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Unit Fractions Demo

Unit Fractions Demo
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2017-10-22 18:02
Probability & StatisticsGeometric Construction
This example demonstrates the visualization and geometric construction of unit fractions. It involves core math concepts like fractions, geometric transformations, and probability statistics (Binomial Distribution, Normal Distribution). Constructed using commands such as Random, Element, Sequence, Segment, Point, OrthogonalLine, Intersect, Polygon. Suitable for high school mathematics teaching, providing an intuitive understanding of fractions, geometric transformations, and the application of probability distributions.

GeoGebra Commands & Parameters

  1. Random(5, 12) → lengthoftape
  2. Random(1, 6) → chooser
  3. Element(list2, chooser) → denominator
  4. Sequence((x(A) + (i * fractionwidth), y(A) + tapeheight), i, 0, denominator) → DotsTop
  5. Sequence((x(A) + (i * fractionwidth), y(A)), i, 0, denominator) → DotsBottom
  6. Sequence(Segment[Element[DotsBottom, i], Element[DotsTop, i]], i, 1, denominator + 1) → drawverticals
  7. Segment(Element[DotsBottom, 1], Element[DotsBottom, denominator + 1]) → horizontalbottom
  8. Segment(Element[DotsTop, 1], Element[DotsTop, denominator + 1]) → horizontaltop
  9. Segment(Element[DotsBottom, 1], Element[DotsTop, 1]) → verticalleft
  10. Segment(Element[DotsBottom, denominator + 1], Element[DotsTop, denominator + 1]) → verticalright
  11. Point(horizontalbottom) → B
  12. Point(horizontalbottom) → C
  13. OrthogonalLine(C, horizontalbottom) → f
  14. Point(horizontalbottom) → D
  15. Point(horizontalbottom) → E
  16. Point(horizontalbottom) → F
  17. Point(horizontalbottom) → G
  18. Point(horizontalbottom) → H
  19. Point(horizontalbottom) → I
  20. Point(horizontalbottom) → J
  21. Point(horizontalbottom) → K
  22. OrthogonalLine(B, horizontaltop) → g
  23. OrthogonalLine(D, horizontaltop) → h
  24. OrthogonalLine(E, horizontaltop) → i
  25. OrthogonalLine(F, horizontaltop) → j
  26. OrthogonalLine(G, horizontaltop) → k
  27. OrthogonalLine(H, horizontaltop) → l
  28. OrthogonalLine(I, horizontaltop) → m
  29. OrthogonalLine(J, horizontaltop) → n
  30. OrthogonalLine(K, horizontaltop) → p
  31. Intersect(f, horizontaltop) → L
  32. Intersect(g, horizontaltop) → M
  33. Intersect(h, horizontaltop) → N
  34. Intersect(i, horizontaltop) → O
  35. Intersect(j, horizontaltop) → P
  36. Intersect(k, horizontaltop) → Q
  37. Intersect(l, horizontaltop) → R
  38. Intersect(m, horizontaltop) → S
  39. Intersect(n, horizontaltop) → T
  40. Intersect(p, horizontaltop) → U
  41. Segment(C, L) → q
  42. Segment(B, M) → r
  43. Segment(D, N) → s
  44. Segment(E, O) → t
  45. Segment(F, P) → a
  46. Segment(G, Q) → b
  47. Segment(H, R) → c
  48. Segment(I, S) → d
  49. Segment(J, T) → e
  50. Segment(K, U) → f_1
  51. Sequence(Element[DotsTop, i], i, 2, denominator) → DotsTopRevealed
  52. Polygon(Element[DotsBottom, 1], Element[DotsBottom, denominator + 1], Element[DotsTop, denominator + 1], Element[DotsTop, 1]) → poly1, g_1, h_1, i_1, j_1