- Topics At a Glance
- Variables
- Variables as Unknown Quantities
- Variable Notations
- Constants
- Expressions and Equations
- Rearranging Expressions
- Commutative Properties
- Associative Properties
- Distributive Properties
- Factoring (Distributive Property in Reverse)
- Combining Like Terms
- Eliminating Parentheses
- Simplifying
- Equations, Functions, and Formulas
- Equations
- Functions
- Independent and Dependent Variables
- Formulas
- Applications to Toolbox
- Evaluating Expressions by Substitution
- Evaluating Formulas by Substitution
**Geometric Formulas**- Four-Sided Shapes
- Three-Sided Shapes
**Circles**- Unit Conversion
- Temperatures
- Weights
- Distances and Speeds
- Money
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

A **circle** is the collection of all points at a given distance *r* from a specified point. If you have grown tired of collecting baseball cards or Wii games and want to take up a new hobby, start collecting points, and perhaps you too can one day be a circle. It is a lofty goal, but who are we to tell you it will never happen? Dream on, dreamer.

The specified point we are referring to is called the **center** of the circle, and the distance *r* is called the **radius** of the circle.

Here's a fun—and yet, at the same time, incredibly frustrating—puzzle to consider: how many sides does a circle have? Depending on how "side" is defined, potential answers may vary. If a "side" must be a straight line, then a circle clearly has no sides. If a "side" can be curved, then a circle has one side. Perhaps a circle has infinitely many sides? Or maybe it has a "good side" and a "bad side." It does look a little more handsome when it turns to the left. The question, "How many sides does a circle have?" appears to be too ambiguous to answer. We will answer it with an equally ambiguous, "Hmm...eh."

Since we can't add the side lengths of a circle to find its perimeter, we need a special formula, and a special, fancy name to go along with it. The perimeter of a circle is called its **circumference**, and is given by the formula

*C* = 2π*r,*

where *C* means circumference, and *r* means radius.

The area *A* of a circle is given by *A* = π*r*^{2}.