A circle is the collection of all points at a given distance r from a specified point. If you've 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's a lofty goal, but who are we to tell you it'll never happen? Dream on, dreamer.
The specific point we're 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?" is basically too ambiguous to answer. We'll 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 fancy name to go along with it. The perimeter of a circle is called its circumference, and it's given by the formula:
C = 2πr
...where C means circumference, and r means radius.
The area A of a circle is given by A = πr2. And don't forget, π is an irrational number that comes out to about 3.14 when we round it.