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CHAPTER

2

othon

2.1 Objectives

To understand how computers can help solve real problems

To further explore numeric expressions, variables, and assignment

To understand the accumulator pattern

To utilize the math library

To further explore simple iteration patterns

To understand simple selection statements

To use random numbers to approximate an area

2.2 What Is Pi?

In this chapter we will continue to explore computer science, problem solving, and the

Python programming language by considering one of the most famous numbers of all: the

number pi, often represented by the Greek letter π. Almost everyone has at one time or

another used the value pi. In fact, we used π in Chapter 1 in our circle calculations.

Pi is deﬁned to be the ratio of a circle’s circumference to its diameter (see Figure 2.1).

This relationship, π = C/d, gives rise to the familiar equation C = πd used to compute

the circumference of a circle given the diameter. Since the diameter of a circle is twice the

radius, this can also be written C =2πr where r is the radius.

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46 CHAPTER 2

π

thon

C

d

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

2

,

the volume of a sphere with radius r, V =

4

3

πr

3

, and the surface area of a sphere with

radius r, S =4πr

2

. 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

3.14159265358979323846264338327950288419716939937510...

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

22

7

,

355

113

, and the more complex

9801

2206

√

2

.

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