MathPlotAI Logo MathPlotAI

GeoGebra Fraction Comparison Example

GeoGebra Fraction Comparison Example
Loading the math board and drawing, please wait…
2017-05-02 00:50
VectorCoordinate GeometryProbability & StatisticsGeometric Construction
This example demonstrates how to use GeoGebra to compare different fractions visually. It involves core math concepts like fractions, distributions, 3D vectors, rotation, means, and histograms. Key GeoGebra commands and objects used include If, Division, Intersect, Point, Sequence, Circle, Translate, BarFraction, and Improp. Suitable for high school mathematics teaching or self-learning to intuitively understand fraction comparison and data analysis.

GeoGebra Commands & Parameters

  1. If(m, (a_1 * b), If[d, a_1 / b, If[a, a_1 + b, If[s, a_1 - b]]]) → i
  2. If(m, (n * g), If[d, n / g, If[a, n + g, If[s, n - g]]]) → j
  3. Division(a_1, n) → list8
  4. Intersect(xAxis, yAxis) → A
  5. Point(yAxis) → B
  6. Sequence(Rotate[B, (((-i) * 360) * ° / n), A], i, 0, n) → list1
  7. Circle(A, B) → c
  8. Sequence(Rotate[D, (((-i) * 360) * ° / If[m, (n * g), If[d, n / g, If[a, n + g, If[s, n - g]]]]), C], i, 0, If[m, (n * g), If[d, n / g, If[a, n + g, If[s, n - g]]]]) → list4
  9. Circle(C, D) → f
  10. Sequence(Sector[c, Element[list1, i + 1], Element[list1, i]], i, 1, n) → list2
  11. Sequence(Sector[f, Element[list4, i + 1], Element[list4, i]], i, 1, If[m, (n * g), If[d, n / g, If[a, n + g, If[s, n - g]]]]) → list5
  12. Division(i, j) → list11
  13. If(n > a_1, Sequence[Sector[c, Element[list1, i + 1], Element[list1, i]], i, 1, a_1], Sequence[Sector[c, Element[list1, i + 1], Element[list1, i]], i, 1, a_1]) → list3
  14. Circle(E, G) → p
  15. Circle(F, H) → q
  16. Sequence(Rotate[G, (((-i) * 360) * ° / o), E], i, 0, o) → list14
  17. Sequence(Sector[p, Element[list14, i + 1], Element[list14, i]], i, 1, o) → list12
  18. If(l > o, Sequence[Sector[p, Element[list14, i + 1], Element[list14, i]], i, 1, l], Sequence[Sector[p, Element[list14, i + 1], Element[list14, i]], i, 1, l]) → list15
  19. Sequence(Sector[p, Element[list14, i + 1], Element[list14, i]], i, 1, o) → list16
  20. Sequence(Rotate[H, (((-i) * 360) * ° / If[u, (o * t), If[w, o / t, If[a, o + t, If[s, o - t]]]]), F], i, 0, If[u, (o * t), If[w, o / g, If[a, o + t, If[s, o - t]]]]) → list17
  21. Sequence(Sector[q, Element[list17, i + 1], Element[list17, i]], i, 1, If[u, (o * t), If[w, o / t, If[a, o + t, If[s, o - t]]]]) → list18
  22. If(u, (l * r), If[w, l / r, If[a, a_1 + b, If[s, a_1 - b]]]) → b_1
  23. If(u, (o * t), If[w, o / t, If[a, n + g, If[s, n - g]]]) → c_1
  24. Division(b_1, c_1) → list20
  25. Sequence(Element[list10, i] - (0, 8), i, 1, Length[list10]) → list22
  26. If(j ≥ i, Sequence[Sector[f, Element[list4, n + 1], Element[list4, n]], n, 1, i], Sequence[Sector[f, Element[list4, i + 1], Element[list4, i]], i, 1, Element[list11, 2]]) → list6
  27. If(i > j, Sequence[Circle[Element[list10, i], 0.8], i, 0, Element[list11, 1], 1]) → list9
  28. If(b_1 > c_1, Sequence[Circle[Element[list22, i], 0.8], i, 0, Element[list20, 1], 1]) → list21
  29. Translate({list3, list15}, (v, 0)) → list13
  30. Translate({list6}, (0, g_1)) → list23
  31. BarFraction(a_1, n, I) → list24, list25
  32. BarFraction(l, o, J) → list26, list27
  33. If(m ≟ 1, (a_1 * b), a_1 / b) → r_5
  34. If(m ≟ 1, (n * g), n / g) → s_5
  35. If(u ≟ 1, (o * t), o / t) → v_5
  36. If(u ≟ 1, (l * r), l / r) → t_5
  37. Translate(list24, (v, ((1 / 20 * v) * (v - 8)))) → list25'
  38. Translate(list26, (v, ((1 / 20 * v) * (v - 8)))) → list26'
  39. If(c_1 ≥ b_1, Sequence[Sector[q, Element[list17, o + 1], Element[list17, o]], o, 1, b_1], Sequence[Sector[q, Element[list17, i + 1], Element[list17, i]], i, 1, Element[list20, 2]]) → list19
  40. Improp(v_5, t_5, L) → list31_3, list31, list32
  41. If(t_5 > v_5, Sequence[Polygon[P - (0, i), P - (0, i) + (3, 0), P - (0, i) + (3, 0.5), P - (0, i) + (0, 0.5)], i, 0, Element[list32, 1] - 1]) → list30
  42. If(t_5 > v_5, Sequence[Polygon[P - (0, i), P - (0, i) + (3, 0), P - (0, i) + (3, 0.5), P - (0, i) + (0, 0.5)], i, 0, Element[list32, 1] - 1]) → list33
  43. Improp(s_5, r_5, K) → list28, list29, list34
  44. If(r_5 > s_5, Sequence[Polygon[O - (0, i), O - (0, i) + (3, 0), O - (0, i) + (3, 0.5), O - (0, i) + (0, 0.5)], i, 0, Element[list34, 1] - 1]) → list35
  45. If(r_5 > s_5, Sequence[Polygon[O - (0, i), O - (0, i) + (3, 0), O - (0, i) + (3, 0.5), O - (0, i) + (0, 0.5)], i, 0, Element[list34, 1] - 1]) → list36
  46. If(i > j, Sequence[Circle[Element[list10, i], 0.8], i, 0, Element[list11, 1], 1]) → list37
  47. If(b_1 > c_1, Sequence[Circle[Element[list22, i], 0.8], i, 0, Element[list20, 1], 1]) → list38
  48. Translate(list28, (0, (1.045 * g_1))) → list28'