转点A得到点A1，并用P0和A1画一条新的线段rt1。接着，围绕P1旋转点B1得到点C1，并用P1和C1画一条射线sr1。线段rt1和射线sr1相交于点F1。以此类推，通过旋转和相交操作，逐步调整线段的方向和位置，最终得到多个旋转后的线段和点。
以上提示语为根据原始绘图命令整理而来，仅供参考。