Multiples Jump: Three Blank Circles Demo

Multiples Jump: Three Blank Circles Demo
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2020-08-30 13:27
① This example demonstrates an animation where multiples jump across three blank circles, visualizing the distribution and periodicity of integer multiples. ② Core mathematical concepts include multiples, arithmetic sequences, modular arithmetic, and random selection. ③ Construction highlights: Sequence generates the multiples list, RandomElement picks random items, Point and Circle create the geometric objects, CurveCartesian draws auxiliary curves, Corner positions UI components, and buttons, a timer (semitimer), and a speed slider provide interactive control. ④ Suitable for upper‑primary to lower‑secondary mathematics lessons, as well as for number‑sense practice and introductory computational thinking.

GeoGebra Commands & Parameters

  1. Corner(5) → dims
  2. Sequence(0, (10 * mM), mM) → l1
  3. CurveCartesian((mM / ((2 * π)) * (t - sin(t))), (mM / ((2 * π)) * (1 - cos(t))), t, 0, ((semitimer * 2) * π / mM)) → ballc
  4. Point(ballc, semitimer) → ball
  5. Sequence((n, 0), n, 0, semitimer, 1) → l2
  6. Sequence((n, 0), n, 0, semitimer, mM) → l3
  7. RandomElement(Remove[l1, {0, (10 * mM)}]) → ransq
  8. RandomElement(Remove[l1, {0, ransq}]) → rantr
  9. RandomElement(Remove[l1, {0, ransq, rantr, (10 * mM)}]) → rancir
  10. Sequence(Text[Element[l1, n], (Element[l1, n] - (0.05 * mM), (-0.1 * top))], n, 1, (semitimer + mM) / mM) → l4