A circle is a two-dimensional shape defined as the set of all points in a plane that are at a fixed distance from a given point, the center.

This fixed distance from the center to any point on the circle is called the radius (r).

A circle is a perfect example of geometric symmetry.

Diameter (d): A straight line segment that passes through the center of the circle and whose endpoints lie on the circle. The diameter is always twice the length of the radius (d = 2r).

Circumference (C): The distance around the outside of the circle. It is the perimeter of the circle.

Chord: A straight line segment whose endpoints both lie on the circle. The diameter is the longest possible chord.

Arc: A portion of the circumference of a circle.

Sector: A region of a circle enclosed by two radii and an arc, like a slice of pizza.

The ratio of a circle's circumference to its diameter is a constant value for every circle, no matter its size. This special constant is called Pi (π).

Pi is an irrational number, which means its decimal representation never ends and never repeats. We often approximate it as 3.14159 or 22/7.

Formula for Circumference: C = πd or C = 2πr.

The area of a circle is the amount of two-dimensional space it occupies.

It is calculated using the radius and the constant Pi.

Formula for Area: A = πr² (Pi times the radius squared).

Notice that the area grows much faster than the radius because it depends on the square of the radius.

Circles are fundamental to engineering, physics, and design.

Engineering: Wheels, gears, pipes, and bearings all rely on the properties of circles for smooth and efficient operation.

Physics: The orbits of planets and the wave patterns of light and sound are often modeled using circles and spheres.

Design: Clocks, logos, plates, and architectural domes use circles for aesthetic appeal and functional design.