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a{+2} + b{+2} = c{+2}

This tablet, created nearly 4,000 years ago, shows that the Babylonians had calculated the square root of two to great accuracy.
This tablet, created nearly 4,000 years ago, shows that the Babylonians had calculated the square root of two to great accuracy. (Courtesy Of Bill Casselman -- University Of British Columbia)
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Monday, October 6, 2008

The Dawn of Math

For ancient civilizations, knowing math was a matter of life and death. To build city walls that could repel raiding tribes required geometry. To build irrigation ditches or develop a calendar that would tell when to plant crops required complex calculations.

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Some ancients went for extra credit: The Chinese developed an advanced astronomical system; the Egyptians showed off their geometry with the pyramids; the Babylonians cultivated the dry lands of Mesopotamia; the Greeks and Romans built remarkable amphitheaters, aqueducts, arenas and arches. It all took math.

As soon as humans learned to write, they were writing word problems: how to divide wheat evenly among people, how to determine the perimeter of a building and so on. Some even included teachers' corrections.

"Seven houses contain seven cats. Each cat kills seven mice. Each mouse had eaten seven ears of grain. Each ear of grain would have produced seven hekats of wheat. What is the total of all of these?" goes a problem from the Rhind Mathematical Papyrus, written by an Egyptian mathematician named Ahmes about 1600 BC. (The problem illustrates geometrical progressions.)

A piece of clay in the Yale Babylonian Collection shows that the Babylonians had calculated the square root of two to a great degree of accuracy, almost 4,000 years before it could be punched into a calculator.

In the ancient world as today, mathematics was associated with basic reasoning ability. Plato, in his dialogue "Meno," has Socrates help a slave boy discover how to solve a geometry problem.

Of the oldest mathematicians, Pythagoras is probably remembered best.

The theorem named after him, which he almost certainly didn't discover, shows the relationship between the legs of a right triangle (call them a and b) and the hypotenuse, c. To this day, it's taught in geometry classes: a{+2} + b{+2} = c{+2}


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