Nearly everyone has 10 fingers and 10 toes, and it's been like that for a long, long time. So, it's probably natural that we count by tens—so natural that the decimal system is, by far, the most common way of expressing numbers in both spoken and written language around the world.

In ancient times, Pythagoras and his followers taught that "everything is number." They considered 10 to be special because it's the sum of the first four numbers, 1, 2, 3, and 4, and sets of 1, 2, 3, and 4 items can be arranged to form a triangle (like the pins in a bowling alley). To the Pythagoreans, this triangle was sacred, and they even swore oaths by it.

Ten objects (billiard balls) arranged to form a triangle (above).

However, 10 isn't quite so convenient when you have to measure out small amounts or take fractions of a whole. In the decimal system, it's easy to deal only with halves and tenths. But if you're slicing a pizza, halves, fourths, eighths, and sixteenths are much handier. That's what European merchants realized hundreds of years ago. Even though they used a number system based on 10 for counting and calculations, their systems of weights and measures often involved quarters, eighths, twelfths, twentieths, twenty-fourths, or sixtieths—anything but tenths. For example, there are 2 pints in a quart, 4 quarts in a gallon, 12 inches in a foot, 16 ounces in a pound, 24 hours in a day, and so on. Many people still use such measures today.

The English language shows traces of this past. Notice that the numbers from 1 to 12 all have distinctive names, though "eleven" is related to "one" and "two" to "twelve." It's only at 13 that the names for numbers begin to follow a standard, ten-based pattern: thirteen = three + ten.

So, just because we happen to have 10 fingers and 10 toes, we celebrate tens. If we had 12 fingers and 12 toes, we might have ended up with a number system based on 12. And for fraction fanatics, that would have been much tidier.

Muse, January 2007, p. 22.

## MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for *Muse* magazine.

## July 4, 2007

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