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One-Third Arcs

One-Third Arcs
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2019-11-17 10:43
CircleVectorProbability & StatisticsGeometric Construction
This example demonstrates the construction of one-third arcs using GeoGebra, involving core concepts like circles, vectors, random elements, and geometric constructions. Key commands used include Point, Sequence, CircleArc, and RandomElement, making it suitable for high school mathematics education to illustrate the application of probability and geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Sequence(Rotate[A, ((w * 2) * π / 6)], w, 1, 6) → l1
  3. Point(l1) → B
  4. Point(l1) → C
  5. Point(xAxis) → D
  6. CircleArc(B, C, D) → c
  7. Point(xAxis) → E
  8. Point(l1) → F
  9. CircleArc(E, F, C) → d
  10. Point(l1) → G
  11. RandomElement({0, (2 * π / 6), (4 * π / 6)}) → a
  12. CircleArc(G, D, F) → e
  13. Sequence(Sequence[Translate[Rotate[{c}, RandomElement[{0, (2 * π / 3), (4 * π / 3)}]], (u * (F - D)) + (v * (C - D))], u, -15, 15], v, -15, 15) → l2