Definition of a Circle - Geometry Made Easy!

# Circles

A circle is the set of points on a plane that are all the same distance from a center point. Or, you could think of a circle as the part of the plane that lies inside those points. A circle is flat - it has no thickness. But every circle has a radius, a diameter, a circumference, and an area.

The radius of a circle is the distance from the center point to any point on the edge of the circle, as shown in the picture. The diameter of a circle is twice the radius - the distance all the way across the circle at its widest point. The circumference of a circle (from "circa", the Latin word for "around") is the distance around the edge of the circle. And the area of the circle is all of the points on the plane inside the circle, taken together. A cool thing about circles is that we know one of these, we can figure out all of the others. If we know the radius of a circle, we can figure out its diameter, its circumference, and its area - or if we know the circumference, we can figure out the radius, the diameter, and the area. And we can prove that this will always work, for any circle.

Say we know that the radius of a certain circle is 10 centimeters. Click on the links to see how to calculate the diameter, the circumference, and the area of that circle.

If we draw a circle as a solid, not just in one plane, but all of the points in any direction that are the same distance from the center point, then we have a sphere.

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Professor Carr

Karen Eva Carr, PhD.
Assoc. Professor Emerita, History
Portland State University

Professor Carr holds a B.A. with high honors from Cornell University in classics and archaeology, and her M.A. and PhD. from the University of Michigan in Classical Art and Archaeology. She has excavated in Scotland, Cyprus, Greece, Israel, and Tunisia, and she has been teaching history to university students for a very long time.

Professor Carr's PSU page

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