Difference between revisions of "Circle"
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A '''circle''' is the [[set]] of all the points in a given [[plane]] that are the same distance, called the [[radius]], ''r'', from a given [[point]] called the center. | A '''circle''' is the [[set]] of all the points in a given [[plane]] that are the same distance, called the [[radius]], ''r'', from a given [[point]] called the center. | ||
| − | A circle may also be defined [[algebra]]ically, as the solutions to an equation of the form: | + | A circle may also be defined [[algebra]]ically, as the set of solutions to an equation of the form: |
| − | :<math>x^2 + y^2 = r^2</math> | + | :<math>(x-a)^2 + (y-b)^2 = r^2</math>, |
| + | where <math>(a,b)</math> is the center of the circle. | ||
| − | The | + | The distance around the circle, or circumference, is given by: |
:<math>C = 2\pi*r</math> | :<math>C = 2\pi*r</math> | ||
Revision as of 22:10, May 7, 2007
A circle is the set of all the points in a given plane that are the same distance, called the radius, r, from a given point called the center.
A circle may also be defined algebraically, as the set of solutions to an equation of the form:
- <math>(x-a)^2 + (y-b)^2 = r^2</math>,
where <math>(a,b)</math> is the center of the circle.
The distance around the circle, or circumference, is given by:
- <math>C = 2\pi*r</math>
The area inside the circle is calculated using the formula:
- <math>A = \pi*r^2</math>
A circle is a conic section, the intersection of a plane with a cone such that the plane is perpendicular to the axis of the cone.
Circles can readily be constructed by using a fixed distance between a pencil point and the center. A compass is a tool for doing this easily.
A circle with <math>r = 1</math> is called the unit circle, and is used extensively in trignometry.