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Visualizing Modular Arithmetic

Visualizing Modular Arithmetic
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2016-02-01 07:30
Geometric Construction
This example demonstrates the visualization of addition in modular arithmetic using a clock with n hours. It involves core math concepts like modular arithmetic and number theory. Construction uses commands like Line, Segment, Circle, Mod, Rotate, Sequence, Arc. Suitable for high school mathematics learning and understanding the visual representation of modular operations.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Segment(Point[{0, 7}], C) → d
  3. Circle(E, 10) → h
  4. Mod(f, l) → i
  5. Rotate(G, (((24 - b / 2 - c / 2) * 30))°, E) → G_p
  6. Rotate(F, (((24 - b) * 30))°, E) → F_b
  7. Sequence(Segment[((t * 20 / l), 6), ((t * 20 / l), 8)], t, 0, (2 * l), 1) → list1
  8. Segment(C, D) → e
  9. Sequence(Rotate[F, ((t * 360 / l))°, E], t, 1, l, 1) → list2
  10. Sequence(Segment[E, Rotate[F, ((t * 360 / l))°, E]], t, 0, l, 1) → list3
  11. Rotate(G, (((l - b) * 360 / l))°, E) → G_b
  12. Rotate(G, (((l - b - c) * 360 / l))°, E) → G_c
  13. Rotate(G_2, (((l - b - c) * 360 / l))°, E) → G_r
  14. Arc(h, Rotate[F, (((l - b) * 360 / l))°, E], F) → k
  15. Arc(h, Rotate[F, (((l - b - c) * 360 / l))°, E], Rotate[F, (((l - b) * 360 / l))°, E]) → p