Head First 2D Geometry

Pi

25 p

i

eces of p

epp

eroni

32 p

i

ec

es of p

epp

eroni

50 p

i

relationship between circumference and diameter

The pepperoni perimeter is 3 (and a bit)

times diameter

There’s a pattern: no matter what size the pizza, the pepperoni

perimeter is a little more than three times the diameter.

8"

10"

ec

es of p

epp

eroni

16"

25 = 3.123

8

32 = 3.2

10

50 = 3.125

16

A circle’s circumference is diameter x Pi

In geometry terms, a circle’s perimeter is called the circumference,

and no matter how big or small that circle is, you can find the

circumference by multiplying the diameter by the same number.

Roughly it’s just barely over three, and we call this number Pi. Pi is

T

he circumf

er

ence of a

circle is given by:

Circumf

er

enc

e =

π

D

or

Circumf

er

enc

e = 2

π

r

T

hese ar

e equa

l

because D = 2r.

usually written using this symbol:

π

214 Chapter 5

Y

ou can probabl

y find a Pi

button on your ca

lcul

a

t

or. It

might give y

ou 3.14159, or it

might give y

ou something wi

th

ev

en mor

e decimal pl

ac

es.

No ca

lcul

a

t

or?

Subs

ti

tute the

frac

tion 22/7

f

or a close

approxima

tion

t

o Pi.

circles

Ha ha…very funny. Not.

The chapter is about pizza

and now you’re throwing in

a made-up number called

"Pie"....

“Pi” is actually a letter from

the Greek alphabet.

It’s used to stand in for the number

that you always get when you divide a

circle’s circumference by its diameter.

Why do you think “math people” find Pi, or π, more useful

than 3.1415926535897932384626433832795…?

you are here 4 215

pi is a ratio

Q:

When you showed the formula for circumference, you

put πD but also 2πr—does it matter which I use?

A:D is diameter, and r is radius, so the two formulas always

give the same answer since D = 2r. It doesn’t matter which you

use—it just depends on whether you’ve got the diameter or the

radius available.

Q:

So, in like two pages you’ve shown Pi as “just barely

over three,” 3.14159, a way-long decimal, and even 22/7…

which is it?

A:Pi is what is known as an irrational number. That means

that even if you used a billion decimal places you couldn’t write it

down completely. Depending on what you’re using Pi for you might

need to use a more or less precise version of it. On an exam, you’ll

usually be told what to use, otherwise just take whatever your

calculator gives you when you press the π button, and remember to

round your answer to fit with the question.

OK, so Pi is really nothing more than

a placeholder for the ratio between

a circle’s circumference and its

diameter? I guess it’s quicker than

writing or saying 3.14159265358979

32384626433832795…?

Exactly.

Math geeks talk about Pi as if it’s kind of magic—and

it’s certainly pretty useful because it works for every

circle, every time—but really Pi is just a quick way of

saying “that big long number that you get when you

divide circumference by diameter.”

216 Chapter 5