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Fraction Stretching

Fraction Stretching
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2016-10-27 01:53
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the concept of fraction stretching, involving fractions and rational numbers. Using GeoGebra commands such as Ray, Point, Polygon, etc., complex geometric shapes can be constructed. Suitable for middle school and above students to learn about geometric transformations and rational numbers.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a geometric figure illustrating fraction stretching. Start with several rays from vertices, place points on them, and connect these points to form four quadrilaterals. Inside, draw a polyline crossing these shapes, pick two points on it, create a horizontal segment, then a perpendicular line intersecting the polyline. Use the least common multiple of certain x-coordinates to generate multiple parallel segments dividing the quadrilaterals into equal parts. Finally, draw a line between two specific points. The overall composition shows rational number relationships through geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.