Geometry: Tangents


You might have observed that I occasionally go off on a tangent. In fact, I've gone off on several tangents just in this section alone! When someone goes off on a tangent, it's usually because some memory or thought is triggered. It usually involves going off the subject, in some completely different direction, and the audience is left wondering how the current topic of conversation relates to the one they just came from. The phrase “going off on a tangent” has its basis in geometry. A tangent is a line that intersects a circle at exactly one point. The point of intersection is the point of tangency.

Figure 17.7 shows a circle with a tangent line. Notice that the line only intersects the circle once and seems to glance off of the circle as it travels on its way. If you draw the radius of the circle that passes through the point of tangency, you will see that that radius and the tangent line are perpendicular.

Figure 17.7A line tangent to a circle.

Tangent Line

Tangent lines have their applications in physics as well. If you put a stone in a sling and spin it around, faster and faster, you are spinning the stone and the sling in the shape of a circle. If you then release the stone, it will travel in a direction tangent to the spinning circle.

Excerpted from The Complete Idiot's Guide to Geometry © 2004 by Denise Szecsei, Ph.D.. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.

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