# Locus

## Applications

There are many other interesting loci, for example the cycloid.

Figure 2. Illustration by Hans & Cassidy. Courtesy of Gale Group.

Figure 3. Illustration by Hans & Cassidy. Courtesy of Gale Group.

The cycloid is the locus of a point on a circle as the circle rolls in a straight line along a flat surface. The cycloid is the path that a falling body takes on a windy day in order to reach the ground in the shortest possible time. Some interesting loci can be described by using the moving point definition of locus. For example, consider this simple mechanism. (Figure 3.)

It has a pencil at point A, pivots at points B and C and point D is able to slide toward and away from point C. When point D slides back and forth, the pencil moves up and down drawing a line perpendicular to the base (a line through C and D). More complicated devices are capable of tracing figures while simultaneously enlarging or reducing them.

## Resources

### Books

Fuller, Gordon, and Dalton Tarwater. Analytic Geometry. 6th ed. Reading, MA: Addison Wesley, 1986.

Gowar, Norman. An Invitation to Mathematics. New York: Oxford University Press, 1979.

Larson, Ron. Calculus With Analytic Geometry. Boston: Houghton Mifflin College, 2002.

Smith, Stanley A., Charles W. Nelson, Roberta K. Koss, Mervin L. Keedy, and Marvin L. Bittinger. Addison Wesley Informal Geometry. Reading, MA: Addison Wesley, 1992.

## KEY TERMS

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Conic section

—A conic section is a figure that results from the intersection of a right circular cone with a plane. The conic sections are the circle, ellipse, parabola, and hyperbola.

Line

—A line is a collection of points. A line has length, but no width or thickness.

Plane

—A plane is also a collection of points. It has length and width, but no thickness.

Point

—In geometric terms a point is a location. It has no size associated with it, no length, width, or thickness.

Right circular cone

—The surface that results from rotating two intersecting lines in a circle about an axis that is at a right angle to the circle of rotation.