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Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...

P. G. Tait undertook a study of knots in response to Kelvin's conjecture that the atoms were composed of knotted vortex tubes of ether (Thomson 1869). He categorized knots in ...

There are a number of hypotraceable and hypohamiltonian graphs associated with Carsten Thomassen. These graphs, illustrated above, are implemented in the Wolfram Language as ...

Triangulation is the division of a surface or plane polygon into a set of triangles, usually with the restriction that each triangle side is entirely shared by two adjacent ...

The twinplex graph is the graph illustrated above in a number of embeddings which corresponds to the graph labeled Gamma_2 in Fischer and Little (2011). It is a cubic ...

There are a number of algebraic identities involving sets of four vectors. An identity known as Lagrange's identity is given by (AxB)·(CxD)=(A·C)(B·D)-(A·D)(B·C) (1) ...

A walk is a sequence v_0, e_1, v_1, ..., v_k of graph vertices v_i and graph edges e_i such that for 1<=i<=k, the edge e_i has endpoints v_(i-1) and v_i (West 2000, p. 20). ...

A diamond-shaped neighborhood that can be used to define a set of cells surrounding a given cell (x_0,y_0) that may affect the evolution of a two-dimensional cellular ...

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...

Solve the Pell equation x^2-92y^2=1 in integers. The smallest solution is x=1151, y=120.