Education: Wonderful World

While U.S. teachers and parents hotly debate how best to teach Johnny his reading, many are also wondering: What about his math? For those worried about Johnny's lack of interest, new hope came last week in the form of a colorfully illustrated book called The Wonderful World of Mathematics (Garden City Books; $2.95). Written by Lancelot

(Mathematics for the Million) Hogben, professor of medical statistics at Britain's University of Birmingham, Wonderful World is a fast-paced history of the subject from the days when people "thought of any quantity greater than three as a heap or pile'' to the age of Albert Einstein's

Author Hogben's purpose is not to teach his young readers their algebra, but to show how man built up his world of signs and symbols to solve the problems of his everyday existence and then to expand his civilization. He starts with the sun and the moon, man's first clocks and calendars, and with the notches that the shepherd cut when counting his flock. Then come the calendar keepers, the powerful group who could tell people when to plant crops. Later men developed more complicated desires. The farmer wanted to know how much land he had, the sailor what course to plot, the priest what taxes to collect. Out of each of these developed an addition to mathematics.

Dot, Dash. To keep track of the seasons, the calendar makers had to have records, and this meant a system of written numbers. Of all these early systems, the most efficient was that of the Mayans, who used only three symbols—a dot (1), a dash (5), and an oval that could multiply each number 20 times. Meanwhile, other civilizations had other inventions. The Egyptians had to find ways to make a right angle so that the base of each pyramid would be an absolute square; they also had to find out how to measure land for taxes. Thus emerged their first knowledge of what became geometry (named after the Greek words meaning earth and measure).

The Egyptian Ahmes, the Moonborn, described the almost exact formula for determining the area of a circle. By using tables of squared numbers,* the Mesopotamians learned to multiply without the use of an abacus. Pythagoras, who was the leader of a secret mathematical and religious sect, stated his famous theorem about right triangles (the square of the hypotenuse is equal to the sum of the squares of the other two sides). After him came even greater names: Euclid, Archimedes, Eratosthenes, who estimated the circumference of the earth (about 24,000 miles), and Hipparchus, who anticipated the modern tables of sines. But to many Greeks, mathematics was also a game. They were the first to notice that adding ten consecutive odd numbers, beginning with i, is the same as multiplying ten times ten, and that adding 20 such numbers is the same as squaring 20. Zeno also pretended to prove arithmetically that if a tortoise got one-tenth of a mile head start, Achilles, running ten times as fast, could apparently never overtake him.