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Unit Fraction Demonstration

Unit Fraction Demonstration
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2017-05-23 07:35
VectorCoordinate GeometryGeometric Construction
This example dynamically demonstrates the concept of unit fractions and their geometric applications. It involves core math concepts like fractions, geometric constructions, 3D vectors, and parabolas. Key GeoGebra commands used include Random, Element, Sequence, Segment, Point, OrthogonalLine, Intersect, and Polygon to create interactive geometric elements. Suitable for high school mathematics education to understand the integration of fractions and geometry.

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