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Unit Fractions

Unit Fractions
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2020-04-14 04:54
FunctionSequenceGeometric Construction
This example demonstrates the concept of unit fractions, which are fractions with a numerator of 1. Using GeoGebra commands such as Random, Vector, Mod, etc., dynamic displays of unit fractions' properties and applications are shown. Suitable for students from upper elementary to middle school learning basic fraction concepts.

GeoGebra Commands & Parameters

  1. Random(2, 12) → d
  2. Vector((0, 0), (1, 0)) → u
  3. Mod(n, d) → remainder
  4. If(remainder ≟ 0, whole, whole + 1) → endNumber
  5. Polygon(A, B, 4) → poly1, a, b, c, e, C, D
  6. Sequence(B + (i * u), i, 0, whole) → SecondLow
  7. Sequence(A + (i * u), i, 0, whole) → FirstLow
  8. Zip(Polygon[X, Y, 4], X, FirstLow, Y, SecondLow) → list1
  9. Sequence(Point[A, Vector[(i * u / d)]], i, 1, n) → PtBottom
  10. Sequence(Point[D, Vector[(i * u / d)]], i, 1, n) → PtTop
  11. Append(D, Take[PtTop, 1, n - 1]) → PtTop1
  12. Append(A, Take[PtBottom, 1, n - 1]) → PtBottom1
  13. Zip(Polygon[E, F, G, H], E, PtBottom1, F, PtBottom, G, PtTop, H, PtTop1) → list2
  14. Polygon(C, B, 4) → poly2, f, g, h, i, E, F
  15. Polygon(F, E, 4) → poly3, j, k, l, m, G, H
  16. Polygon(H, G, 4) → poly4, p, q, r, s, I, J
  17. Polygon(J, I, 4) → poly5, t, a_1, b_1, c_1, K, L
  18. Polygon(L, K, 4) → poly6, d_1, e_1, f_1, g_1, M, N
  19. Sequence(Point[OO, Vector[(i * u / d)]], i, 1, (10 * d)) → list3
  20. Element(list3, n) → Z
  21. Zip(Segment[M, N], M, list3, N, PtBottom) → list4
  22. Segment(A, OO) → h_1
  23. Sequence(Point[D, Vector[(i * u / d)]], i, 1, (d * endNumber)) → allTop
  24. Sequence(Point[A, Vector[(i * u / d)]], i, 1, (d * endNumber)) → allBott
  25. Zip(Segment[M, N], M, allTop, N, allBott) → list5
  26. Corner(text3, 2) → BB
  27. Corner(text3, 3) → CC
  28. Corner(text3, 4) → DD
  29. Corner(text3, 1) → AA
  30. Polygon(AA, BB, CC, DD) → frame, aa, bb, cc, dd
  31. Midpoint(AA, BB) → MM
  32. Point(xAxis) → O

AI Drawing Prompt Reference

Draw a dynamic display of unit fractions, including a unit vector u and two sequence point sets FirstLow and SecondLow, forming a series of polygons. Adjust the denominator d and numerator n to observe the properties and applications of unit fractions. Finally, display a series of line segments parallel to the unit vector and a frame containing these segments.
The prompt above was compiled from the original drawing commands and is for reference only.