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Every circle's hidden number

What Is Pi and Why Does It Never End?

Pi is how many diameters fit around a circle, and it is the same for every circle there is.

πMeasure around a circleMeasure straight acrossitDivide one by the otherAlways about 3.14
Every circle hides the same number.
  1. Step 1 of 5

    Every circle has two natural measurements.

    Around the edgeThe circumferenceStraight across The diameter

    The distance around the outside, and the distance straight across through the centre. Those two are all pi needs.

  2. Step 2 of 5

    Dividing one by the other always gives the same number.

    1Measure around2÷Divide byacross3πAlways about3.14

    Try it on a mug, a coin or a stadium and the answer never changes. About 3.14 diameters fit around any circle at all.

  3. Step 3 of 5

    So a circle is a bit over three times around.

    Three diametersA small gapleftSo 3.14 intotal

    Three diameters nearly wraps the circle, leaving a small gap. That leftover fourteen hundredths is what makes pi awkward.

  4. Step 4 of 5

    The digits never repeat and never stop.

    22/7close but wrong3.14159closer, stillnot exact

    Pi cannot be written exactly as a fraction, so its decimals run forever without settling into any repeating pattern.

  5. Step 5 of 5

    A few digits are plenty in practice.

    3.14fine for aclassroom3.14159fine forengineering15 decimalsfine for thesolar system

    Fifteen decimal places would place a circle the size of the solar system to within the width of a finger. Nobody needs more.

    NASA uses 15 decimal places of pi, enough to calculate a circle the size of Earth's orbit to within a couple of centimetres.

The short version

Pi is how many diameters fit around a circle, the same for every circle, and its decimals run forever without repeating.

Try it yourself

Wrap string around a mug, then measure across the top. The string is always a bit over three times the width.

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