The radius of the sphere of which a lens surface or curved mirror forms a part is called the radius of curvature.
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In each point, there is a line. The curvature of the surface in this direction is zero. Therefore the maximum curvature is positive and the minimum is negative. Gauss curvature in this point is the product of this max and min, and therefore is negative (or zero).
Radius on a guitar usually refers to the slight curvature of the surface of some fretboards, the arc of which is part of an imaginary circle. The radius of that circle is 12 to 17 inches for most steel-string acoustic guitars, smaller and hence more curved for some electrics. The only practical way to measure it is with a special gauge. If you had a diagram of it, you could calculate it with Pythagoreus' theorem. A straight line connecting the two sides of the fingerboard is the hypotenuse of a right triangle with two equal legs that are also radii.
It means to multiply the radius by itself: radius x radius
When you try to figure out an area of a circle, you square the radius, then multiply it by pi to get the area of a circle. A radius square is radius x radius, or radius squared.