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分数拉伸

分数拉伸
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2016-10-27 01:53
函数解析几何几何作图
这个范例演示了分数拉伸的概念，涉及分数和有理数。通过使用GeoGebra命令如Ray, Point, Polygon等，可以构造出复杂的几何图形。适合初中及以上学生学习几何变换和有理数的相关知识。

GeoGebra 命令及参数

  1. Ray(D, I) → i
  2. Point(i) → L
  3. Ray(A, F) → f
  4. Ray(B, G) → g
  5. Ray(C, H) → h
  6. Ray(E, J) → j
  7. Point(j) → K
  8. Point(g) → N
  9. Point(f) → O
  10. Polygon(E, K, K_1, D) → poly1, e, k, k_1, d
  11. Polygon(D, L, L_1, C) → poly2, d_1, l, l_1, c
  12. Polygon(B, N, N_1, A) → poly3, b, n, n_2, a
  13. Polygon(A, O, O_1, M) → poly4, a_1, o, o_1, m
  14. LCM(x(L), x(O)) → myLCM
  15. PolyLine((0, 0), (0.13336413657667023, 0), (1.2002772291900499, 0.2000462048649997), (1.3003003316225499, 0.2333872390091597), (1.4003234340550499, 0.2667282731533297), (1.50034653648755, 0.3000693072974997), (1.60036963892005, 0.3334103414416697), (1.70039274135255, 0.3667513755858297), (1.80041584378505, 0.4000924097299997), (1.8670979120733495, 0.5001155121624997), (1.9671210145058495, 0.5334565463066697), (2.033803082794151, 0.6334796487391697), (0.23338723900917024, 0.0333410341441599), (2.1338261852266514, 0.6668206828833397), (2.167167219370848, 0.7668437853158397), (2.2338492876591496, 0.8668668877483396), (2.3005313559475504, 0.9668899901808397), (2.4005544583800487, 1.0335720584691699), (2.433895492524148, 1.13359516090167), (2.4672365266683487, 1.2336182633341748), (2.5672596291008487, 1.3003003316225086), (2.600600663245049, 1.40032343405501), (2.667282731533351, 1.5003465364875108), (0.3667513755858405, 0.0333410341441599), (2.73396479982175, 1.6003696389200113), (2.767305833965847, 1.7003927413525113), (2.8006468681100474, 1.8004158437850122), (2.833987902254248, 1.900438946217513), (2.900669970542549, 2.000462048650014), (2.9340110046867514, 2.1004851510825158), (2.9673520388308487, 2.2005082535150167), (3.0006930729750487, 2.3005313559475176), (3.0340341071192496, 2.4005544583800185), (3.0340341071192496, 2.533918594956687), (0.4667744780183405, 0.06668206828832968), (3.0673751412633505, 2.633941697389188), (3.0673751412633505, 2.7673058339658554), (3.1007161754075514, 2.8673289363983563), (3.1340572095517523, 2.967352038830858), (3.1673982436958497, 3.067375141263358), (3.1673982436958497, 3.200739277840029), (3.20073927784005, 3.300762380272529), (3.23408031198425, 3.4007854827050292), (3.3007623802725523, 3.5008085851375292), (3.334103414416753, 3.60083168757003), (0.6001386145950107, 0.1000231024324999), (3.4341265168492523, 3.66751375585836), (3.4674675509933537, 3.7675368582908715), (3.5341496192817554, 3.867559960723373), (3.600831687570054, 3.9675830631558733), (3.7008547900025572, 4.034265131444203), (3.767536858290856, 4.134288233876703), (3.8675599607233586, 4.167629268020873), (3.967583063155857, 4.234311336309203), (4.067606165588359, 4.300993404597543), (4.167629268020857, 4.334334438741703), (0.7335027511716508, 0.1333641365766599), (4.267652370453359, 4.401016507030043), (4.367675472885857, 4.467698575318373), (4.467698575318359, 4.501039609462543), (4.567721677750857, 4.567721677750873), (4.667744780183359, 4.601062711895043), (4.767767882615857, 4.634403746039212), (4.867790985048359, 4.667744780183373), (4.967814087480857, 4.701085814327543), (5.067837189913458, 4.734426848471713), (5.16786029234596, 4.767767882615884), (0.8668668877483512, 0.1333641365766599), (5.301224428922559, 4.767767882615884), (5.401247531355057, 4.801108916760043), (5.53461166793176, 4.801108916760043), (5.634634770364258, 4.834449950904213), (5.73465787279676, 4.867790985048384), (5.868022009373458, 4.867790985048384), (5.96804511180596, 4.901132019192543), (6.101409248382559, 4.901132019192543), (6.234773384959256, 4.901132019192543), true, (0.9668899901808512, 0.1667051707208297), (1.1002541267575499, 0.1667051707208297)) → stroke1
  16. Point(stroke1) → P
  17. Point(stroke1) → Q
  18. Segment(P, (x(Q), y(P))) → p
  19. Point(p) → smoothAnim
  20. OrthogonalLine(smoothAnim, p) → q
  21. Intersect(q, stroke1) → S
  22. Polygon(E, T, V, D) → poly5, e_1, t, v, d_2
  23. Polygon(D, R, U, C) → poly6, d_3, r, u, c_1
  24. Sequence(Segment[(((x(R) * k) * 1 / x(L)), y(U)), (((x(R) * k) * 1 / x(L)), y(R))], k, 1, x(L) - 1) → list1
  25. Sequence(Segment[(((x(R) * k) * 1 / x(L)), y(T)), (((x(R) * k) * 1 / x(L)), y(V))], k, 1, x(K) - 1) → list2
  26. Sequence(Segment[(((x(R) * k) * 1 / x(L)), 0), (((x(R) * k) * 1 / x(L)), 2)], k, 1, x(L) - 1) → list3
  27. Line(T, V) → s

AI 绘图提示语参考

绘制一个由多个多边形和射线构成的几何图形，展示分数拉伸的概念。从几个顶点出发引出射线，在射线上取点，连接这些点形成四个四边形。在图形内部，用一条折线穿过这些四边形，并在折线上取两个点，作水平线段，再作该线段的垂线与折线相交。根据某些点的横坐标计算最小公倍数，用于生成多组平行线段，将四边形分割成等份。最后，在特定两点间作一条直线。整体图形体现分数与几何变换的关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。