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Einstein summation is a notational convention for simplifying expressions including summations of vectors, matrices, and general tensors. There are essentially three rules of ...

Through a point K in the plane of a triangle DeltaABC, draw parallelians through a point as illustrated above. Then there exist four points K for which ...

Given a first-order ordinary differential equation (dy)/(dx)=F(x,y), (1) if F(x,y) can be expressed using separation of variables as F(x,y)=X(x)Y(y), (2) then the equation ...

A subset E of a topological space S is said to be of first category in S if E can be written as the countable union of subsets which are nowhere dense in S, i.e., if E is ...

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 ...

In general, a graph product of two graphs G and H is a new graph whose vertex set is V(G)×V(H) and where, for any two vertices (g,h) and (g^',h^') in the product, the ...

The determination of whether a Turing machine will come to a halt given a particular input program. The halting problem is solvable for machines with less than four states. ...

The plane figure formed by a sequence of circles C_1, C_2, C_3, ... that are all tangent to each other at the same point and such that the sequence of radii converges to ...

The regular tessellation {6,3} consisting of regular hexagons (i.e., a hexagonal grid). In general, the term honeycomb is used to refer to a tessellation in n dimensions for ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...