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Rosetones Coimbra

Rosetones Coimbra
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2023-03-13 20:15
CalculusGeometric Construction
In collections geometriadinamica.es
This example demonstrates the mathematical construction of Rosetones Coimbra, involving core concepts like continuity, area, real numbers, squares, and upper and lower sums or Riemann sums. It utilizes GeoGebra commands/objects such as If, Circle, OrthogonalLine, Intersect, Rotate, and CircleSector. Suitable for high school students and educators for teaching demonstrations and exploration.

GeoGebra Commands & Parameters

  1. If(tiempo2 ≥ (2 * cambio) ∧ tiempo2 < (3 * cambio), 1, 0) → test03
  2. Circle(AC, (2.95 * r1)) → c
  3. OrthogonalLine(AC, xAxis) → a
  4. Intersect(c, a, 1) → AV
  5. Rotate(AV, 329.99999999999994°, AC) → AV330
  6. Rotate(AV, 210°, AC) → AV210
  7. Rotate(AV, 180°, AC) → AV180
  8. Rotate(AV, 150.00000000000003°, AC) → AV150
  9. Rotate(AV, 119.99999999999999°, AC) → AV120
  10. Rotate(AV, 29.999999999999996°, AC) → AV030
  11. If(tiempo2 < cambio, 1, 0) → test01
  12. Rotate(AV, 36°, AC) → AV036
  13. If(tiempo2 ≥ cambio ∧ tiempo2 < (2 * cambio), 1, 0) → test02
  14. If(tiempo2 ≥ (3 * cambio) ∧ tiempo2 < (4 * cambio), 1, 0) → test04
  15. If(tiempo2 ≥ (4 * cambio) ∧ tiempo2 < (5 * cambio), 1, 0) → test05
  16. If(tiempo2 ≥ (5 * cambio) ∧ tiempo2 < (6 * cambio), 1, 0) → test06
  17. If(tiempo2 ≥ (6 * cambio) ∧ tiempo2 < (7 * cambio), 1, 0) → test07
  18. If(tiempo2 ≥ (7 * cambio) ∧ tiempo2 < (8 * cambio), 1, 0) → test08
  19. If(tiempo2 ≥ (8 * cambio) ∧ tiempo2 < (9 * cambio), 1, 0) → test09
  20. If(tiempo2 ≥ (9 * cambio) ∧ tiempo2 < (10 * cambio), 1, 0) → test10
  21. If(tiempo2 ≥ (10 * cambio) ∧ tiempo2 < (11 * cambio), 1, 0) → test11
  22. If(tiempo2 ≥ (11 * cambio) ∧ tiempo2 < (12 * cambio), 1, 0) → test12
  23. If(tiempo2 ≥ (12 * cambio) ∧ tiempo2 < (13 * cambio), 1, 0) → test13
  24. If(tiempo2 ≥ (13 * cambio) ∧ tiempo2 < (14 * cambio), 1, 0) → test14
  25. If(tiempo2 ≥ (14 * cambio) ∧ tiempo2 < (15 * cambio), 1, 0) → test15
  26. If(tiempo2 ≥ (15 * cambio) ∧ tiempo2 < (16 * cambio), 1, 0) → test16
  27. If(tiempo2 ≥ (16 * cambio) ∧ tiempo2 < (17 * cambio), 1, 0) → test17
  28. If(tiempo2 ≥ (17 * cambio) ∧ tiempo2 < (18 * cambio), 1, 0) → test18
  29. If(tiempo2 ≥ (18 * cambio) ∧ tiempo2 < (19 * cambio), 1, 0) → test19
  30. If(tiempo2 ≥ (19 * cambio) ∧ tiempo2 < (20 * cambio), 1, 0) → test20
  31. If(tiempo2 ≥ (20 * cambio) ∧ tiempo2 < (21 * cambio), 1, 0) → test21
  32. Rotate(AV, 72°, AC) → AV072
  33. Rotate(AV, 108°, AC) → AV108
  34. Rotate(AV, 144°, AC) → AV144
  35. Rotate(AV, 216°, AC) → AV216
  36. Rotate(AV, 252°, AC) → AV252
  37. Rotate(AV, 288°, AC) → AV288
  38. Rotate(AV, 324°, AC) → AV324
  39. CircleSector(AC / test01, AV036 / ver, AV072) → s1a036a072
  40. CircleSector(AC / test01, AV072 / ver, AV108) → s1a072a108
  41. CircleSector(AC / test01, AV108 / ver, AV144) → s1a108a144
  42. CircleSector(AC / test01, AV144 / ver, AV180) → s1a144a180
  43. CircleSector(AC / test01, AV180 / ver, AV216) → s1a180a216
  44. CircleSector(AC / test01, AV216 / ver, AV252) → s1a216a252
  45. CircleSector(AC / test01, AV252 / ver, AV288) → s1a252a288
  46. CircleSector(AC / test01, AV288 / ver, AV324) → s1a288a324
  47. CircleSector(AC / test01, AV324 / ver, AV) → s1a324a360
  48. CircleSector(AC / test01, AV / ver, AV036) → s1a000a036
  49. Rotate(AV, 59.99999999999999°, AC) → AV060
  50. Rotate(AV, 239.99999999999997°, AC) → AV240
  51. Rotate(AV, 300.00000000000006°, AC) → AV300
  52. CircleSector(AC / test02, AV / ver, AV060) → s2a000a060
  53. CircleSector(AC / test02, AV060 / ver, AV120) → s2a060a120
  54. CircleSector(AC / test02, AV120 / ver, AV180) → s2a120a180
  55. CircleSector(AC / test02, AV180 / ver, AV240) → s2a180a240
  56. CircleSector(AC / test02, AV240 / ver, AV300) → s2a240a300
  57. CircleSector(AC / test02, AV300 / ver, AV) → s2a300a360
  58. Rotate(AV, 45°, AC) → AV045
  59. Rotate(AV, 90°, AC) → AV090
  60. Rotate(AV, 135°, AC) → AV135
  61. Rotate(AV, 225°, AC) → AV225
  62. Rotate(AV, 270°, AC) → AV270
  63. Rotate(AV, 315°, AC) → AV315
  64. CircleSector(AC / test03, AV030 / ver, AV060) → s3a030a060
  65. CircleSector(AC / test03, AV060 / ver, AV090) → s3a060a090
  66. CircleSector(AC / test03, AV090 / ver, AV120) → s3a090a120
  67. CircleSector(AC / test03, AV150 / ver, AV180) → s3a150a180
  68. CircleSector(AC / test03, AV / ver, AV030) → s3a000a030
  69. CircleSector(AC / test03, AV120 / ver, AV150) → s3a120a150
  70. CircleSector(AC / test03, AV180 / ver, AV210) → s3a180a210
  71. CircleSector(AC / test03, AV210 / ver, AV240) → s3a210a240
  72. CircleSector(AC / test03, AV240 / ver, AV270) → s3a240a270
  73. CircleSector(AC / test03, AV270 / ver, AV300) → s3a270a300
  74. CircleSector(AC / test03, AV300 / ver, AV330) → s3a300a330
  75. CircleSector(AC / test03, AV330 / ver, AV) → s3a330a360
  76. CircleSector(AC / test04, AV / ver, AV060) → s4a000a060
  77. CircleSector(AC / test04, AV060 / ver, AV120) → s4a060a120
  78. CircleSector(AC / test04, AV120 / ver, AV180) → s4a120a180
  79. CircleSector(AC / test04, AV180 / ver, AV240) → s4a180a240
  80. CircleSector(AC / test04, AV240 / ver, AV300) → s4a240a300
  81. CircleSector(AC / test04, AV300 / ver, AV) → s4a300a360
  82. CircleSector(AC / test05, AV / ver, AV030) → s5a000a030
  83. CircleSector(AC / test05, AV030 / ver, AV060) → s5a030a060
  84. CircleSector(AC / test05, AV060 / ver, AV090) → s5a060a090
  85. CircleSector(AC / test05, AV090 / ver, AV120) → s5a090a120
  86. CircleSector(AC / test05, AV120 / ver, AV150) → s5a120a150
  87. CircleSector(AC / test05, AV150 / ver, AV180) → s5a150a180
  88. CircleSector(AC / test05, AV180 / ver, AV210) → s5a180a210
  89. CircleSector(AC / test05, AV210 / ver, AV240) → s5a210a240
  90. CircleSector(AC / test05, AV240 / ver, AV270) → s5a240a270
  91. CircleSector(AC / test05, AV270 / ver, AV300) → s5a270a300
  92. CircleSector(AC / test05, AV300 / ver, AV330) → s5a300a330
  93. CircleSector(AC / test05, AV330 / ver, AV) → s5a330a360
  94. CircleSector(AC / test06, AV / ver, AV045) → s6a000a045
  95. CircleSector(AC / test06, AV045 / ver, AV090) → s6a045a090
  96. CircleSector(AC / test06, AV090 / ver, AV135) → s6a090a135
  97. CircleSector(AC / test06, AV135 / ver, AV180) → s6a135a180
  98. CircleSector(AC / test06, AV180 / ver, AV225) → s6a180a225
  99. CircleSector(AC / test06, AV225 / ver, AV270) → s6a225a270
  100. CircleSector(AC / test06, AV270 / ver, AV315) → s6a270a315
  101. CircleSector(AC / test06, AV315 / ver, AV) → s6a315a360
  102. CircleSector(AC / test07, AV / ver, AV060) → s7a000a060
  103. CircleSector(AC / test07, AV060 / ver, AV120) → s7a060a120
  104. CircleSector(AC / test07, AV120 / ver, AV180) → s7a120a180
  105. CircleSector(AC / test07, AV180 / ver, AV240) → s7a180a240
  106. CircleSector(AC / test07, AV240 / ver, AV300) → s7a240a300
  107. CircleSector(AC / test07, AV300 / ver, AV) → s7a300a360
  108. Rotate(AV, 22.5°, AC) → AV022
  109. Rotate(AV, 67.5°, AC) → AV067
  110. Rotate(AV, 112.5°, AC) → AV112
  111. Rotate(AV, 157.5°, AC) → AV157
  112. Rotate(AV, 202.49999999999997°, AC) → AV202
  113. Rotate(AV, 247.5°, AC) → AV247
  114. Rotate(AV, 292.50000000000006°, AC) → AV292
  115. Rotate(AV, 337.5000000000001°, AC) → AV337
  116. CircleSector(AC / test08, AV / ver, AV022) → s8a000a022
  117. CircleSector(AC / test08, AV022 / ver, AV045) → s8a022a045
  118. CircleSector(AC / test08, AV045 / ver, AV067) → s8a045a067
  119. CircleSector(AC / test08, AV067 / ver, AV090) → s8a067a090
  120. CircleSector(AC / test08, AV090 / ver, AV112) → s8a090a112
  121. CircleSector(AC / test08, AV112 / ver, AV135) → s8a112a135
  122. CircleSector(AC / test08, AV135 / ver, AV157) → s8a135a157
  123. CircleSector(AC / test08, AV157 / ver, AV180) → s8a157a180
  124. CircleSector(AC / test08, AV180 / ver, AV202) → s8a180a202
  125. CircleSector(AC / test08, AV202 / ver, AV225) → s8a202a225
  126. CircleSector(AC / test08, AV225 / ver, AV247) → s8a225a247
  127. CircleSector(AC / test08, AV247 / ver, AV270) → s8a247a270
  128. CircleSector(AC / test08, AV270 / ver, AV292) → s8a270a292
  129. CircleSector(AC / test08, AV292 / ver, AV315) → s8a292a315
  130. CircleSector(AC / test08, AV315 / ver, AV337) → s8a315a337
  131. CircleSector(AC / test08, AV337 / ver, AV) → s8a337a360
  132. CircleSector(AC / test09, AV / ver, AV045) → s9a000a045
  133. CircleSector(AC / test09, AV045 / ver, AV090) → s9a045a090
  134. CircleSector(AC / test09, AV090 / ver, AV135) → s9a090a135
  135. CircleSector(AC / test09, AV135 / ver, AV180) → s9a135a180
  136. CircleSector(AC / test09, AV180 / ver, AV225) → s9a180a225
  137. CircleSector(AC / test09, AV225 / ver, AV270) → s9a225a270
  138. CircleSector(AC / test09, AV270 / ver, AV315) → s9a270a315
  139. CircleSector(AC / test09, AV315 / ver, AV) → s9a315a360
  140. CircleSector(AC / test10, AV / ver, AV060) → s10a000a060
  141. CircleSector(AC / test10, AV060 / ver, AV120) → s10a060a120
  142. CircleSector(AC / test10, AV120 / ver, AV180) → s10a120a180
  143. CircleSector(AC / test10, AV180 / ver, AV240) → s10a180a240
  144. CircleSector(AC / test10, AV240 / ver, AV300) → s10a240a300
  145. CircleSector(AC / test10, AV300 / ver, AV) → s10a300a360
  146. CircleSector(AC / test11, AV / ver, AV045) → s11a000a045
  147. CircleSector(AC / test11, AV045 / ver, AV090) → s11a045a090
  148. CircleSector(AC / test11, AV090 / ver, AV135) → s11a090a135
  149. CircleSector(AC / test11, AV135 / ver, AV180) → s11a135a180
  150. CircleSector(AC / test11, AV180 / ver, AV225) → s11a180a225
  151. CircleSector(AC / test11, AV225 / ver, AV270) → s11a225a270
  152. CircleSector(AC / test11, AV270 / ver, AV315) → s11a270a315
  153. CircleSector(AC / test11, AV315 / ver, AV) → s11a315a360
  154. CircleSector(AC / test12, AV / ver, AV060) → s12a000a060
  155. CircleSector(AC / test12, AV060 / ver, AV120) → s12a060a120
  156. CircleSector(AC / test12, AV120 / ver, AV180) → s12a120a180
  157. CircleSector(AC / test12, AV180 / ver, AV240) → s12a180a240
  158. CircleSector(AC / test12, AV240 / ver, AV300) → s12a240a300
  159. CircleSector(AC / test12, AV300 / ver, AV) → s12a300a360
  160. CircleSector(AC / test13, AV / ver, AV045) → s13a000a045
  161. CircleSector(AC / test13, AV045 / ver, AV090) → s13a045a090
  162. CircleSector(AC / test13, AV090 / ver, AV135) → s13a090a135
  163. CircleSector(AC / test13, AV135 / ver, AV180) → s13a135a180
  164. CircleSector(AC / test13, AV180 / ver, AV225) → s13a180a225
  165. CircleSector(AC / test13, AV225 / ver, AV270) → s13a225a270
  166. CircleSector(AC / test13, AV270 / ver, AV315) → s13a270a315
  167. CircleSector(AC / test13, AV315 / ver, AV) → s13a315a360
  168. CircleSector(AC / test14, AV / ver, AV022) → s14a000a022
  169. CircleSector(AC / test14, AV022 / ver, AV045) → s14a022a045
  170. CircleSector(AC / test14, AV045 / ver, AV067) → s14a045a067
  171. CircleSector(AC / test14, AV067 / ver, AV090) → s14a067a090
  172. CircleSector(AC / test14, AV090 / ver, AV112) → s14a090a112
  173. CircleSector(AC / test14, AV112 / ver, AV135) → s14a112a135
  174. CircleSector(AC / test14, AV135 / ver, AV157) → s14a135a157
  175. CircleSector(AC / test14, AV157 / ver, AV180) → s14a157a180
  176. CircleSector(AC / test14, AV180 / ver, AV202) → s14a180a202
  177. CircleSector(AC / test14, AV202 / ver, AV225) → s14a202a225
  178. CircleSector(AC / test14, AV225 / ver, AV247) → s14a225a247
  179. CircleSector(AC / test14, AV247 / ver, AV270) → s14a247a270
  180. CircleSector(AC / test14, AV270 / ver, AV292) → s14a270a292
  181. CircleSector(AC / test14, AV292 / ver, AV315) → s14a292a315
  182. CircleSector(AC / test14, AV315 / ver, AV337) → s14a315a337
  183. CircleSector(AC / test14, AV337 / ver, AV) → s14a337a360
  184. CircleSector(AC / test15, AV / ver, AV060) → s15a000a060
  185. CircleSector(AC / test15, AV060 / ver, AV120) → s15a060a120
  186. CircleSector(AC / test15, AV120 / ver, AV180) → s15a120a180
  187. CircleSector(AC / test15, AV180 / ver, AV240) → s15a180a240
  188. CircleSector(AC / test15, AV240 / ver, AV300) → s15a240a300
  189. CircleSector(AC / test15, AV300 / ver, AV) → s15a300a360
  190. CircleSector(AC / test16, AV / ver, AV036) → s16a000a036
  191. CircleSector(AC / test16, AV036 / ver, AV072) → s16a036a072
  192. CircleSector(AC / test16, AV072 / ver, AV108) → s16a072a108
  193. CircleSector(AC / test16, AV108 / ver, AV144) → s16a108a144
  194. CircleSector(AC / test16, AV144 / ver, AV180) → s16a144a180
  195. CircleSector(AC / test16, AV180 / ver, AV216) → s16a180a216
  196. CircleSector(AC / test16, AV216 / ver, AV252) → s16a216a252
  197. CircleSector(AC / test16, AV252 / ver, AV288) → s16a252a288
  198. CircleSector(AC / test16, AV288 / ver, AV324) → s16a288a324
  199. CircleSector(AC / test16, AV324 / ver, AV) → s16a324a360
  200. CircleSector(AC / test17, AV / ver, AV060) → s17a000a060
  201. CircleSector(AC / test17, AV060 / ver, AV120) → s17a000a120
  202. CircleSector(AC / test17, AV120 / ver, AV180) → s17a120a180
  203. CircleSector(AC / test17, AV180 / ver, AV240) → s17a180a240
  204. CircleSector(AC / test17, AV240 / ver, AV300) → s17a240a300
  205. CircleSector(AC / test17, AV300 / ver, AV) → s17a300a360
  206. CircleSector(AC / test18, AV / ver, AV045) → s18a000a045
  207. CircleSector(AC / test18, AV045 / ver, AV090) → s18a045a090
  208. CircleSector(AC / test18, AV090 / ver, AV135) → s18a090a135
  209. CircleSector(AC / test18, AV135 / ver, AV180) → s18a135a180
  210. CircleSector(AC / test18, AV180 / ver, AV225) → s18a180a225
  211. CircleSector(AC / test18, AV225 / ver, AV270) → s18a225a270
  212. CircleSector(AC / test18, AV270 / ver, AV315) → s18a270a315
  213. CircleSector(AC / test18, AV315 / ver, AV) → s18a315a360
  214. CircleSector(AC / test19, AV / ver, AV030) → s19a000a030
  215. CircleSector(AC / test19, AV030 / ver, AV060) → s19a030a060
  216. CircleSector(AC / test19, AV060 / ver, AV090) → s19a060a090
  217. CircleSector(AC / test19, AV090 / ver, AV120) → s19a090a120
  218. CircleSector(AC / test19, AV120 / ver, AV150) → s19a120a150
  219. CircleSector(AC / test19, AV150 / ver, AV180) → s19a150a180
  220. CircleSector(AC / test19, AV180 / ver, AV210) → s19a180a210
  221. CircleSector(AC / test19, AV210 / ver, AV240) → s19a210a240
  222. CircleSector(AC / test19, AV240 / ver, AV270) → s19a240a270
  223. CircleSector(AC / test19, AV270 / ver, AV300) → s19a270a300
  224. CircleSector(AC / test19, AV300 / ver, AV330) → s19a300a330
  225. CircleSector(AC / test19, AV330 / ver, AV) → s19a330a360
  226. CircleSector(AC / test20, AV / ver, AV060) → s20a000a060
  227. CircleSector(AC / test20, AV060 / ver, AV120) → s20a060a120
  228. CircleSector(AC / test20, AV120 / ver, AV180) → s20a120a180
  229. CircleSector(AC / test20, AV180 / ver, AV240) → s20a180a240
  230. CircleSector(AC / test20, AV240 / ver, AV300) → s20a240a300
  231. CircleSector(AC / test20, AV300 / ver, AV) → s20a300a360

AI Drawing Prompt Reference

The graph consists of multiple circular sectors forming a rose flower shape. First, a circle is drawn, then a line segment is rotated to various angles to intersect the circle at multiple points. Using these intersection points as sector boundaries, circular sectors are drawn to create petal-like rose flower patterns. The construction order is: draw circle, rotate line segment, then draw sectors. The graph features symmetric circular arcs, reflecting geometric symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.