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乘法表互动演示：从自然数乘法到函数与几何的融合

乘法表互动演示：从自然数乘法到函数与几何的融合
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2020-07-27 18:45
多边形角函数数列函数图像
该范例通过GeoGebra构建了一个交互式乘法表（Tabliczka mnożenia），直观展示自然数乘法运算结果在网格中的分布规律。核心数学概念包括自然数乘法、数列生成、整除与取模运算，以及通过分段函数和单位圆等元素将算术与几何、微积分初步概念联系起来。作图要点包括使用Product、Sequence、Segment、Polygon等命令生成乘法表网格和线段，利用If、Unique、Join、Element、Div、Mod等命令处理数据与条件逻辑，并通过Text、klawisz（按钮）和滑块实现动态交互。适合小学高年级至初中学生理解乘法表结构，也可作为高中阶段探讨函数图像、角度与单位圆关系的拓展素材，兼具教学演示与探索功能。

GeoGebra 命令及参数

  1. Product(lista4) → l
  2. If(Element[lista1, 5] ≠ Element[lista2, 5], 60 - Element[lista1, 2] + Element[lista2, 2], (3600 * (Element[lista2, 4] - Element[lista1, 4])) + (60 * (Element[lista2, 3] - Element[lista1, 3])) + Element[lista2, 2] - Element[lista1, 2]) → b
  3. If(b > 10, 0, 10 - b) → c
  4. Unique(Join[Sequence[Sequence[(i * j), j, 1, 10], i, 1, 10]]) → lista3
  5. Join(Sequence[Sequence[{i, j}, j, 1, 10], i, 1, 10]) → m1
  6. Segment(A, C) → d
  7. Segment(B, D) → e
  8. Sequence(Segment[((10 - i) / 10 * A) + (i / 10 * C), ((10 - i) / 10 * B) + (i / 10 * D)], i, 0, 10) → lista5
  9. Element(lista3, A1) → B1
  10. Element(lista3, A2) → B2
  11. Element(lista3, A3) → B3
  12. Element(lista3, A4) → B4
  13. Element(lista3, A5) → B5
  14. Element(lista3, A6) → B6
  15. Element(lista3, A7) → B7
  16. Element(lista3, A8) → B8
  17. Element(lista3, A9) → B9
  18. Element(lista3, A10) → B10
  19. Element(lista3, A11) → B11
  20. Element(lista3, A12) → B12
  21. Element(lista3, A13) → B13
  22. Element(lista3, A14) → B14
  23. Element(lista3, A15) → B15
  24. Element(lista3, A16) → B16
  25. Element(lista3, A17) → B17
  26. Element(lista3, A18) → B18
  27. Element(lista3, A19) → B19
  28. Element(lista3, A20) → B20
  29. Element(lista3, A21) → B21
  30. Element(lista3, A22) → B22
  31. Element(lista3, A23) → B23
  32. Element(lista3, A24) → B24
  33. Element(lista3, A25) → B25
  34. Element(lista3, A26) → B26
  35. Element(lista3, A27) → B27
  36. Element(lista3, A28) → B28
  37. Element(lista3, A29) → B29
  38. Element(lista3, A30) → B30
  39. Element(lista3, A31) → B31
  40. Element(lista3, A32) → B32
  41. Element(lista3, A33) → B33
  42. Element(lista3, A34) → B34
  43. Element(lista3, A35) → B35
  44. Element(lista3, A36) → B36
  45. Element(lista3, A37) → B37
  46. Element(lista3, A38) → B38
  47. Element(lista3, A39) → B39
  48. Element(lista3, A40) → B40
  49. Element(lista3, A41) → B41
  50. Element(lista3, A42) → B42
  51. Div(A1 - 1, 7) → C1
  52. Div(A2 - 1, 7) → C2
  53. Div(A3 - 1, 7) → C3
  54. Div(A4 - 1, 7) → C4
  55. Div(A5 - 1, 7) → C5
  56. Div(A6 - 1, 7) → C6
  57. Div(A7 - 1, 7) → C7
  58. Div(A8 - 1, 7) → C8
  59. Div(A9 - 1, 7) → C9
  60. Div(A10 - 1, 7) → C10
  61. Div(A11 - 1, 7) → C11
  62. Div(A12 - 1, 7) → C12
  63. Div(A13 - 1, 7) → C13
  64. Div(A14 - 1, 7) → C14
  65. Div(A15 - 1, 7) → C15
  66. Div(A16 - 1, 7) → C16
  67. Div(A17 - 1, 7) → C17
  68. Div(A18 - 1, 7) → C18
  69. Div(A19 - 1, 7) → C19
  70. Div(A20 - 1, 7) → C20
  71. Div(A21 - 1, 7) → C21
  72. Div(A22 - 1, 7) → C22
  73. Div(A23 - 1, 7) → C23
  74. Div(A24 - 1, 7) → C24
  75. Div(A25 - 1, 7) → C25
  76. Div(A26 - 1, 7) → C26
  77. Div(A27 - 1, 7) → C27
  78. Div(A28 - 1, 7) → C28
  79. Div(A29 - 1, 7) → C29
  80. Div(A30 - 1, 7) → C30
  81. Div(A31 - 1, 7) → C31
  82. Div(A32 - 1, 7) → C32
  83. Div(A33 - 1, 7) → C33
  84. Div(A34 - 1, 7) → C34
  85. Div(A35 - 1, 7) → C35
  86. Div(A36 - 1, 7) → C36
  87. Div(A37 - 1, 7) → C37
  88. Div(A38 - 1, 7) → C38
  89. Div(A39 - 1, 7) → C39
  90. Div(A40 - 1, 7) → C40
  91. Div(A41 - 1, 7) → C41
  92. Div(A42 - 1, 7) → C42
  93. Mod(A1 - 1, 7) → D1
  94. Mod(A2 - 1, 7) → D2
  95. Mod(A3 - 1, 7) → D3
  96. Mod(A4 - 1, 7) → D4
  97. Mod(A5 - 1, 7) → D5
  98. Mod(A6 - 1, 7) → D6
  99. Mod(A7 - 1, 7) → D7
  100. Mod(A8 - 1, 7) → D8
  101. Mod(A9 - 1, 7) → D9
  102. Mod(A10 - 1, 7) → D10
  103. Mod(A11 - 1, 7) → D11
  104. Mod(A12 - 1, 7) → D12
  105. Mod(A13 - 1, 7) → D13
  106. Mod(A14 - 1, 7) → D14
  107. Mod(A15 - 1, 7) → D15
  108. Mod(A16 - 1, 7) → D16
  109. Mod(A17 - 1, 7) → D17
  110. Mod(A18 - 1, 7) → D18
  111. Mod(A19 - 1, 7) → D19
  112. Mod(A20 - 1, 7) → D20
  113. Mod(A21 - 1, 7) → D21
  114. Mod(A22 - 1, 7) → D22
  115. Mod(A23 - 1, 7) → D23
  116. Mod(A24 - 1, 7) → D24
  117. Mod(A25 - 1, 7) → D25
  118. Mod(A26 - 1, 7) → D26
  119. Mod(A27 - 1, 7) → D27
  120. Mod(A28 - 1, 7) → D28
  121. Mod(A29 - 1, 7) → D29
  122. Mod(A30 - 1, 7) → D30
  123. Mod(A31 - 1, 7) → D31
  124. Mod(A32 - 1, 7) → D32
  125. Mod(A33 - 1, 7) → D33
  126. Mod(A34 - 1, 7) → D34
  127. Mod(A35 - 1, 7) → D35
  128. Mod(A36 - 1, 7) → D36
  129. Mod(A37 - 1, 7) → D37
  130. Mod(A38 - 1, 7) → D38
  131. Mod(A39 - 1, 7) → D39
  132. Mod(A40 - 1, 7) → D40
  133. Mod(A41 - 1, 7) → D41
  134. Mod(A42 - 1, 7) → D42
  135. Text(B1, E1, true, true) → F1
  136. Text(B2, E2, true, true) → F2
  137. Text(B3, E3, true, true) → F3
  138. Text(B4, E4, true, true) → F4
  139. Text(B5, E5, true, true) → F5
  140. Text(B6, E6, true, true) → F6
  141. Text(B7, E7, true, true) → F7
  142. Text(B8, E8, true, true) → F8
  143. Text(B9, E9, true, true) → F9
  144. Text(B10, E10, true, true) → F10
  145. Text(B11, E11, true, true) → F11
  146. Text(B12, E12, true, true) → F12
  147. Text(B13, E13, true, true) → F13
  148. Text(B14, E14, true, true) → F14
  149. Text(B15, E15, true, true) → F15
  150. Text(B16, E16, true, true) → F16
  151. Text(B17, E17, true, true) → F17
  152. Text(B18, E18, true, true) → F18
  153. Text(B19, E19, true, true) → F19
  154. Text(B20, E20, true, true) → F20
  155. Text(B21, E21, true, true) → F21
  156. Text(B22, E22, true, true) → F22
  157. Text(B23, E23, true, true) → F23
  158. Text(B24, E24, true, true) → F24
  159. Text(B25, E25, true, true) → F25
  160. Text(B26, E26, true, true) → F26
  161. Text(B27, E27, true, true) → F27
  162. Text(B28, E28, true, true) → F28
  163. Text(B29, E29, true, true) → F29
  164. Text(B30, E30, true, true) → F30
  165. Text(B31, E31, true, true) → F31
  166. Text(B32, E32, true, true) → F32
  167. Text(B33, E33, true, true) → F33
  168. Text(B34, E34, true, true) → F34
  169. Text(B35, E35, true, true) → F35
  170. Text(B36, E36, true, true) → F36
  171. Text(B37, E37, true, true) → F37
  172. Text(B38, E38, true, true) → F38
  173. Text(B39, E39, true, true) → F39
  174. Text(B40, E40, true, true) → F40
  175. Text(B41, E41, true, true) → F41
  176. Text(B42, E42, true, true) → F42
  177. Text(B1, G1, true, true) → H1
  178. Text(B2, G2, true, true) → H2
  179. Text(B3, G3, true, true) → H3
  180. Text(B4, G4, true, true) → H4
  181. Text(B5, G5, true, true) → H5
  182. Text(B6, G6, true, true) → H6
  183. Text(B7, G7, true, true) → H7
  184. Text(B8, G8, true, true) → H8
  185. Text(B9, G9, true, true) → H9
  186. Text(B10, G10, true, true) → H10
  187. Text(B11, G11, true, true) → H11
  188. Text(B12, G12, true, true) → H12
  189. Text(B13, G13, true, true) → H13
  190. Text(B14, G14, true, true) → H14
  191. Text(B15, G15, true, true) → H15
  192. Text(B16, G16, true, true) → H16
  193. Text(B17, G17, true, true) → H17
  194. Text(B18, G18, true, true) → H18
  195. Text(B19, G19, true, true) → H19
  196. Text(B20, G20, true, true) → H20
  197. Text(B21, G21, true, true) → H21
  198. Text(B22, G22, true, true) → H22
  199. Text(B23, G23, true, true) → H23
  200. Text(B24, G24, true, true) → H24
  201. Text(B25, G25, true, true) → H25
  202. Text(B26, G26, true, true) → H26
  203. Text(B27, G27, true, true) → H27
  204. Text(B28, G28, true, true) → H28
  205. Text(B29, G29, true, true) → H29
  206. Text(B30, G30, true, true) → H30
  207. Text(B31, G31, true, true) → H31
  208. Text(B32, G32, true, true) → H32
  209. Text(B33, G33, true, true) → H33
  210. Text(B34, G34, true, true) → H34
  211. Text(B35, G35, true, true) → H35
  212. Text(B36, G36, true, true) → H36
  213. Text(B37, G37, true, true) → H37
  214. Text(B38, G38, true, true) → H38
  215. Text(B39, G39, true, true) → H39
  216. Text(B40, G40, true, true) → H40
  217. Text(B41, G41, true, true) → H41
  218. Text(B42, G42, true, true) → H42
  219. klawisz(E1) → I1
  220. klawisz(E2) → I2
  221. klawisz(E3) → I3
  222. klawisz(E4) → I4
  223. klawisz(E5) → I5
  224. klawisz(E6) → I6
  225. klawisz(E7) → I7
  226. klawisz(E8) → I8
  227. klawisz(E9) → I9
  228. klawisz(E10) → I10
  229. klawisz(E11) → I11
  230. klawisz(E12) → I12
  231. klawisz(E13) → I13
  232. klawisz(E14) → I14
  233. klawisz(E15) → I15
  234. klawisz(E16) → I16
  235. klawisz(E17) → I17
  236. klawisz(E18) → I18
  237. klawisz(E19) → I19
  238. klawisz(E20) → I20
  239. klawisz(E21) → I21
  240. klawisz(E22) → I22
  241. klawisz(E23) → I23
  242. klawisz(E24) → I24
  243. klawisz(E25) → I25
  244. klawisz(E26) → I26
  245. klawisz(E27) → I27
  246. klawisz(E28) → I28
  247. klawisz(E29) → I29
  248. klawisz(E30) → I30
  249. klawisz(E31) → I31
  250. klawisz(E32) → I32
  251. klawisz(E33) → I33
  252. klawisz(E34) → I34
  253. klawisz(E35) → I35
  254. klawisz(E36) → I36
  255. klawisz(E37) → I37
  256. klawisz(E38) → I38
  257. klawisz(E39) → I39
  258. klawisz(E40) → I40
  259. klawisz(E41) → I41
  260. klawisz(E42) → I42
  261. Polygon(K1, L1, L2, K2) → M1, N1, O1, P1, Q1
  262. Polygon(K2, L2, L3, K3) → M2, N2, O2, P2, Q2
  263. Polygon(K3, L3, L4, K4) → M3, N3, O3, P3, Q3
  264. Polygon(K4, L4, L5, K5) → M4, N4, O4, P4, Q4
  265. Polygon(K5, L5, L6, K6) → M5, N5, O5, P5, Q5
  266. Polygon(K6, L6, L7, K7) → M6, N6, O6, P6, Q6
  267. Polygon(K7, L7, L8, K8) → M7, N7, O7, P7, Q7
  268. Polygon(K8, L8, L9, K9) → M8, N8, O8, P8, Q8
  269. Polygon(K9, L9, L10, K10) → M9, N9, O9, P9, Q9
  270. Polygon(K10, L10, L11, K11) → M10, N10, O10, P10, Q10

AI 绘图提示语参考

绘制一个10x10的乘法表，每个格子显示两个数相乘的结果。使用角度和单位圆展示乘法表中的模式，通过动态网格和条件逻辑，改变角度和颜色来表示不同的乘积。
以上提示语为根据原始绘图命令整理而来，仅供参考。