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Consider a formula in prenex normal form, Q_1x_1...Q_nx_nN. If Q_i is the existential quantifier (1<=i<=n) and x_k, ..., x_m are all the universal quantifier variables such ...

A triple of three arbitrary vectors with common vertex (Altshiller-Court 1979), often called a trihedral angle since it determines three planes. The vectors are often taken ...

The maximum and minimum of the normal curvature kappa_1 and kappa_2 at a given point on a surface are called the principal curvatures. The principal curvatures measure the ...

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. ...

An asymptotic direction at a point p of a regular surface M in R^3 is a direction in which the normal curvature of M vanishes. 1. There are no asymptotic directions at an ...

The French metro metric is an example for disproving apparently intuitive but false properties of metric spaces. The metric consists of a distance function on the plane such ...

Integer division is division in which the fractional part (remainder) is discarded is called integer division and is sometimes denoted \. Integer division can be defined as ...

Let G be a group, then there exists a piecewise linear knot K^(n-2) in S^n for n>=5 with G=pi_1(S^n-K) iff G satisfies 1. G is finitely presentable, 2. The Abelianization of ...

At each point on a given a two-dimensional surface, there are two "principal" radii of curvature. The larger is denoted R_1, and the smaller R_2. The "principal directions" ...

Let m and m+h be two consecutive critical indices of f and let F be (m+h)-normal. If the polynomials p^~_k^((n)) are defined by p^~_0^((n))(u) = 1 (1) p^~_(k+1)^((n))(u) = ...