“91974˙CH02˙ﬁnal” — 2012/12/14 — 13:58 — page 46 — #2
46 CHAPTER 2
Figure 2.1 Pi—the ratio of circumference (C ) to diameter (d)
Other common formulas that utilize pi include the area of a circle with radius r, A = πr
the volume of a sphere with radius r, V =
, and the surface area of a sphere with
radius r, S =4πr
. In this chapter, we are more interested in the value of pi itself, not in
the way that pi is used.
The value of pi has been a matter of interest for thousands of years. Writings from ancient
Egypt and Babylon as well as the Bible contain references to this mystical number. In
your math class, it is likely that you were told to use 3.14 or 3.14159 as the value of pi. In
fact, these values worked fairly well for many of the problems that you were asked to solve.
However, it turns out that the exact value of pi is not as simple as this would make it seem.
Pi is known in mathematics as an irrational number. This means that pi is a ﬂoating-point
number with an inﬁnite, nonrepeating pattern of decimal digits. The actual value of pi is
where the ... indicates the inﬁnite digits.
Because pi cannot be stated exactly, the best that we can do is provide an approximation,
for example 3.14. Other usual approximations are
, and the more complex