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随机比例分割 by Daniel Little

随机比例分割 by Daniel Little
几何画板及绘图内容加载中，请稍等……
2018-06-06 17:54
向量数列
①本范例演示如何使用 GeoGebra 将图形按随机比例分割；②涉及核心数学概念包括比例、数列、组合数学和向量；③作图要点：使用 Point, Polygon, GCD, PolyLine 命令创建了点、多边形、线段，并计算最大公约数；④适合高中及以上数学学习者，用于理解比例分割和几何作图的实践应用。

GeoGebra 命令及参数

  1. Point(xAxis) → A_1
  2. Point(xAxis) → B_2
  3. Polygon(A_1, B_2, C_2, D) → q1, a_1, b_1, c_1, d
  4. Point(xAxis) → E
  5. Polygon(E, F, G, H) → q2, e, f, g, h
  6. Polygon(M, N, O, P) → q4, m, n, o, p
  7. Polygon(Q, R, S, T) → q5, q, r, s, t
  8. Polygon(I, J, K, L) → q3, i_2, j_2, k_1, l
  9. GCD({a, b, c}) → o_1
  10. GCD({a, b}) → p_1
  11. PolyLine((NaN, NaN), (12.996313657792996, 4.8140344806669635), (NaN, NaN), true) → stroke5
  12. PolyLine((10.17265394531381, 5.659986543848662), (NaN, NaN), (10.43058439981912, 5.2100120421562695), (10.38985853858144, 5.138016121885486), (10.349132677343759, 5.066020201614704), (10.308406816106078, 5.030022241479312), (NaN, NaN), (10.21337980655149, 5.174014082020878), (NaN, NaN), (10.21337980655149, 5.174014082020878), (10.226955093630718, 5.228011022223965), (10.226955093630718, 5.120017141817791), (10.17265394531381, 5.659986543848662), (10.226955093630718, 5.048021221547008), (10.267680954868398, 4.994024281343921), (10.349132677343759, 4.976025301276225), (10.43058439981912, 4.976025301276225), (10.51203612229448, 4.976025301276225), (10.566337270611388, 4.976025301276225), true, (10.25410566778917, 5.659986543848662), (10.321982103185306, 5.641987563780966), (10.362707964422986, 5.587990623577879), (10.38985853858144, 5.533993683374792), (10.43058439981912, 5.4619977631040095), (10.457734973977574, 5.3360049026301395), (10.444159686898347, 5.282007962427052)) → stroke1
  13. PolyLine((8.855851098628806, 5.551992663442488), (NaN, NaN), (9.249534423926384, 5.300006942494748), (9.249534423926384, 5.228011022223965), (9.235959136847157, 5.174014082020878), (9.195233275609477, 5.138016121885486), (9.140932127292569, 5.084019181682399), (9.100206266054888, 5.030022241479312), (NaN, NaN), (8.910152246945712, 5.156015101953182), (NaN, NaN), (8.910152246945712, 5.156015101953182), (8.855851098628806, 5.551992663442488), (8.950878108183392, 5.2100120421562695), (8.937302821104167, 5.156015101953182), (8.937302821104167, 5.084019181682399), (8.937302821104167, 4.994024281343921), (8.950878108183392, 4.9400273411408335), (8.978028682341847, 4.886030400937747), (9.059480404817208, 4.850032440802355), (9.113781553134116, 4.832033460734659), (9.195233275609477, 4.850032440802355), (9.276684998084837, 4.850032440802355), (8.896576959866486, 5.569991643510184), true, (8.96445339526262, 5.551992663442488), (9.0051792565003, 5.533993683374792), (9.04590511773798, 5.515994703307096), (9.140932127292569, 5.4619977631040095), (9.195233275609477, 5.408000822900922), (9.235959136847157, 5.354003882697835)) → stroke2
  14. GCD({a, b}) → r_1

AI 绘图提示语参考

绘制一个四边形ABCD，然后在x轴上选取点E、F、G、H，构造四边形EFGH。接着在x轴上选取点I、J、K、L，构造四边形IJKL。使用随机比例将四边形ABCD、EFGH、IJKL分别分割成多个部分，并计算每部分的面积比。最后，使用PolyLine命令绘制分割线，确保分割线平滑连接各部分边界。
以上提示语为根据原始绘图命令整理而来，仅供参考。