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Fraction Comparison by suresan c

Fraction Comparison by suresan c
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2015-12-31 12:48
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to visually compare the sizes of two fractions. It involves core mathematical concepts such as fractions, denominators, numerators, geometric representation, and trigonometric functions. The construction uses GeoGebra commands/objects like Segment, Sequence, Circle, Point, Rotate, CircleSector, and Polygon. Suitable for middle school students and above to learn and understand the geometric meaning of fraction comparison, as well as for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Segment(A, A + (unitsize1, 0)) → line1
  2. Segment(B, B + (unitsize2, 0)) → line2
  3. Sequence((x(A) + i * unitsize1 / denominator1, y(A)), i, 1, denominator1) → numdots1
  4. Sequence((x(B) + i * unitsize2 / denominator2, y(B)), i, 1, denominator2) → numdots2
  5. Segment(E, (x(E), y(E) - (y(A) - y(B)))) → showcomparison_1
  6. Segment(A, E) → showfrac1_1
  7. Segment(B, F) → showfrac2_1
  8. Circle(G, unitradius) → c
  9. Point(c) → H
  10. Segment(G, H) → a
  11. Rotate(G, 360 * ° / denominator1, G) → G'
  12. Sequence(Segment[Rotate[G, i * 360 * ° / denominator1, G], Rotate[H, i * 360 * ° / denominator1, G]], i, 1, denominator1) → denominatorwedges1
  13. Circle(I, unitradius) → d
  14. Point(d) → J
  15. Segment(I, J) → b
  16. Sequence(Segment[Rotate[I, i * 360 * ° / denominator2, I], Rotate[J, i * 360 * ° / denominator2, I]], i, 1, denominator2) → denominatorwedges2
  17. Rotate(H, numerator1 * 360 * ° / denominator1, G) → H'
  18. Rotate(J, numerator2 * 360 * ° / denominator2, I) → J'
  19. CircleSector(G, H, H') → numeratorwedge1
  20. CircleSector(I, J, J') → numeratorwedge2
  21. Polygon(K, (x(K), y(K) - boxheight), (x(K) + boxwidth, y(K) - boxheight), (x(K) + boxwidth, y(K))) → poly1, e, f, g, h
  22. Polygon(L, (x(L), y(L) - boxheight), (x(L) + boxwidth, y(L) - boxheight), (x(L) + boxwidth, y(L))) → poly2, l, i, j, k