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代数瓷砖 by Duane Habecker

代数瓷砖 by Duane Habecker
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2017-01-07 12:21
解析几何几何作图
使用代数瓷砖来乘以二项式。通过点击瓷砖来切换正负状态。本例演示了二项式乘法的概念，涉及的核心数学概念包括代数和多项式。构造摘要中使用了Random, Circle, Point, Polygon, Segment, OrthogonalLine, Intersect, Line, Ray等GeoGebra命令/对象。适合初中及以上学生学习代数。

GeoGebra 命令及参数

  1. Random(-2, 2) → c
  2. Circle(A_1, tilewidth) → c_1
  3. Point(c_1) → B_1
  4. Polygon(B_1, A_1, 4) → Unit2, f_1, g_1, h_1, i_1, C_1, D_1
  5. Circle(A_2, tilewidth) → c_2
  6. Point(c_2) → B_2
  7. Polygon(B_2, A_2, 4) → Unit4, f_2, g_2, h_2, i_2, C_2, D_2
  8. Circle(A_3, tilewidth) → c_3
  9. Point(c_3) → B_3
  10. Polygon(B_3, A_3, 4) → Unit5, f_3, g_3, h_3, i_3, C_3, D_3
  11. Circle(A_4, tilewidth) → c_4
  12. Point(c_4) → B_4
  13. Polygon(B_4, A_4, 4) → Unit3, f_4, g_4, h_4, i_4, C_4, D_4
  14. Circle(A_5, tilewidth) → c_5
  15. Point(c_5) → B_5
  16. Polygon(B_5, A_5, 4) → Unit6, f_5, g_5, h_5, i_5, C_5, D_5
  17. Circle(A_6, tilewidth) → c_6
  18. Point(c_6) → B_6
  19. Polygon(B_6, A_6, 4) → Unit7, f_6, g_6, h_6, i_6, C_6, D_6
  20. Circle(A_7, tilewidth) → c_7
  21. Point(c_7) → B_7
  22. Polygon(B_7, A_7, 4) → Unit8, f_7, g_7, h_7, i_7, C_7, D_7
  23. Circle(A_8, tilewidth) → c_8
  24. Point(c_8) → B_8
  25. Polygon(B_8, A_8, 4) → Unit9, f_8, g_8, h_8, i_8, C_8, D_8
  26. Circle(A_9, tilewidth) → c_9
  27. Point(c_9) → B_9
  28. Polygon(B_9, A_9, 4) → Unit10, f_9, g_9, h_9, i_9, C_9, D_9
  29. Circle(A_{10}, tilewidth) → c_{10}
  30. Point(c_{10}) → B_{10}
  31. Polygon(B_{10}, A_{10}, 4) → Unit11, f_{10}, g_{10}, h_{10}, i_{10}, C_{10}, D_{10}
  32. Circle(A_{11}, tilewidth) → c_{11}
  33. Point(c_{11}) → B_{11}
  34. Polygon(B_{11}, A_{11}, 4) → Unit12, f_{11}, g_{11}, h_{11}, i_{11}, C_{11}, D_{11}
  35. Circle(A_{12}, tilewidth) → c_{12}
  36. Point(c_{12}) → B_{12}
  37. Polygon(B_{12}, A_{12}, 4) → Unit13, f_{12}, g_{12}, h_{12}, i_{12}, C_{12}, D_{12}
  38. Circle(A_{13}, tilewidth) → c_{13}
  39. Point(c_{13}) → B_{13}
  40. Polygon(B_{13}, A_{13}, 4) → Unit14, f_{13}, g_{13}, h_{13}, i_{13}, C_{13}, D_{13}
  41. Circle(A_{14}, tilewidth) → c_{14}
  42. Point(c_{14}) → B_{14}
  43. Polygon(B_{14}, A_{14}, 4) → Unit15, f_{14}, g_{14}, h_{14}, i_{14}, C_{14}, D_{14}
  44. Circle(A_{15}, tilewidth) → c_{15}
  45. Point(c_{15}) → B_{15}
  46. Polygon(B_{15}, A_{15}, 4) → Unit16, f_{15}, g_{15}, h_{15}, i_{15}, C_{15}, D_{15}
  47. Circle(A_{16}, tilewidth) → c_{16}
  48. Point(c_{16}) → B_{16}
  49. Polygon(B_{16}, A_{16}, 4) → Unit17, f_{16}, g_{16}, h_{16}, i_{16}, C_{16}, D_{16}
  50. Circle(A_{17}, tilewidth) → c_{17}
  51. Point(c_{17}) → B_{17}
  52. Polygon(B_{17}, A_{17}, 4) → Unit18, f_{17}, g_{17}, h_{17}, i_{17}, C_{17}, D_{17}
  53. Random(1, 4) → d
  54. Segment(E, F) → j
  55. Random(1, 3) → e
  56. OrthogonalLine(F, j) → k
  57. Intersect(e, k, 2) → G
  58. Line(E, k) → l
  59. OrthogonalLine(G, l) → m
  60. Intersect(l, m) → H
  61. Polygon(E, F, G, H) → Xrod01, e_1, f_{18}, g_{18}, h_{18}
  62. Circle(E_1, tilewidth) → d_1
  63. Point(d_1) → F_1
  64. Segment(E_1, F_1) → j_1
  65. OrthogonalLine(F_1, j_1) → k_1
  66. Circle(F_1, (2.5 * tilewidth)) → e_2
  67. Intersect(e_2, k_1, 2) → G_1
  68. Line(E_1, k_1) → l_1
  69. OrthogonalLine(G_1, l_1) → m_1
  70. Intersect(l_1, m_1) → H_1
  71. Polygon(E_1, F_1, G_1, H_1) → Xrod02, e_3, f_{19}, g_{19}, h_{19}
  72. Circle(E_2, tilewidth) → d_2
  73. Point(d_2) → F_2
  74. Segment(E_2, F_2) → j_2
  75. OrthogonalLine(F_2, j_2) → k_2
  76. Circle(F_2, (2.5 * tilewidth)) → e_5
  77. Intersect(e_5, k_2, 2) → G_2
  78. Line(E_2, k_2) → l_2
  79. OrthogonalLine(G_2, l_2) → m_2
  80. Intersect(l_2, m_2) → H_2
  81. Polygon(E_2, F_2, G_2, H_2) → Xrod03, e_4, f_{20}, g_{20}, h_{20}
  82. Circle(E_4, tilewidth) → d_4
  83. Point(d_4) → F_3
  84. Segment(E_4, F_3) → j_3
  85. OrthogonalLine(F_3, j_3) → k_3
  86. Circle(F_3, (2.5 * tilewidth)) → e_7
  87. Intersect(e_7, k_3, 2) → G_3
  88. Line(E_4, k_3) → l_3
  89. OrthogonalLine(G_3, l_3) → m_3
  90. Intersect(l_3, m_3) → H_3
  91. Polygon(E_4, F_3, G_3, H_3) → Xrod04, e_6, f_{21}, g_{21}, h_{21}
  92. Circle(E_5, tilewidth) → d_5
  93. Point(d_5) → F_4
  94. Segment(E_5, F_4) → j_4
  95. OrthogonalLine(F_4, j_4) → k_4
  96. Circle(F_4, (2.5 * tilewidth)) → e_{10}
  97. Intersect(e_{10}, k_4, 2) → G_5
  98. Line(E_5, k_4) → l_4
  99. OrthogonalLine(G_5, l_4) → m_4
  100. Intersect(l_4, m_4) → H_5
  101. Polygon(E_5, F_4, G_5, H_5) → Xrod05, e_8, f_{22}, g_{22}, h_{22}
  102. Circle(E_6, tilewidth) → d_6
  103. Point(d_6) → F_5
  104. Segment(E_6, F_5) → j_5
  105. OrthogonalLine(F_5, j_5) → k_5
  106. Circle(F_5, (2.5 * tilewidth)) → e_{11}
  107. Intersect(e_{11}, k_5, 2) → G_4
  108. Line(E_6, k_5) → l_5
  109. OrthogonalLine(G_4, l_5) → m_5
  110. Intersect(l_5, m_5) → H_4
  111. Polygon(E_6, F_5, G_4, H_4) → Xrod06, e_9, f_{23}, g_{23}, h_{23}
  112. Circle(E_7, tilewidth) → d_7
  113. Point(d_7) → F_6
  114. Segment(E_7, F_6) → j_6
  115. OrthogonalLine(F_6, j_6) → k_6
  116. Circle(F_6, (2.5 * tilewidth)) → e_{16}
  117. Intersect(e_{16}, k_6, 2) → G_9
  118. Line(E_7, k_6) → l_6
  119. OrthogonalLine(G_9, l_6) → m_6
  120. Intersect(l_6, m_6) → H_9
  121. Polygon(E_7, F_6, G_9, H_9) → Xrod07, e_{12}, f_{24}, g_{24}, h_{24}
  122. Circle(E_8, tilewidth) → d_8
  123. Point(d_8) → F_7
  124. Segment(E_8, F_7) → j_7
  125. OrthogonalLine(F_7, j_7) → k_7
  126. Circle(F_7, (2.5 * tilewidth)) → e_{17}
  127. Intersect(e_{17}, k_7, 2) → G_8
  128. Line(E_8, k_7) → l_7
  129. OrthogonalLine(G_8, l_7) → m_7
  130. Intersect(l_7, m_7) → H_8
  131. Polygon(E_8, F_7, G_8, H_8) → Xrod08, e_{13}, f_{25}, g_{25}, h_{25}
  132. Circle(E_9, tilewidth) → d_9
  133. Point(d_9) → F_8
  134. Segment(E_9, F_8) → j_8
  135. OrthogonalLine(F_8, j_8) → k_8
  136. Circle(F_8, (2.5 * tilewidth)) → e_{18}
  137. Intersect(e_{18}, k_8, 2) → G_7
  138. Line(E_9, k_8) → l_8
  139. OrthogonalLine(G_7, l_8) → m_8
  140. Intersect(l_8, m_8) → H_7
  141. Polygon(E_9, F_8, G_7, H_7) → Xrod09, e_{14}, f_{26}, g_{26}, h_{26}
  142. Circle(E_{10}, tilewidth) → d_{10}
  143. Point(d_{10}) → F_9
  144. Segment(E_{10}, F_9) → j_9
  145. OrthogonalLine(F_9, j_9) → k_9
  146. Circle(F_9, (2.5 * tilewidth)) → e_{19}
  147. Intersect(e_{19}, k_9, 2) → G_6
  148. Line(E_{10}, k_9) → l_9
  149. OrthogonalLine(G_6, l_9) → m_9
  150. Intersect(l_9, m_9) → H_6
  151. Polygon(E_{10}, F_9, G_6, H_6) → Xrod10, e_{15}, f_{27}, g_{27}, h_{27}
  152. Circle(E_{11}, tilewidth) → d_{11}
  153. Point(d_{11}) → F_{10}
  154. Segment(E_{11}, F_{10}) → j_{10}
  155. OrthogonalLine(F_{10}, j_{10}) → k_{10}
  156. Circle(F_{10}, (2.5 * tilewidth)) → e_{28}
  157. Intersect(e_{28}, k_{10}, 2) → G_{17}
  158. Line(E_{11}, k_{10}) → l_{10}
  159. OrthogonalLine(G_{17}, l_{10}) → m_{10}
  160. Intersect(l_{10}, m_{10}) → H_{17}
  161. Polygon(E_{11}, F_{10}, G_{17}, H_{17}) → Xrod11, e_{20}, f_{28}, g_{28}, h_{28}
  162. Circle(E_{12}, tilewidth) → d_{12}
  163. Point(d_{12}) → F_{11}
  164. Segment(E_{12}, F_{11}) → j_{11}
  165. OrthogonalLine(F_{11}, j_{11}) → k_{11}
  166. Circle(F_{11}, (2.5 * tilewidth)) → e_{29}
  167. Intersect(e_{29}, k_{11}, 2) → G_{16}
  168. Line(E_{12}, k_{11}) → l_{11}
  169. OrthogonalLine(G_{16}, l_{11}) → m_{11}
  170. Intersect(l_{11}, m_{11}) → H_{16}
  171. Polygon(E_{12}, F_{11}, G_{16}, H_{16}) → Xrod12, e_{21}, f_{29}, g_{29}, h_{29}
  172. Circle(E_{13}, tilewidth) → d_{13}
  173. Point(d_{13}) → F_{12}
  174. Segment(E_{13}, F_{12}) → j_{12}
  175. OrthogonalLine(F_{12}, j_{12}) → k_{12}
  176. Circle(F_{12}, (2.5 * tilewidth)) → e_{30}
  177. Intersect(e_{30}, k_{12}, 2) → G_{15}
  178. Line(E_{13}, k_{12}) → l_{12}
  179. OrthogonalLine(G_{15}, l_{12}) → m_{12}
  180. Intersect(l_{12}, m_{12}) → H_{15}
  181. Polygon(E_{13}, F_{12}, G_{15}, H_{15}) → Xrod13, e_{22}, f_{30}, g_{30}, h_{30}
  182. Circle(E_{14}, tilewidth) → d_{14}
  183. Point(d_{14}) → F_{13}
  184. Segment(E_{14}, F_{13}) → j_{13}
  185. OrthogonalLine(F_{13}, j_{13}) → k_{13}
  186. Circle(F_{13}, (2.5 * tilewidth)) → e_{31}
  187. Intersect(e_{31}, k_{13}, 2) → G_{14}
  188. Line(E_{14}, k_{13}) → l_{13}
  189. OrthogonalLine(G_{14}, l_{13}) → m_{13}
  190. Intersect(l_{13}, m_{13}) → H_{14}
  191. Polygon(E_{14}, F_{13}, G_{14}, H_{14}) → Xrod14, e_{23}, f_{31}, g_{31}, h_{31}
  192. Circle(E_{15}, tilewidth) → d_{15}
  193. Point(d_{15}) → F_{14}
  194. Segment(E_{15}, F_{14}) → j_{14}
  195. OrthogonalLine(F_{14}, j_{14}) → k_{14}
  196. Circle(F_{14}, (2.5 * tilewidth)) → e_{32}
  197. Intersect(e_{32}, k_{14}, 2) → G_{13}
  198. Line(E_{15}, k_{14}) → l_{14}
  199. OrthogonalLine(G_{13}, l_{14}) → m_{14}
  200. Intersect(l_{14}, m_{14}) → H_{13}
  201. Polygon(E_{15}, F_{14}, G_{13}, H_{13}) → Xrod15, e_{24}, f_{32}, g_{32}, h_{32}
  202. Circle(E_{16}, tilewidth) → d_{16}
  203. Point(d_{16}) → F_{15}
  204. Segment(E_{16}, F_{15}) → j_{15}
  205. OrthogonalLine(F_{15}, j_{15}) → k_{15}
  206. Circle(F_{15}, (2.5 * tilewidth)) → e_{33}
  207. Intersect(e_{33}, k_{15}, 2) → G_{12}
  208. Line(E_{16}, k_{15}) → l_{15}
  209. OrthogonalLine(G_{12}, l_{15}) → m_{15}
  210. Intersect(l_{15}, m_{15}) → H_{12}
  211. Polygon(E_{16}, F_{15}, G_{12}, H_{12}) → Xrod16, e_{25}, f_{33}, g_{33}, h_{33}
  212. Circle(E_{18}, tilewidth) → d_{18}
  213. Point(d_{18}) → F_{17}
  214. Segment(E_{18}, F_{17}) → j_{17}
  215. OrthogonalLine(F_{17}, j_{17}) → k_{17}
  216. Circle(F_{17}, (2.5 * tilewidth)) → e_{35}
  217. Intersect(e_{35}, k_{17}, 2) → G_{10}
  218. Line(E_{18}, k_{17}) → l_{17}
  219. OrthogonalLine(G_{10}, l_{17}) → m_{17}
  220. Intersect(l_{17}, m_{17}) → H_{10}
  221. Polygon(E_{18}, F_{17}, G_{10}, H_{10}) → Xrod17, e_{27}, f_{35}, g_{35}, h_{35}
  222. Circle(E_{19}, tilewidth) → d_{19}
  223. Point(d_{19}) → F_{18}
  224. Segment(E_{19}, F_{18}) → j_{18}
  225. OrthogonalLine(F_{18}, j_{18}) → k_{18}
  226. Circle(F_{18}, (2.5 * tilewidth)) → e_{37}
  227. Intersect(e_{37}, k_{18}, 2) → G_{18}
  228. Line(E_{19}, k_{18}) → l_{18}
  229. OrthogonalLine(G_{18}, l_{18}) → m_{18}
  230. Intersect(l_{18}, m_{18}) → H_{18}
  231. Polygon(E_{19}, F_{18}, G_{18}, H_{18}) → Xrod18, e_{36}, f_{36}, g_{36}, h_{36}
  232. Circle(I, (2.5 * tilewidth)) → p
  233. Point(p) → J
  234. Polygon(I, J, 4) → Xsquare01, n, q, r, s, K, L
  235. Circle(I_1, (2.5 * tilewidth)) → p_1
  236. Point(p_1) → J_1
  237. Polygon(I_1, J_1, 4) → Xsquare02, n_1, q_1, r_1, s_1, K_1, L_1
  238. Circle(I_2, (2.5 * tilewidth)) → p_2
  239. Point(p_2) → J_2
  240. Polygon(I_2, J_2, 4) → Xsquare03, n_2, q_2, r_2, s_2, K_2, L_2
  241. Circle(I_3, (2.5 * tilewidth)) → p_3
  242. Point(p_3) → J_3
  243. Polygon(I_3, J_3, 4) → Xsquare04, n_3, q_3, r_3, s_3, K_5, L_5
  244. Circle(I_4, (2.5 * tilewidth)) → p_4
  245. Point(p_4) → J_4
  246. Polygon(I_4, J_4, 4) → Xsquare05, n_4, q_4, r_4, s_4, K_4, L_4
  247. Circle(I_5, (2.5 * tilewidth)) → p_5
  248. Point(p_5) → J_5
  249. Polygon(I_5, J_5, 4) → Xsquare06, n_5, q_5, r_5, s_5, K_3, L_3
  250. Circle(I_6, (2.5 * tilewidth)) → p_6
  251. Point(p_6) → J_6
  252. Polygon(I_6, J_6, 4) → Xsquare07, n_6, q_6, r_6, s_6, K_{11}, L_{11}
  253. Circle(I_7, (2.5 * tilewidth)) → p_7
  254. Point(p_7) → J_7
  255. Polygon(I_7, J_7, 4) → Xsquare08, n_7, q_7, r_7, s_7, K_{10}, L_{10}
  256. Circle(I_8, (2.5 * tilewidth)) → p_8
  257. Point(p_8) → J_8
  258. Polygon(I_8, J_8, 4) → Xsquare09, n_8, q_8, r_8, s_8, K_9, L_9
  259. Circle(I_9, (2.5 * tilewidth)) → p_9
  260. Point(p_9) → J_9
  261. Polygon(I_9, J_9, 4) → Xsquare10, n_9, q_9, r_9, s_9, K_8, L_8
  262. Circle(I_{10}, (2.5 * tilewidth)) → p_{10}
  263. Point(p_{10}) → J_{10}
  264. Polygon(I_{10}, J_{10}, 4) → Xsquare11, n_{10}, q_{10}, r_{10}, s_{10}, K_7, L_7
  265. Circle(I_{11}, (2.5 * tilewidth)) → p_{11}
  266. Point(p_{11}) → J_{11}
  267. Polygon(I_{11}, J_{11}, 4) → Xsquare12, n_{11}, q_{11}, r_{11}, s_{11}, K_6, L_6
  268. Circle(I_{12}, (2.5 * tilewidth)) → p_{12}
  269. Point(p_{12}) → J_{12}
  270. Polygon(I_{12}, J_{12}, 4) → Xsquare13, n_{12}, q_{12}, r_{12}, s_{12}, K_{15}, L_{15}
  271. Circle(I_{13}, (2.5 * tilewidth)) → p_{13}
  272. Point(p_{13}) → J_{13}
  273. Polygon(I_{13}, J_{13}, 4) → Xsquare14, n_{13}, q_{13}, r_{13}, s_{13}, K_{14}, L_{14}
  274. Circle(I_{14}, (2.5 * tilewidth)) → p_{14}
  275. Point(p_{14}) → J_{14}
  276. Polygon(I_{14}, J_{14}, 4) → Xsquare15, n_{14}, q_{14}, r_{14}, s_{14}, K_{13}, L_{13}
  277. Circle(I_{15}, (2.5 * tilewidth)) → p_{15}
  278. Point(p_{15}) → J_{15}
  279. Polygon(I_{15}, J_{15}, 4) → Xsquare16, n_{15}, q_{15}, r_{15}, s_{15}, K_{12}, L_{12}
  280. Circle(I_{16}, (2.5 * tilewidth)) → p_{16}
  281. Point(p_{16}) → J_{16}
  282. Polygon(I_{16}, J_{16}, 4) → Xsquare17, n_{16}, q_{16}, r_{16}, s_{16}, K_{19}, L_{19}
  283. Circle(I_{17}, (2.5 * tilewidth)) → p_{17}
  284. Point(p_{17}) → J_{17}
  285. Polygon(I_{17}, J_{17}, 4) → Xsquare18, n_{17}, q_{17}, r_{17}, s_{17}, K_{18}, L_{18}
  286. Circle(I_{18}, (2.5 * tilewidth)) → p_{18}
  287. Point(p_{18}) → J_{18}
  288. Polygon(I_{18}, J_{18}, 4) → Xsquare19, n_{18}, q_{18}, r_{18}, s_{18}, K_{17}, L_{17}
  289. Circle(I_{19}, (2.5 * tilewidth)) → p_{19}
  290. Point(p_{19}) → J_{19}
  291. Polygon(I_{19}, J_{19}, 4) → Xsquare20, n_{19}, q_{19}, r_{19}, s_{19}, K_{16}, L_{16}
  292. Random(-3, 3) → a
  293. Random(-2, 4) → b
  294. Circle(M, tilewidth) → t
  295. Point(t) → N
  296. Point(t) → O
  297. Ray(N, M) → t_1
  298. Ray(O, M) → a_1
  299. Random(2, 4) → f
  300. Random(1, 3) → g
  301. Random(1, 3) → h
  302. Random(-2, 2) → c_{18}
  303. Random(1, 4) → d_3
  304. Random(-3, 3) → a_2
  305. Random(-2, 4) → b_1
  306. Random(-2, 2) → c_{18}
  307. Random(1, 4) → d_{17}
  308. Random(-3, 3) → a_3
  309. Random(-2, 4) → b_2