CHAPTER 2 Overcoming Mathophobia: Reading and Understanding Mathematical Expressions 17

Checking out the building

blocks of formulas

No matter how they’re written, formulas are essentially recipes that tell you how

to calculate a result, or how a value is defined. To cook up your own result, you

need to know how to follow the recipe. When initially approaching a formula, it’s

helpful to start by examining the building blocks from which formulas are con-

structed. These include constants, which are numbers with specified values, and

variables, which represent quantities that can take on different values at different

times.

Constants

Constants are values that can be represented explicitly (using the numerals 0

through 9 with or without a decimal point), or symbolically (using a letter in the

Greek or Roman alphabet). Symbolic constants represent a particular value impor-

tant in mathematics, physics, or some other discipline, such as:»

» ^{The Greek letter π usually represents 3.14159 (plus a zillion more digits). This}

Greek letter is spelled pi and pronounced pie, and represents the ratio of the

circumference of any circle to its diameter.»

» ^{The number 2.71828 (plus a zillion more digits) is represented by e (which is}

italicized when written, and is pronounced like the letter “e”). Later in this

chapter, we describe one way e is used. You’ll see e in statistical formulas

throughout this book and in almost every other mathematical and statistical

textbook. Whenever you see an italicized e in this book, it refers to the

number 2.718 unless we explicitly say otherwise.

The official mathematical definition of e is: The value of the expression

1 1/n

n, which approaches infinity as n gets larger and larger. Unlike π, e

has no simple geometrical interpretation. Here is an example used to help

learners envision e: Assume you put exactly one dollar in a bank account that’s

paying 100 percent annual interest, compounded continuously. After exactly

one year, your account will have e dollars in it. That includes the interest on

your original dollar, plus the interest on the interest — about $1.72 (to the

nearest penny) — added to the original dollar for a total of $2.72. (This is just

an example. We don’t think there is a single bank out there advertising annual

returns in terms of e!)

Mathematicians and scientists use lots of other specific Greek and Roman letters

as symbols for specific constants, but you need only a few of them in your biosta-

tistics work. π and e are the most common, and we define others in this book as

they come up in topics we present.