# Locus

## Applications

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

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.

J. R. Maddocks

## Additional topics

Science EncyclopediaScience & Philosophy: *Linear expansivity* to *Macrocosm and microcosm*Locus - Compound Loci, Applications