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The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

An alternating multilinear form on a real vector space V is a multilinear form F:V tensor ... tensor V->R (1) such that ...

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

For a system of n first-order ordinary differential equations (or more generally, Pfaffian forms), the 2n-dimensional space consisting of the possible values of ...

Call a number of the form n^2-k a "near-square number." Numbers of the form n^2-5 for n=1, 2, ... are -4, -1, 4, 11, 20, 31, 44, 59, 76, 95, ... (OEIS A028875). These are ...

A series of the form sum_(k=1)^infty(-1)^(k+1)a_k (1) or sum_(k=1)^infty(-1)^ka_k, (2) where a_k>0. A series with positive terms can be converted to an alternating series ...

The Schläfli graph is a strongly regular graph on 27 nodes which is the graph complement of the generalized quadrangle GQ(2,4). It is the unique strongly regular graph with ...

The inverse curve of the cochleoid r=(sintheta)/theta (1) with inversion center at the origin and inversion radius k is the quadratrix of Hippias. x = ktcottheta (2) y = kt. ...

Mills' theorem states that there exists a real constant A such that |_A^(3^n)_| is prime for all positive integers n (Mills 1947). While for each value of c>=2.106, there are ...

Let a triangle have angles A, B, and C, then inequalities include sinA+sinB+sinC<=3/2sqrt(3) (1) 1<=cosA+cosB+cosC<=3/2 (2) sin(1/2A)sin(1/2B)sin(1/2C)<=1/8 (3) ...