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.

One Groove Over. As Author Hogben approaches modern times, he takes his readers painlessly through the discoveries of Galileo and Newton, through Descartes to Karl Gauss. Just as painlessly, he introduces them to algebra, the laws of acceleration, the concepts of mass and weight, binary numbers, and the graph plottings of the parabola and the ellipse. But his major accomplishment will be to give his readers the notion of mathematics as a major part of their heritage:

"Even when we use the electronic calculator we are indebted to the long-forgotten Eastern merchant who first adapted number signs to the layout of the abacus. His predecessor, the temple scribe who gave each pebble a number value ten times as great when moved one groove to the left, first gave ordinary men a clear idea of the use of a fixed base in mathematics. The electronic calculator of today still makes use of a fixed base, though it commonly employs a base of two instead of ten . . . All our modern aids to calculation are the rewards of work done in the past. But the mathematicians of the age of power are using the heritage of the past to forge new tools of scientific thought for the use of future generations."

*--' Expressing the relativistic increase of mass. **E.g., to multiply 102 by 96: add 102 to 96 and divide the result by 2 to find the average (99); take 96 from 102, divide the result by 2 to find half the difference between the two numbers (3); look up in the table the square of 99 (9,801); look up in the table the square of 3 (9); take 9 from 9,801 for the correct answer: 9,792.

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