A circle is the set of all points in a plane equidistant from a fixed point called the center.
A circle is a fundamental geometric shape defined by its center and radius. Key features include the radius (distance from center to edge), diameter (twice the radius, passing through center), circumference (the perimeter), chord (any line segment connecting two points on the circle), arc (a portion of the circumference), and sector (a slice of the circle). Circles are perfectly symmetric and appear throughout nature, science, and engineering.
Circles have been studied since prehistory. The ancient Babylonians estimated π ≈ 3.125, while Egyptians approximated it as 3.16. Greek mathematician Euclid devoted much of his "Elements" to circle geometry. Archimedes computed π between 3.1408 and 3.1429. The circle has been a symbol of perfection, infinity, and cycles across cultures. The study of circle geometry remains fundamental in mathematics.