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Radius Unwrapper v2.0

Radius Unwrapper v2.0
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2014-07-08 01:28
CircleAngleGeometric Construction
In collections Geometry Review
This is an improved version of the radius unwrapping demonstration that fixes bugs from earlier versions. It illustrates the geometric construction of radius unwrapping, involving circles, angles, and segments. Using GeoGebra commands such as Circle, Segment, CircleArc, and Ray, the process of radius unwrapping can be dynamically observed. Suitable for students at the junior high school level and above to learn about circles.

GeoGebra Commands & Parameters

  1. Circle((0, 0), r) → c
  2. Segment(A, B) → a
  3. Segment(B, C) → b
  4. CircleArc(B, C, A) → d
  5. Ray(B21, D21) → E21
  6. Circle(B21, (1 - A21) * l) → F21
  7. Intersect(F21, E21) → G21,
  8. Segment(B21, G21) → H21
  9. Ray(B22, D22) → E22
  10. Circle(B22, (1 - A22) * l) → F22
  11. Intersect(F22, E22) → G22,
  12. Segment(B22, G22) → H22
  13. Ray(B23, D23) → E23
  14. Circle(B23, (1 - A23) * l) → F23
  15. Intersect(F23, E23) → G23,
  16. Segment(B23, G23) → H23
  17. Ray(B24, D24) → E24
  18. Circle(B24, (1 - A24) * l) → F24
  19. Intersect(F24, E24) → G24,
  20. Segment(B24, G24) → H24
  21. Ray(B25, D25) → E25
  22. Circle(B25, (1 - A25) * l) → F25
  23. Intersect(F25, E25) → G25,
  24. Segment(B25, G25) → H25
  25. Ray(B26, D26) → E26
  26. Circle(B26, (1 - A26) * l) → F26
  27. Intersect(F26, E26) → G26,
  28. Segment(B26, G26) → H26
  29. Ray(B27, D27) → E27
  30. Circle(B27, (1 - A27) * l) → F27
  31. Intersect(F27, E27) → G27,
  32. Segment(B27, G27) → H27
  33. Ray(B28, D28) → E28
  34. Circle(B28, (1 - A28) * l) → F28
  35. Intersect(F28, E28) → G28,
  36. Segment(B28, G28) → H28
  37. Ray(B29, D29) → E29
  38. Circle(B29, (1 - A29) * l) → F29
  39. Intersect(F29, E29) → G29,
  40. Segment(B29, G29) → H29
  41. Ray(B30, D30) → E30
  42. Circle(B30, (1 - A30) * l) → F30
  43. Intersect(F30, E30) → G30,
  44. Segment(B30, G30) → H30
  45. Ray(B31, D31) → E31
  46. Circle(B31, (1 - A31) * l) → F31
  47. Intersect(F31, E31) → G31,
  48. Segment(B31, G31) → H31
  49. Ray(B32, D32) → E32
  50. Circle(B32, (1 - A32) * l) → F32
  51. Intersect(F32, E32) → G32,
  52. Segment(B32, G32) → H32
  53. Ray(B33, D33) → E33
  54. Circle(B33, (1 - A33) * l) → F33
  55. Intersect(F33, E33) → G33,
  56. Segment(B33, G33) → H33
  57. Ray(B34, D34) → E34
  58. Circle(B34, (1 - A34) * l) → F34
  59. Intersect(F34, E34) → G34,
  60. Segment(B34, G34) → H34
  61. Ray(B35, D35) → E35
  62. Circle(B35, (1 - A35) * l) → F35
  63. Intersect(F35, E35) → G35,
  64. Segment(B35, G35) → H35
  65. Ray(B36, D36) → E36
  66. Circle(B36, (1 - A36) * l) → F36
  67. Intersect(F36, E36) → G36,
  68. Segment(B36, G36) → H36
  69. Ray(B37, D37) → E37
  70. Circle(B37, (1 - A37) * l) → F37
  71. Intersect(F37, E37) → G37,
  72. Segment(B37, G37) → H37
  73. Ray(B38, D38) → E38
  74. Circle(B38, (1 - A38) * l) → F38
  75. Intersect(F38, E38) → G38,
  76. Segment(B38, G38) → H38
  77. Ray(B39, D39) → E39
  78. Circle(B39, (1 - A39) * l) → F39
  79. Intersect(F39, E39) → G39,
  80. Segment(B39, G39) → H39
  81. Ray(B40, D40) → E40
  82. Circle(B40, (1 - A40) * l) → F40
  83. Intersect(F40, E40) → G40,
  84. Segment(B40, G40) → H40
  85. Ray(B41, D41) → E41
  86. Circle(B41, (1 - A41) * l) → F41
  87. Intersect(F41, E41) → G41,
  88. Segment(B41, G41) → H41
  89. Ray(B42, D42) → E42
  90. Circle(B42, (1 - A42) * l) → F42
  91. Intersect(F42, E42) → G42,
  92. Segment(B42, G42) → H42
  93. Ray(B43, D43) → E43
  94. Circle(B43, (1 - A43) * l) → F43
  95. Intersect(F43, E43) → G43,
  96. Segment(B43, G43) → H43
  97. Ray(B44, D44) → E44
  98. Circle(B44, (1 - A44) * l) → F44
  99. Intersect(F44, E44) → G44,
  100. Segment(B44, G44) → H44
  101. Ray(B45, D45) → E45
  102. Circle(B45, (1 - A45) * l) → F45
  103. Intersect(F45, E45) → G45,
  104. Segment(B45, G45) → H45
  105. Ray(B46, D46) → E46
  106. Circle(B46, (1 - A46) * l) → F46
  107. Intersect(F46, E46) → G46,
  108. Segment(B46, G46) → H46
  109. Ray(B47, D47) → E47
  110. Circle(B47, (1 - A47) * l) → F47
  111. Intersect(F47, E47) → G47,
  112. Segment(B47, G47) → H47
  113. Ray(B48, D48) → E48
  114. Circle(B48, (1 - A48) * l) → F48
  115. Intersect(F48, E48) → G48,
  116. Segment(B48, G48) → H48
  117. Ray(B49, D49) → E49
  118. Circle(B49, (1 - A49) * l) → F49
  119. Intersect(F49, E49) → G49,
  120. Segment(B49, G49) → H49
  121. Ray(B50, D50) → E50
  122. Circle(B50, (1 - A50) * l) → F50
  123. Intersect(F50, E50) → G50,
  124. Segment(B50, G50) → H50
  125. Ray(B51, D51) → E51
  126. Circle(B51, (1 - A51) * l) → F51
  127. Intersect(F51, E51) → G51,
  128. Segment(B51, G51) → H51
  129. Ray(B52, D52) → E52
  130. Circle(B52, (1 - A52) * l) → F52
  131. Intersect(F52, E52) → G52,
  132. Segment(B52, G52) → H52
  133. Ray(B53, D53) → E53
  134. Circle(B53, (1 - A53) * l) → F53
  135. Intersect(F53, E53) → G53,
  136. Segment(B53, G53) → H53
  137. Ray(B54, D54) → E54
  138. Circle(B54, (1 - A54) * l) → F54
  139. Intersect(F54, E54) → G54,
  140. Segment(B54, G54) → H54
  141. Ray(B55, D55) → E55
  142. Circle(B55, (1 - A55) * l) → F55
  143. Intersect(F55, E55) → G55,
  144. Segment(B55, G55) → H55
  145. Ray(B56, D56) → E56
  146. Circle(B56, (1 - A56) * l) → F56
  147. Intersect(F56, E56) → G56,
  148. Segment(B56, G56) → H56
  149. Ray(B57, D57) → E57
  150. Circle(B57, (1 - A57) * l) → F57
  151. Intersect(F57, E57) → G57,
  152. Segment(B57, G57) → H57
  153. Ray(B58, D58) → E58
  154. Circle(B58, (1 - A58) * l) → F58
  155. Intersect(F58, E58) → G58,
  156. Segment(B58, G58) → H58
  157. Ray(B59, D59) → E59
  158. Circle(B59, (1 - A59) * l) → F59
  159. Intersect(F59, E59) → G59,
  160. Segment(B59, G59) → H59
  161. Ray(B60, D60) → E60
  162. Circle(B60, (1 - A60) * l) → F60
  163. Intersect(F60, E60) → G60,
  164. Segment(B60, G60) → H60
  165. Ray(B61, D61) → E61
  166. Circle(B61, (1 - A61) * l) → F61
  167. Intersect(F61, E61) → G61,
  168. Segment(B61, G61) → H61
  169. Ray(B62, D62) → E62
  170. Circle(B62, (1 - A62) * l) → F62
  171. Intersect(F62, E62) → G62,
  172. Segment(B62, G62) → H62
  173. Ray(B63, D63) → E63
  174. Circle(B63, (1 - A63) * l) → F63
  175. Intersect(F63, E63) → G63,
  176. Segment(B63, G63) → H63
  177. Ray(B64, D64) → E64
  178. Circle(B64, (1 - A64) * l) → F64
  179. Intersect(F64, E64) → G64,
  180. Segment(B64, G64) → H64
  181. Ray(B65, D65) → E65
  182. Circle(B65, (1 - A65) * l) → F65
  183. Intersect(F65, E65) → G65,
  184. Segment(B65, G65) → H65
  185. Ray(B66, D66) → E66
  186. Circle(B66, (1 - A66) * l) → F66
  187. Intersect(F66, E66) → G66,
  188. Segment(B66, G66) → H66
  189. Ray(B67, D67) → E67
  190. Circle(B67, (1 - A67) * l) → F67
  191. Intersect(F67, E67) → G67,
  192. Segment(B67, G67) → H67
  193. Ray(B68, D68) → E68
  194. Circle(B68, (1 - A68) * l) → F68
  195. Intersect(F68, E68) → G68,
  196. Segment(B68, G68) → H68
  197. Ray(B69, D69) → E69
  198. Circle(B69, (1 - A69) * l) → F69
  199. Intersect(F69, E69) → G69,
  200. Segment(B69, G69) → H69
  201. Ray(B70, D70) → E70
  202. Circle(B70, (1 - A70) * l) → F70
  203. Intersect(F70, E70) → G70,
  204. Segment(B70, G70) → H70
  205. Ray(B71, D71) → E71
  206. Circle(B71, (1 - A71) * l) → F71
  207. Intersect(F71, E71) → G71,
  208. Segment(B71, G71) → H71
  209. Ray(B72, D72) → E72
  210. Circle(B72, (1 - A72) * l) → F72
  211. Intersect(F72, E72) → G72,
  212. Segment(B72, G72) → H72
  213. Ray(B73, D73) → E73
  214. Circle(B73, (1 - A73) * l) → F73
  215. Intersect(F73, E73) → G73,
  216. Segment(B73, G73) → H73
  217. Ray(B74, D74) → E74
  218. Circle(B74, (1 - A74) * l) → F74
  219. Intersect(F74, E74) → G74,
  220. Segment(B74, G74) → H74
  221. Ray(B75, D75) → E75
  222. Circle(B75, (1 - A75) * l) → F75
  223. Intersect(F75, E75) → G75,
  224. Segment(B75, G75) → H75
  225. Ray(B76, D76) → E76
  226. Circle(B76, (1 - A76) * l) → F76
  227. Intersect(F76, E76) → G76,
  228. Segment(B76, G76) → H76
  229. Ray(B77, D77) → E77
  230. Circle(B77, (1 - A77) * l) → F77
  231. Intersect(F77, E77) → G77,
  232. Segment(B77, G77) → H77
  233. Ray(B78, D78) → E78
  234. Circle(B78, (1 - A78) * l) → F78
  235. Intersect(F78, E78) → G78,
  236. Segment(B78, G78) → H78
  237. Ray(B79, D79) → E79
  238. Circle(B79, (1 - A79) * l) → F79
  239. Intersect(F79, E79) → G79,
  240. Segment(B79, G79) → H79
  241. Ray(B80, D80) → E80
  242. Circle(B80, (1 - A80) * l) → F80
  243. Intersect(F80, E80) → G80,
  244. Segment(B80, G80) → H80
  245. Ray(B81, D81) → E81
  246. Circle(B81, (1 - A81) * l) → F81
  247. Intersect(F81, E81) → G81,
  248. Segment(B81, G81) → H81
  249. Ray(B82, D82) → E82
  250. Circle(B82, (1 - A82) * l) → F82
  251. Intersect(F82, E82) → G82,
  252. Segment(B82, G82) → H82
  253. Ray(B83, D83) → E83
  254. Circle(B83, (1 - A83) * l) → F83
  255. Intersect(F83, E83) → G83,
  256. Segment(B83, G83) → H83
  257. Ray(B84, D84) → E84
  258. Circle(B84, (1 - A84) * l) → F84
  259. Intersect(F84, E84) → G84,
  260. Segment(B84, G84) → H84
  261. Ray(B85, D85) → E85
  262. Circle(B85, (1 - A85) * l) → F85
  263. Intersect(F85, E85) → G85,
  264. Segment(B85, G85) → H85
  265. Ray(B86, D86) → E86
  266. Circle(B86, (1 - A86) * l) → F86
  267. Intersect(F86, E86) → G86,
  268. Segment(B86, G86) → H86
  269. Ray(B87, D87) → E87
  270. Circle(B87, (1 - A87) * l) → F87
  271. Intersect(F87, E87) → G87,
  272. Segment(B87, G87) → H87
  273. Ray(B88, D88) → E88
  274. Circle(B88, (1 - A88) * l) → F88
  275. Intersect(F88, E88) → G88,
  276. Segment(B88, G88) → H88
  277. Ray(B89, D89) → E89
  278. Circle(B89, (1 - A89) * l) → F89
  279. Intersect(F89, E89) → G89,
  280. Segment(B89, G89) → H89
  281. Ray(B90, D90) → E90
  282. Circle(B90, (1 - A90) * l) → F90
  283. Intersect(F90, E90) → G90,
  284. Segment(B90, G90) → H90
  285. Ray(B91, D91) → E91
  286. Circle(B91, (1 - A91) * l) → F91
  287. Intersect(F91, E91) → G91,
  288. Segment(B91, G91) → H91
  289. Ray(B92, D92) → E92
  290. Circle(B92, (1 - A92) * l) → F92
  291. Intersect(F92, E92) → G92,
  292. Segment(B92, G92) → H92
  293. Ray(B93, D93) → E93
  294. Circle(B93, (1 - A93) * l) → F93
  295. Intersect(F93, E93) → G93,
  296. Segment(B93, G93) → H93
  297. Ray(B94, D94) → E94
  298. Circle(B94, (1 - A94) * l) → F94
  299. Intersect(F94, E94) → G94,
  300. Segment(B94, G94) → H94
  301. Ray(B95, D95) → E95
  302. Circle(B95, (1 - A95) * l) → F95
  303. Intersect(F95, E95) → G95,
  304. Segment(B95, G95) → H95
  305. Ray(B96, D96) → E96
  306. Circle(B96, (1 - A96) * l) → F96
  307. Intersect(F96, E96) → G96,
  308. Segment(B96, G96) → H96
  309. Ray(B97, D97) → E97
  310. Circle(B97, (1 - A97) * l) → F97
  311. Intersect(F97, E97) → G97,
  312. Segment(B97, G97) → H97
  313. Ray(B98, D98) → E98
  314. Circle(B98, (1 - A98) * l) → F98
  315. Intersect(F98, E98) → G98,
  316. Segment(B98, G98) → H98
  317. Ray(B99, D99) → E99
  318. Circle(B99, (1 - A99) * l) → F99
  319. Intersect(F99, E99) → G99,
  320. Segment(B99, G99) → H99
  321. Ray(B100, D100) → E100
  322. Circle(B100, (1 - A100) * l) → F100
  323. Intersect(F100, E100) → G100,
  324. Segment(B100, G100) → H100
  325. Ray(B101, D101) → E101
  326. Circle(B101, (1 - A101) * l) → F101
  327. Intersect(F101, E101) → G101,
  328. Segment(B101, G101) → H101
  329. Ray(B2, D2) → E2
  330. Circle(B2, (1 - A2) * l) → F2
  331. Intersect(F2, E2) → G2,
  332. Segment(B2, G2) → H2
  333. Ray(B3, D3) → E3
  334. Circle(B3, (1 - A3) * l) → F3
  335. Intersect(F3, E3) → G3,
  336. Segment(B3, G3) → H3
  337. Ray(B4, D4) → E4
  338. Circle(B4, (1 - A4) * l) → F4
  339. Intersect(F4, E4) → G4,
  340. Segment(B4, G4) → H4
  341. Ray(B5, D5) → E5
  342. Circle(B5, (1 - A5) * l) → F5
  343. Intersect(F5, E5) → G5,
  344. Segment(B5, G5) → H5
  345. Ray(B6, D6) → E6
  346. Circle(B6, (1 - A6) * l) → F6
  347. Intersect(F6, E6) → G6,
  348. Segment(B6, G6) → H6
  349. Ray(B7, D7) → E7
  350. Circle(B7, (1 - A7) * l) → F7
  351. Intersect(F7, E7) → G7,
  352. Segment(B7, G7) → H7
  353. Ray(B8, D8) → E8
  354. Circle(B8, (1 - A8) * l) → F8
  355. Intersect(F8, E8) → G8,
  356. Segment(B8, G8) → H8
  357. Ray(B9, D9) → E9
  358. Circle(B9, (1 - A9) * l) → F9
  359. Intersect(F9, E9) → G9,
  360. Segment(B9, G9) → H9
  361. Ray(B10, D10) → E10
  362. Circle(B10, (1 - A10) * l) → F10
  363. Intersect(F10, E10) → G10,
  364. Segment(B10, G10) → H10
  365. Ray(B11, D11) → E11
  366. Circle(B11, (1 - A11) * l) → F11
  367. Intersect(F11, E11) → G11,
  368. Segment(B11, G11) → H11
  369. Ray(B12, D12) → E12
  370. Circle(B12, (1 - A12) * l) → F12
  371. Intersect(F12, E12) → G12,
  372. Segment(B12, G12) → H12
  373. Ray(B13, D13) → E13
  374. Circle(B13, (1 - A13) * l) → F13
  375. Intersect(F13, E13) → G13,
  376. Segment(B13, G13) → H13
  377. Ray(B14, D14) → E14
  378. Circle(B14, (1 - A14) * l) → F14
  379. Intersect(F14, E14) → G14,
  380. Segment(B14, G14) → H14
  381. Ray(B15, D15) → E15
  382. Circle(B15, (1 - A15) * l) → F15
  383. Intersect(F15, E15) → G15,
  384. Segment(B15, G15) → H15
  385. Ray(B16, D16) → E16
  386. Circle(B16, (1 - A16) * l) → F16
  387. Intersect(F16, E16) → G16,
  388. Segment(B16, G16) → H16
  389. Ray(B17, D17) → E17
  390. Circle(B17, (1 - A17) * l) → F17
  391. Intersect(F17, E17) → G17,
  392. Segment(B17, G17) → H17
  393. Ray(B18, D18) → E18
  394. Circle(B18, (1 - A18) * l) → F18
  395. Intersect(F18, E18) → G18,
  396. Segment(B18, G18) → H18
  397. Ray(B19, D19) → E19
  398. Circle(B19, (1 - A19) * l) → F19
  399. Intersect(F19, E19) → G19,
  400. Segment(B19, G19) → H19
  401. Ray(B20, D20) → E20
  402. Circle(B20, (1 - A20) * l) → F20
  403. Intersect(F20, E20) → G20,
  404. Segment(B20, G20) → H20
  405. Arc(c, C, B21) → I21
  406. Arc(c, C, B2) → I2
  407. Arc(c, C, B3) → I3
  408. Arc(c, C, B4) → I4
  409. Arc(c, C, B5) → I5
  410. Arc(c, C, B6) → I6
  411. Arc(c, C, B7) → I7
  412. Arc(c, C, B8) → I8
  413. Arc(c, C, B9) → I9
  414. Arc(c, C, B10) → I10
  415. Arc(c, C, B11) → I11
  416. Arc(c, C, B12) → I12
  417. Arc(c, C, B13) → I13
  418. Arc(c, C, B14) → I14
  419. Arc(c, C, B15) → I15
  420. Arc(c, C, B16) → I16
  421. Arc(c, C, B17) → I17
  422. Arc(c, C, B18) → I18
  423. Arc(c, C, B19) → I19
  424. Arc(c, C, B20) → I20
  425. Arc(c, C, B22) → I22
  426. Arc(c, C, B23) → I23
  427. Arc(c, C, B24) → I24
  428. Arc(c, C, B25) → I25
  429. Arc(c, C, B26) → I26
  430. Arc(c, C, B27) → I27
  431. Arc(c, C, B28) → I28
  432. Arc(c, C, B29) → I29
  433. Arc(c, C, B30) → I30
  434. Arc(c, C, B31) → I31
  435. Arc(c, C, B32) → I32
  436. Arc(c, C, B33) → I33
  437. Arc(c, C, B34) → I34
  438. Arc(c, C, B35) → I35
  439. Arc(c, C, B36) → I36
  440. Arc(c, C, B37) → I37
  441. Arc(c, C, B38) → I38
  442. Arc(c, C, B39) → I39
  443. Arc(c, C, B40) → I40
  444. Arc(c, C, B41) → I41
  445. Arc(c, C, B42) → I42
  446. Arc(c, C, B43) → I43
  447. Arc(c, C, B44) → I44
  448. Arc(c, C, B45) → I45
  449. Arc(c, C, B46) → I46
  450. Arc(c, C, B47) → I47
  451. Arc(c, C, B48) → I48
  452. Arc(c, C, B49) → I49
  453. Arc(c, C, B50) → I50
  454. Arc(c, C, B51) → I51
  455. Arc(c, C, B52) → I52
  456. Arc(c, C, B53) → I53
  457. Arc(c, C, B54) → I54
  458. Arc(c, C, B55) → I55
  459. Arc(c, C, B56) → I56
  460. Arc(c, C, B57) → I57
  461. Arc(c, C, B58) → I58
  462. Arc(c, C, B59) → I59
  463. Arc(c, C, B60) → I60
  464. Arc(c, C, B61) → I61
  465. Arc(c, C, B62) → I62
  466. Arc(c, C, B63) → I63
  467. Arc(c, C, B64) → I64
  468. Arc(c, C, B65) → I65
  469. Arc(c, C, B66) → I66
  470. Arc(c, C, B67) → I67
  471. Arc(c, C, B68) → I68
  472. Arc(c, C, B69) → I69
  473. Arc(c, C, B70) → I70
  474. Arc(c, C, B71) → I71
  475. Arc(c, C, B72) → I72
  476. Arc(c, C, B73) → I73
  477. Arc(c, C, B74) → I74
  478. Arc(c, C, B75) → I75
  479. Arc(c, C, B76) → I76
  480. Arc(c, C, B77) → I77
  481. Arc(c, C, B78) → I78
  482. Arc(c, C, B79) → I79
  483. Arc(c, C, B80) → I80
  484. Arc(c, C, B81) → I81
  485. Arc(c, C, B82) → I82
  486. Arc(c, C, B83) → I83
  487. Arc(c, C, B84) → I84
  488. Arc(c, C, B85) → I85
  489. Arc(c, C, B86) → I86
  490. Arc(c, C, B87) → I87
  491. Arc(c, C, B88) → I88
  492. Arc(c, C, B89) → I89
  493. Arc(c, C, B90) → I90
  494. Arc(c, C, B91) → I91
  495. Arc(c, C, B92) → I92
  496. Arc(c, C, B93) → I93
  497. Arc(c, C, B94) → I94
  498. Arc(c, C, B95) → I95
  499. Arc(c, C, B96) → I96
  500. Arc(c, C, B97) → I97
  501. Arc(c, C, B98) → I98
  502. Arc(c, C, B99) → I99
  503. Arc(c, C, B100) → I100
  504. Arc(c, C, B101) → I101
  505. Segment((r, 0), (r, l)) → H1
  506. Circle((0, 0), r) → I1
  507. Segment(D103, D113) → D114
  508. Angle(C, B, A) → α

AI Drawing Prompt Reference

Draw a circle centered at the origin, then draw two intersecting line segments from a point on the circle. Take another point on the circle and draw a circular arc using that point and the intersection of the line segments. Draw a ray from that point, intersect it with a new circle, and repeat this process multiple times to form a series of arcs and line segments, illustrating the process of circle unwrapping.
The prompt above was compiled from the original drawing commands and is for reference only.