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A cipher is an algorithm that converts data (plaintext) to an obfuscated form that is not directly readable. Ciphers are usually used with the intention of hiding the ...

The encrypted form of a plaintext.

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...

The points of tangency t_1 and t_2 for the four lines tangent to two circles with centers x_1 and x_2 and radii r_1 and r_2 are given by solving the simultaneous equations ...

An ellipse intersects a circle in 0, 1, 2, 3, or 4 points. The points of intersection of a circle of center (x_0,y_0) and radius r with an ellipse of semi-major and ...

An (infinite) line determined by two points (x_1,y_1) and (x_2,y_2) may intersect a circle of radius r and center (0, 0) in two imaginary points (left figure), a degenerate ...

Taking the locus of midpoints from a fixed point to a circle of radius r results in a circle of radius r/2. This follows trivially from r(theta) = [-x; 0]+1/2([rcostheta; ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

A circle bundle pi:E->M is a fiber bundle whose fibers pi^(-1)(x) are circles. It may also have the structure of a principal bundle if there is an action of SO(2) that ...

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...