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If a plane cuts the sides AB, BC, CD, and DA of a skew quadrilateral ABCD in points P, Q, R, and S, then (AP)/(PB)·(BQ)/(QC)·(CR)/(RD)·(DS)/(SA)=1 both in magnitude and sign ...

If theta is a given irrational number, then the sequence of numbers {ntheta}, where {x}=x-|_x_|, is dense in the unit interval. Explicitly, given any alpha, 0<=alpha<=1, and ...

The six planes through the midpoints of the edges of a tetrahedron and perpendicular to the opposite edges concur in a point known as the Monge point.

Any entire analytic function whose range omits two points must be a constant function. Of course, an entire function that omits a single point from its range need not be a ...

An alkane graph is a tree in which vertices correspond to atoms and edges to carbon-carbon or hydrogen-carbon bonds in a chemical alkane. In chemistry, an alkane is an ...

Ore (1962) noted that not only does a tree possesses a unique shortest path between any two vertices, but that there also exist also other connected graphs having the same ...

A fixed point for which the stability matrix has equal negative eigenvalues.

A fixed point for which the stability matrix has equal positive eigenvalues.

Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

Let A=a_(ik) be an arbitrary n×n nonsingular matrix with real elements and determinant |A|, then |A|^2<=product_(i=1)^n(sum_(k=1)^na_(ik)^2).