Technical Mathematics, Sixth Edition

6.4. The Circle

A circle, Fig. 6-62, is a plane curve in which all points are at a given distance (called the radius) from a fixed point (called the center). The diameter is twice the radius. The diameter cuts the circle into two semicircles.

6.4.1. Circumference and Pi (π)

The circumference of a circle is its total length, or the distance around.

▪ Exploration:

Try this. Wrap a strip of paper around a circular object, such as a jar lid, and mark the point where it starts to overlap. The length from the mark to the end of the strip is the circumference of the circular object. Next measure the diameter of the lid, divide that number into the circumference, and record. Repeat for several circular objects. What did you find?

You should have gotten a quotient a bit larger than three, regardless of the size of the lid. The ratio of the circumference C of a circle to its diameter d is the same for all circles. It is denoted by the Greek letter π(pi).

Figure 6.62. A circle.

NOTE

Pi is the ratio of the circumference of any circle to its diameter.

Pi (π) is an irrational number with the approximate value 3.1416. It is stored in your calculator to more decimal places than you will probably ever need. Look for a key marked .

We can use the definition of to find the circumference of a ...