Definition:Radius


 * Radius of a Circle: a straight line segment whose endpoints are the center and the circumference of the circle.
 * Radius of an $\epsilon$-Ball: In the open $\epsilon$-ball $B_\epsilon \left({x}\right)$ of the point $x$, the value $\epsilon$ is its radius.
 * Radius of Convergence: The distance from the endpoints to the midpoint of the interval on which a power series is convergent.

Linguistic Note
The plural of radius is radii, pronounced ray-dee-eye.

This irregular plural form stems from the Latin origin of the word radius, meaning ray

The ugly incorrect form radiuses can apparently be found, but rarely in a mathematical context.