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The absolute value of a real number x is denoted |x| and defined as the "unsigned" portion of x, |x| = xsgn(x) (1) = {-x for x<=0; x for x>=0, (2) where sgn(x) is the sign ...

The Boy surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. Two other ...

A "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

An Enriques surface X is a smooth compact complex surface having irregularity q(X)=0 and nontrivial canonical sheaf K_X such that K_X^2=O_X (Endraß). Such surfaces cannot be ...

A map projection on which the azimuths of all points are shown correctly with respect to the center (Snyder 1987, p. 4). A plane tangent to one of the Earth's poles is the ...

A quaternion with complex coefficients. The algebra of biquaternions is isomorphic to a full matrix ring over the complex number field (van der Waerden 1985).

Let A be a commutative complex Banach algebra. A nonzero homomorphism from A onto the field of complex numbers is called a character. Every character is automatically ...

Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves ...

A quadrilateral tiling is a tiling of the plane by identical quadrilaterals. Any nonself-intersecting quadrilateral (Wells 1991, p. 208) tiles the plane, as illustrated above.