TABLE OF CONTENTS Circles have long intrigued humans. Often called the perfect geometric form, the circle occurs frequently in engineering design, art, architecture, and applied mathematics. Almost 2200 years ago, Archimedes sought to find a square with the same area as a given circle. This problem is called squaring the circle.
The circle forms the base for systems of navigation on the sea and in the air. The geometry of circles involves not only the relationships of the principal parts of the circle but also the relation of the circle to lines, angles, and polygons.
A circle is the set of all points in a plane equidistant from a given point. This distance is the length of the radius and the given point is the circle s center. A circle is named by its center point. For example, a circle with center at point O is referred to as circle O.
Circles are symbolic of infin ity, eternity, and complete ness. They appear in the literature and architecture of many cultures.
Figure 19.1 is a drawing of a circle with nearby points. Note that a point may lie either on the circle; or it may lie inside the circle, making it an interior point of the circle; or it may lie outside the circle, making it an exterior point of the circle. A common mistake is to view interior points, including the center, of a circle as part of the circle.
