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A disk with radius 1. The (open) unit disk can also be considered to be the region in the complex plane defined by {z:|z|<1}, where |z| denotes the complex modulus. (The ...

The integral of 1/r over the unit disk U is given by intint_(U)(dA)/r = intint_(U)(dxdy)/(sqrt(x^2+y^2)) (1) = int_0^(2pi)int_0^1(rdrdtheta)/r (2) = 2piint_0^1dr (3) = 2pi. ...

A sphere of radius 1.

A square with side lengths 1. The unit square usually means the one with coordinates (0, 0), (1, 0), (1, 1), (0, 1) in the real plane, or 0, 1, 1+i, and i in the complex ...

The figure formed when the midpoints of the sides of a convex quadrilateral are joined in order is a parallelogram. Equivalently, the bimedians bisect each other. The area of ...

v=(dr)/(dt), (1) where r is the radius vector and d/dt is the derivative with respect to time. Expressed in terms of the arc length, v=(ds)/(dt)T^^, (2) where T^^ is the unit ...

If the top and bottom bases of a solid are equal in area, lie in parallel planes, and every section of the solid parallel to the bases is equal in area to that of the base, ...

A linkage used in the original steam engine to turn back-and-forth motion into approximately straight-line motion.

A nonconformal, equal-area projection which is a special case of the Bonne projection where one of the poles is taken as the standard parallel. Because of its heart shape, ...

An natural equation which expresses a curve in terms of its arc length s and tangential angle phi.