The Circle (Mathematical Concept)

A circle is a set of all points in a plane that are equally distant from a fixed point called the center. The distance from the center to any point on the circle is called the radius. The circle's boundary is called the circumference. Mathematically, the circle's equation in a coordinate plane is \( (x - h)^2 + (y - k)^2 = r^2 \), where \((h,k)\) is the center and \(r\) is the radius. Circles are fundamental in geometry, representing symmetry and continuous curves, and are used in various fields such as engineering, design, and nature.