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"Nordstrand's weird surface" is an attractive quartic surface given by the implicit equation It has 11 ordinary double points located at (2/5,0,0), (-2/5,0,0), ...

If r is an algebraic number of degree n, then the totality of all expressions that can be constructed from r by repeated additions, subtractions, multiplications, and ...

A collection of open sets of a topological space whose union contains a given subset. For example, an open cover of the real line, with respect to the Euclidean topology, is ...

For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and ...

A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthogonal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. Note ...

A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthonormal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

Let 0<p_1<p_2<... be integers and suppose that there exists a lambda>1 such that p_(j+1)/p_j>lambda for j=1, 2, .... Suppose that for some sequence of complex numbers {a_j} ...

The surface of revolution of the parabola which is the shape used in the reflectors of automobile headlights (Steinhaus 1999, p. 242; Hilbert and Cohn-Vossen 1999). It is a ...

Two planes that do not intersect are said to be parallel. Two planes specified in Hessian normal form are parallel iff |n_1^^·n_2^^|=1 or n_1^^xn_2^^=0 (Gellert et al. 1989, ...