Geometry: a new angle on your future - what do I do with …

Career World, Oct, 2003 by Fred N. Springsteel

You've read the directions on the can of latex wall paint and know that a gallon covers 350 square feet. You've measured the room and bought just the right amount. You've calculated the amount of trim that will go around the doors and the octagonal window. You've determined the amount of carpeting you'll need for the room, and even whether the roll of carpeting you bought will make the turn up the narrow stairway.

Congratulations! You know something about the practical uses for geometry (and your bedroom is going to look great, too).

The Unusual "Side" of Geometry

As you know, geometry has a practical, technical side to it. But it has another side too--one that is deeper, and equally important. You will need to learn many new things in your life. If you can learn new skills, you will qualify for the newer jobs, with a chance for better pay. However, to do so, you must develop both sides of your brain, your most powerful instrument.

Your brain is composed of two halves, like a walnut. Your right brain controls your sense of the "whole picture": awareness of space, attitudes, and artistic impulses. Your left brain controls language, math, and musical rhythm--in short, anything linear or sequential. The two halves communicate so that your brain can function at its highest level.

Left, Right, Left

To maximize its power, you must develop both sides of your brain. However, many young people find one thing they enjoy, such as playing the guitar, and spend all their free time doing that. Keeping rhythm uses the left brain slightly. Writing lyrics develops a strong holistic imagination, a right-brain activity. That's what full-time composing overemphasizes. A musical artist who isn't able to manage his or her own business (a left-brain activity) will be fully dependent on someone who can.

In order to be well-rounded, you need to develop your logical analysis and sequential thinking, which reside in the left brain. The Greeks invented the greatest boon to logical thinking ever: Yes, it's geometry. For most people, the main benefit lies in its method of reasoning and thinking about concepts such as circles, lines, points, and composed figures, such as triangles, squares, and other polygons. Scientists are generally left-brain-dominant, with a rational and logical preference. They tend to process information step by step.

Train Your Brain

From about 500 B.C., the secrets of geometry had been hidden away by mystics like Pythagoras. They were first written down two hundred years later, around 300 B.C., by the Greek mathematician Euclid. Euclid wrote about geometry in order to make it available to Greece's literate society.

Why is geometry so good for training your brain? Euclid wrote The Elements, the first book to use the axiomatic method. From a small number (five) of axioms, or self-evident truths, this logical man found an unlimited number of conclusions. The process is called deduction, and it enriches the left brain. Deborah Frank-Alley, a geometry teacher at Oak Park High School in Gladstone, Missouri, says, "I believe that every career uses the logical reasoning learned in geometry. To be competitive in a very demanding market, you must possess these skills."

An Invaluable Tool

Throughout the centuries since Euclid, geometry has been an invaluable tool. The Romans built roads, viaducts, aqueducts, and large public baths. They built arches and even some domes. But around A.D. 400, the skill was lost. Muslim engineers kept the knowledge alive throughout the Middle Ages, building castles, earthworks, and domes. After 1120, The Elements was translated from Arabic to Latin. As a result, in the late Middle Ages, domes were again built in Europe.

In our day, one of the most productive uses of simple geometry is in the building of wood-frame houses. Carpentry involves the use of certain angles (30, 60, and 45 degrees, for example). Boston carpenter Jamie Leef praises the usefulness of geometry: "Oh, we use it every day--either implicitly or explicitly. If you don't know your geometry very well, then you have to trust your tools--your square and so on. If you know it, you can check your work better and become a master carpenter." Leef is also a computer science student at Massachusetts Institute of Technology (MIT).

Geographers and surveyors use geometry as well. Navigators must know how to use compass-and-divider chart navigation ("dead reckoning") in case they can't see the stars and their Global Positioning System (GPS) fails. The satellite-borne GPS is itself built on the truths of geometry's specialty--trigonometry.

A less obvious user of geometry--on the artistic side--is the computer graphics designer, or computer-aided design (CAD) specialist. Virtually all building plans are now done using CAD, which was also developed with geometric principles.

Beyond its everyday uses, geometry is the basis for all later mathematics, from advanced algebra to college math. Even if you don't take more advanced mathematics courses, learning to be logical will help you in problem solving and analytical functioning--essential in speech, debate, persuasive writing--and more.