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The digits of pi run on forever without ever settling into a repeating pattern of any length.

Mathematics Facts, sourced to Wolfram MathWorld.

What it means

A decimal that eventually repeats can always be written as one whole number over another, and pi cannot be, which was proved in the eighteenth century. So the expansion has no period at any scale. It is also transcendental, meaning it is not the solution of any polynomial equation with whole number coefficients, and that is what finally settled the ancient question of squaring the circle.

The claim comes from Wolfram MathWorld, and the page it comes from was read on 2026-08-27 to confirm it still says this.

This is not the kind of claim that goes out of date, which is why it was set as a puzzle rather than a fact with a shelf life.

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