How is the diameter of a circle defined mathematically?

The diameter of a circle is mathematically defined as twice the length of the radius. The radius is the distance from the center of the circle to any point on its circumference, and since the diameter stretches from one point on the circumference, through the center, to another point directly opposite, it encompasses two radii. Therefore, by multiplying the radius by two, one arrives at the diameter. This relationship is fundamental in geometry and is critical for further calculations involving circles, such as determining the circumference or area. Understanding this definition aids in visually and conceptually grasping the properties of circles.