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Unitary Fractions: The Circle Model

Unitary Fractions: The Circle Model
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2016-04-11 20:56
CircleGeometric Construction
This example illustrates the concept of unit fractions using a circle model, demonstrating the geometric meaning of fractions. Key mathematical concepts include fractions and circle geometry. It uses GeoGebra commands such as Sequence and Circle for construction. Suitable for high-grade elementary to junior high school students learning fractions and geometry.

GeoGebra Commands & Parameters

  1. Sequence(Vector[O, Rotate[A, ang / 2 + (ang * i), O]], i, 0, n) → SV
  2. Sequence(Translate[Rotate[A, (ang * i), O], Vector[(separate * Element[SV, Mod[i, n] + 1])]], i, 0, n) → SP
  3. Circle(O, A) → c
  4. Sequence(Translate[Rotate[(0, 0), ang / 2 + (ang * i), (0, 0)], Vector[(separate * Element[SV, Mod[i, n] + 1])]], i, 0, n) → SO
  5. Sequence(Rotate[Element[SP, i], ang, Element[SO, i]], i, 1, Length[SV]) → SQ
  6. Sequence(CircleSector[Element[SO, i], Element[SP, i], Element[SQ, i]], i, 1, n) → SS
  7. Sequence(Rotate[CircleSector[Element[SO, 1], Element[SP, 1], Element[SQ, 1]], ((i * 2) * π / n), O], i, 0, count - 1) → d
  8. Sequence(Rotate[CircleSector[Element[SO, 1], Element[SP, 1], Element[SQ, 1]], ((i * 2) * π / n), O], i, 0, count - 1) → e
  9. Sequence(Translate[Rotate[A, (ang * (i - 1)) + ang / 2, O], Vector[(separate * Element[SV, Mod[i, n] + 1])]], i, 1, count) → SN
  10. Circle(O, A) → f
  11. Circle(O, A) → g