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Can mathematics turn one ball into two?

The Banach-Tarski theorem describes a mathematical ball decomposed into sets of points and rearranged into two balls the size of the original. The word “pieces” is doing unusual work: these are not ordinary slices of rubber or wood. Understanding the result means asking what counts as a set, what motions are allowed, and when a volume can be assigned.

5–7 min

Questions you could explore

  • Which assumption about ordinary cut-up objects makes the theorem sound impossible?
  • Why do the sets in the Banach-Tarski theorem differ from pieces that could be physically cut and reassembled?

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3–5 min

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Maths and statistics

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2–3 min

The leap years the Gregorian calendar skips

Maths and statistics2–3 minMost people learn that a leap year happens every four years, yet the year 1900 had no February 29 while the year 2000 did. Because Earth's orbit takes slightly less than 365.25 days, the Gregorian calendar skips three leap years every four centuries to keep the calendar aligned with the seasons.

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