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Cylinder and Torus Demo

Cylinder and Torus Demo
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2020-06-11 23:17
FunctionSolid GeometryParametric EquationGeometric ConstructionSlider Animation
This example demonstrates the geometric forms and relationships between a cylinder and a torus in 3D space. It involves core math concepts like solid geometry, parametric equations, function graphing, and geometric transformations. GeoGebra commands and objects used include Min, Sequence, Zip, Element, Segment, Midpoint, OrthogonalLine, Circle, PolyLine, CircleArc, and Angle. Suitable for high school and above students studying solid geometry, parametric equations, and spatial shapes.

GeoGebra Commands & Parameters

  1. Min(Max[betaRegularized(2, 2.3, Extend), 0.0001], 0.9999) → Animat1
  2. Sequence(O + (i, 0), i, R, R) → Pointdebut
  3. Zip(Circle[C, B, xOyPlane], B, Pointdebut) → Cercles
  4. Zip(Rotate[B, ((((360 * ° / (((2 * Radius[K]) * π))) * 2) * Distance[O, B]) * π), C], K, Cercles, B, Pointdebut) → PointFins
  5. Element(PointFins, Length[PointFins]) → B'
  6. Segment(B, B') → b
  7. Midpoint(B, B') → D
  8. OrthogonalLine(D, b, xOyPlane) → c
  9. Circle(O, R, xOyPlane) → a
  10. Segment(O, B') → g
  11. Segment(B, B') → h
  12. Sequence(Rotate[B, i, O], i, 0, 6.283185307179586, (2 * π / m)) → liste1
  13. PolyLine(Append[B, PointFins]) → ABS
  14. CircleArc(C, B, B', xOyPlane) → d
  15. Angle(B, C, B', xOyPlane) → α
  16. Sequence(Rotate[B, i, C], i, 0, α, α / m) → liste2
  17. Sequence(Vector[Element[liste2, i], Element[liste2, i + 1]], i, 1, Length[liste2]) → l1
  18. Sequence(Circle[Element[liste2, i], r, Vector[Element[l1, i]]], i, 1, Length[liste2]) → l2
  19. Circle(Element[liste2, A1], r, Vector[Element[l1, A1]]) → B1
  20. Circle(Element[liste2, A2], r, Vector[Element[l1, A2]]) → B2
  21. Circle(Element[liste2, A3], r, Vector[Element[l1, A3]]) → B3
  22. Circle(Element[liste2, A4], r, Vector[Element[l1, A4]]) → B4
  23. Circle(Element[liste2, A5], r, Vector[Element[l1, A5]]) → B5
  24. Circle(Element[liste2, A6], r, Vector[Element[l1, A6]]) → B6
  25. Circle(Element[liste2, A7], r, Vector[Element[l1, A7]]) → B7
  26. Circle(Element[liste2, A8], r, Vector[Element[l1, A8]]) → B8
  27. Circle(Element[liste2, A9], r, Vector[Element[l1, A9]]) → B9
  28. Circle(Element[liste2, A10], r, Vector[Element[l1, A10]]) → B10
  29. Circle(Element[liste2, A11], r, Vector[Element[l1, A11]]) → B11
  30. Circle(Element[liste2, A12], r, Vector[Element[l1, A12]]) → B12
  31. Circle(Element[liste2, A13], r, Vector[Element[l1, A13]]) → B13
  32. Circle(Element[liste2, A14], r, Vector[Element[l1, A14]]) → B14
  33. Circle(Element[liste2, A15], r, Vector[Element[l1, A15]]) → B15
  34. Circle(Element[liste2, A16], r, Vector[Element[l1, A16]]) → B16
  35. Circle(Element[liste2, A17], r, Vector[Element[l1, A17]]) → B17
  36. Circle(Element[liste2, A18], r, Vector[Element[l1, A18]]) → B18
  37. Circle(Element[liste2, A19], r, Vector[Element[l1, A19]]) → B19
  38. Circle(Element[liste2, A20], r, Vector[Element[l1, A20]]) → B20
  39. Circle(Element[liste2, A21], r, Vector[Element[l1, A21]]) → B21
  40. Circle(Element[liste2, A22], r, Vector[Element[l1, A22]]) → B22
  41. Circle(Element[liste2, A23], r, Vector[Element[l1, A23]]) → B23
  42. Circle(Element[liste2, A24], r, Vector[Element[l1, A24]]) → B24
  43. Circle(Element[liste2, A25], r, Vector[Element[l1, A25]]) → B25
  44. Circle(Element[liste2, A26], r, Vector[Element[l1, A26]]) → B26
  45. Circle(Element[liste2, A27], r, Vector[Element[l1, A27]]) → B27
  46. Circle(Element[liste2, A28], r, Vector[Element[l1, A28]]) → B28
  47. Circle(Element[liste2, A29], r, Vector[Element[l1, A29]]) → B29
  48. Circle(Element[liste2, A30], r, Vector[Element[l1, A30]]) → B30
  49. Circle(Element[liste2, A31], r, Vector[Element[l1, A31]]) → B31
  50. Circle(Element[liste2, A32], r, Vector[Element[l1, A32]]) → B32
  51. Circle(Element[liste2, A33], r, Vector[Element[l1, A33]]) → B33
  52. Circle(Element[liste2, A34], r, Vector[Element[l1, A34]]) → B34
  53. Circle(Element[liste2, A35], r, Vector[Element[l1, A35]]) → B35
  54. Circle(Element[liste2, A36], r, Vector[Element[l1, A36]]) → B36
  55. Circle(Element[liste2, A37], r, Vector[Element[l1, A37]]) → B37
  56. Circle(Element[liste2, A38], r, Vector[Element[l1, A38]]) → B38
  57. Circle(Element[liste2, A39], r, Vector[Element[l1, A39]]) → B39
  58. Circle(Element[liste2, A40], r, Vector[Element[l1, A40]]) → B40
  59. Circle(Element[liste2, A41], r, Vector[Element[l1, A41]]) → B41
  60. Circle(Element[liste2, A42], r, Vector[Element[l1, A42]]) → B42
  61. Circle(Element[liste2, A43], r, Vector[Element[l1, A43]]) → B43
  62. Circle(Element[liste2, A44], r, Vector[Element[l1, A44]]) → B44
  63. Circle(Element[liste2, A45], r, Vector[Element[l1, A45]]) → B45
  64. Circle(Element[liste2, A46], r, Vector[Element[l1, A46]]) → B46
  65. Circle(Element[liste2, A47], r, Vector[Element[l1, A47]]) → B47
  66. Circle(Element[liste2, A48], r, Vector[Element[l1, A48]]) → B48
  67. Circle(Element[liste2, A49], r, Vector[Element[l1, A49]]) → B49
  68. Circle(Element[liste2, A50], r, Vector[Element[l1, A50]]) → B50
  69. Circle(Element[liste2, A51], r, Vector[Element[l1, A51]]) → B51
  70. Circle(Element[liste2, A52], r, Vector[Element[l1, A52]]) → B52
  71. Circle(Element[liste2, A53], r, Vector[Element[l1, A53]]) → B53
  72. Circle(Element[liste2, A54], r, Vector[Element[l1, A54]]) → B54
  73. Circle(Element[liste2, A55], r, Vector[Element[l1, A55]]) → B55
  74. Circle(Element[liste2, A56], r, Vector[Element[l1, A56]]) → B56
  75. Circle(Element[liste2, A57], r, Vector[Element[l1, A57]]) → B57
  76. Circle(Element[liste2, A58], r, Vector[Element[l1, A58]]) → B58
  77. Circle(Element[liste2, A59], r, Vector[Element[l1, A59]]) → B59
  78. Circle(Element[liste2, A60], r, Vector[Element[l1, A60]]) → B60
  79. Circle(Element[liste2, A61], r, Vector[Element[l1, A61]]) → B61
  80. Circle(Element[liste2, A62], r, Vector[Element[l1, A62]]) → B62
  81. Circle(Element[liste2, A63], r, Vector[Element[l1, A63]]) → B63
  82. Circle(Element[liste2, A64], r, Vector[Element[l1, A64]]) → B64
  83. Circle(Element[liste2, A65], r, Vector[Element[l1, A65]]) → B65
  84. Circle(Element[liste2, A66], r, Vector[Element[l1, A66]]) → B66
  85. Circle(Element[liste2, A67], r, Vector[Element[l1, A67]]) → B67
  86. Circle(Element[liste2, A68], r, Vector[Element[l1, A68]]) → B68
  87. Circle(Element[liste2, A69], r, Vector[Element[l1, A69]]) → B69
  88. Circle(Element[liste2, A70], r, Vector[Element[l1, A70]]) → B70
  89. Circle(Element[liste2, A71], r, Vector[Element[l1, A71]]) → B71
  90. Circle(Element[liste2, A72], r, Vector[Element[l1, A72]]) → B72
  91. Circle(Element[liste2, A73], r, Vector[Element[l1, A73]]) → B73
  92. Circle(Element[liste2, A74], r, Vector[Element[l1, A74]]) → B74
  93. Circle(Element[liste2, A75], r, Vector[Element[l1, A75]]) → B75
  94. Circle(Element[liste2, A76], r, Vector[Element[l1, A76]]) → B76
  95. Circle(Element[liste2, A77], r, Vector[Element[l1, A77]]) → B77
  96. Circle(Element[liste2, A78], r, Vector[Element[l1, A78]]) → B78
  97. Circle(Element[liste2, A79], r, Vector[Element[l1, A79]]) → B79
  98. Circle(Element[liste2, A80], r, Vector[Element[l1, A80]]) → B80
  99. Circle(Element[liste2, A81], r, Vector[Element[l1, A81]]) → B81
  100. Circle(Element[liste2, A82], r, Vector[Element[l1, A82]]) → B82
  101. Circle(Element[liste2, A83], r, Vector[Element[l1, A83]]) → B83
  102. Circle(Element[liste2, A84], r, Vector[Element[l1, A84]]) → B84
  103. Circle(Element[liste2, A85], r, Vector[Element[l1, A85]]) → B85
  104. Circle(Element[liste2, A86], r, Vector[Element[l1, A86]]) → B86
  105. Circle(Element[liste2, A87], r, Vector[Element[l1, A87]]) → B87
  106. Circle(Element[liste2, A88], r, Vector[Element[l1, A88]]) → B88
  107. Circle(Element[liste2, A89], r, Vector[Element[l1, A89]]) → B89
  108. Circle(Element[liste2, A90], r, Vector[Element[l1, A90]]) → B90
  109. Circle(Element[liste2, A91], r, Vector[Element[l1, A91]]) → B91
  110. Circle(Element[liste2, A92], r, Vector[Element[l1, A92]]) → B92
  111. Circle(Element[liste2, A93], r, Vector[Element[l1, A93]]) → B93
  112. Circle(Element[liste2, A94], r, Vector[Element[l1, A94]]) → B94
  113. Circle(Element[liste2, A95], r, Vector[Element[l1, A95]]) → B95
  114. Circle(Element[liste2, A96], r, Vector[Element[l1, A96]]) → B96
  115. Circle(Element[liste2, A97], r, Vector[Element[l1, A97]]) → B97
  116. Circle(Element[liste2, A98], r, Vector[Element[l1, A98]]) → B98
  117. Circle(Element[liste2, A99], r, Vector[Element[l1, A99]]) → B99
  118. Circle(Element[liste2, A100], r, Vector[Element[l1, A100]]) → B100
  119. Circle(Element[liste2, A101], r, Vector[Element[l1, A101]]) → B101
  120. Circle(Element[liste2, A102], r, Vector[Element[l1, A102]]) → B102
  121. Circle(Element[liste2, A103], r, Vector[Element[l1, A103]]) → B103
  122. Circle(Element[liste2, A104], r, Vector[Element[l1, A104]]) → B104
  123. Circle(Element[liste2, A105], r, Vector[Element[l1, A105]]) → B105
  124. Circle(Element[liste2, A106], r, Vector[Element[l1, A106]]) → B106
  125. Circle(Element[liste2, A107], r, Vector[Element[l1, A107]]) → B107
  126. Circle(Element[liste2, A108], r, Vector[Element[l1, A108]]) → B108
  127. Circle(Element[liste2, A109], r, Vector[Element[l1, A109]]) → B109
  128. Circle(Element[liste2, A110], r, Vector[Element[l1, A110]]) → B110
  129. Circle(Element[liste2, A111], r, Vector[Element[l1, A111]]) → B111
  130. Circle(Element[liste2, A112], r, Vector[Element[l1, A112]]) → B112
  131. Circle(Element[liste2, A113], r, Vector[Element[l1, A113]]) → B113
  132. Circle(Element[liste2, A114], r, Vector[Element[l1, A114]]) → B114
  133. Circle(Element[liste2, A115], r, Vector[Element[l1, A115]]) → B115
  134. Circle(Element[liste2, A116], r, Vector[Element[l1, A116]]) → B116
  135. Circle(Element[liste2, A117], r, Vector[Element[l1, A117]]) → B117
  136. Circle(Element[liste2, A118], r, Vector[Element[l1, A118]]) → B118
  137. Circle(Element[liste2, A119], r, Vector[Element[l1, A119]]) → B119
  138. Circle(Element[liste2, A120], r, Vector[Element[l1, A120]]) → B120
  139. Circle(Element[liste2, A121], r, Vector[Element[l1, A121]]) → B121
  140. Circle(Element[liste2, A122], r, Vector[Element[l1, A122]]) → B122
  141. Circle(Element[liste2, A123], r, Vector[Element[l1, A123]]) → B123
  142. Circle(Element[liste2, A124], r, Vector[Element[l1, A124]]) → B124
  143. Circle(Element[liste2, A125], r, Vector[Element[l1, A125]]) → B125
  144. Circle(Element[liste2, A126], r, Vector[Element[l1, A126]]) → B126
  145. Circle(Element[liste2, A127], r, Vector[Element[l1, A127]]) → B127
  146. Circle(Element[liste2, A128], r, Vector[Element[l1, A128]]) → B128
  147. Circle(Element[liste2, A129], r, Vector[Element[l1, A129]]) → B129
  148. Circle(Element[liste2, A130], r, Vector[Element[l1, A130]]) → B130
  149. Circle(Element[liste2, A131], r, Vector[Element[l1, A131]]) → B131
  150. Circle(Element[liste2, A132], r, Vector[Element[l1, A132]]) → B132
  151. Circle(Element[liste2, A133], r, Vector[Element[l1, A133]]) → B133
  152. Circle(Element[liste2, A134], r, Vector[Element[l1, A134]]) → B134
  153. Circle(Element[liste2, A135], r, Vector[Element[l1, A135]]) → B135
  154. Circle(Element[liste2, A136], r, Vector[Element[l1, A136]]) → B136
  155. Circle(Element[liste2, A137], r, Vector[Element[l1, A137]]) → B137
  156. Circle(Element[liste2, A138], r, Vector[Element[l1, A138]]) → B138
  157. Circle(Element[liste2, A139], r, Vector[Element[l1, A139]]) → B139
  158. Circle(Element[liste2, A140], r, Vector[Element[l1, A140]]) → B140
  159. Circle(Element[liste2, A141], r, Vector[Element[l1, A141]]) → B141
  160. Circle(Element[liste2, A142], r, Vector[Element[l1, A142]]) → B142
  161. Circle(Element[liste2, A143], r, Vector[Element[l1, A143]]) → B143
  162. Circle(Element[liste2, A144], r, Vector[Element[l1, A144]]) → B144
  163. Circle(Element[liste2, A145], r, Vector[Element[l1, A145]]) → B145
  164. Circle(Element[liste2, A146], r, Vector[Element[l1, A146]]) → B146
  165. Circle(Element[liste2, A147], r, Vector[Element[l1, A147]]) → B147
  166. Circle(Element[liste2, A148], r, Vector[Element[l1, A148]]) → B148
  167. Circle(Element[liste2, A149], r, Vector[Element[l1, A149]]) → B149
  168. Circle(Element[liste2, A150], r, Vector[Element[l1, A150]]) → B150

AI Drawing Prompt Reference

Draw a cylinder and a torus in 3D space to demonstrate their geometric forms and relationships. Start by creating a circle and rotate it around an axis to form the lateral surface of the cylinder. Then, use these circles as a base to generate the torus shape through rotation and connection. Finally, outline the cylinder and torus, and label key points and angles to clearly show their geometric construction and mutual relationships.
The prompt above was compiled from the original drawing commands and is for reference only.