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A rolling coin turns relative to two different references

Roll one coin without slipping around another of the same size. The moving coin turns twice relative to the table before returning to its starting point, even though the two circumferences are equal.

3–7 min

Questions you could explore

  • What changes when you count turns relative to the table instead of the other coin?
  • How could marking one point on the coin make its full rotations easier to count?

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  • Wolfram MathWorldCoin Paradox

    Explains the extra rotation by following the moving coin’s center. Its formula assumes circular edges and rolling without slipping.

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Maths and statistics

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3–5 min

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The leap years the Gregorian calendar skips

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2–3 min

The leap years the Gregorian calendar skips

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