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Omm Nom Fractions

Omm Nom Fractions
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2016-10-20 06:04
CircleGeometric Construction
This example demonstrates the application of fractions in geometric shapes, focusing on the concepts of fractions, circles, and symmetry. It uses GeoGebra commands such as Sequence, Point, Ray, Segment, etc., to construct geometric objects like points, line segments, and circles. Suitable for middle school and above students to learn the relationship between fractions and geometric shapes.

GeoGebra Commands & Parameters

  1. Sequence(Circle[B, k], k, 1, 20) → list1
  2. Sequence((x(A) + k, y(A)), k, 1, 20) → list2
  3. Point(list2) → C
  4. Ray(A, C) → f
  5. Segment(A, C) → g
  6. Point(list1) → D
  7. Ray(B, D) → h
  8. Segment(B, D) → i
  9. Sequence((x(B) + (k / i * a), y(B) + (k / i * b)), k, 1, i - 1) → BDpoints
  10. Sequence((x(A) + (k / g * c), y(A) + (k / g * d)), k, 1, g - 1) → ACpoints
  11. Sequence((x(A) + (k / i * c), y(A) + (k / i * d)), k, 1, i - 1) → divPoints
  12. Sequence(Segment[BDpoints(k), divPoints(k)], k, 1, Length[divPoints]) → list3
  13. Segment(D, C) → j
  14. OrthogonalLine(A, g) → k
  15. OrthogonalLine(C, g) → l
  16. Circle(A, 1) → e
  17. Intersect(e, k, 2) → E
  18. OrthogonalLine(E, k) → m
  19. Intersect(l, m) → F
  20. Polygon(A, E, F, C) → poly1, a_1, e_1, f_1, c_1
  21. OrthogonalLine(B, i) → n
  22. OrthogonalLine(D, i) → p
  23. Circle(B, 1) → q
  24. Intersect(q, n, 1) → G
  25. OrthogonalLine(G, n) → r
  26. Intersect(p, r) → H
  27. Polygon(G, B, D, H) → poly2, g_1, b_1, d_1, h_1
  28. Segment(I, J) → s
  29. Sequence(Segment[divPoints(k), (x(divPoints(k)), y(divPoints(k) + 1))], k, 2, Length[divPoints]) → list4
  30. Line(A, C) → t
  31. Line(B, D) → i_1
  32. Angle(i_1, t) → β
  33. Sequence((x(BDpoints(k)) - sin(β), y(BDpoints(k)) - cos(β)), k, 1, Length[BDpoints]) → list5
  34. Sequence(Segment[BDpoints(k), list5(k)], k, 1, Length[BDpoints]) → denomLines
  35. Polygon(K, L, N, M) → poly3, k_1, l_1, n_1, m_1
  36. FractionText(o) → text1
  37. Sequence(Segment[(x(K) + k / Area[poly2], y(K)), (x(K) + k / Area[poly2], y(K) + 1)], k, 1, Area[poly2]) → list6