Pi is represented by the symbolπ(the sixteenth letter of the Greek alphabet) and appears in a number of measurement formulas. These formulas include c = 2πr and A=πr², where c is a circle's circumference or the distance around its outer edge, r is its radius or the distance from the center of the circle to its outer edge, and A is the circle's area. What is pi and why doesπappear in these formulas?

What Is Pi?

What do the following items have in common with each other and all other circular figures: a quarter, approximately 1 inch across; a compact disc, 12 centimeters wide; a circular patio pool, spanning about 23 feet; and Earth's equator, roughly 8,000 miles in diameter. These estimated diameters are summarized in the table below, along with the estimated circumferences of the circular items.

In each case in the table, the circumference is about three times...