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Classroom Spinner: Parametric Curves and Geometric Transformations

Classroom Spinner: Parametric Curves and Geometric Transformations
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2020-10-02 23:35
Solid GeometryProbability & StatisticsParametric Equation
This example demonstrates the relationship between cones and circles through parametric equations and rotations. Key mathematical concepts include parametric curves, geometric transformations, and coordinate geometry. Construction involves using GeoGebra commands like Rotate, CircleSector, and Parametric Curves. Suitable for high school students or math enthusiasts to explore geometric transformations and parametric applications.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a probability spinner teaching demonstration featuring a conical spiral surface created with parametric curves and circular sectors. Create multiple sector regions representing different probability intervals, define a driver point using parametric equations that rotates along a circular path. Show the parametric relationship between cones and circles, demonstrating geometric transformation processes suitable for high school mathematics teaching.
The prompt above was compiled from the original drawing commands and is for reference only.