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The homomorphism S which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism S ...

The term Euclidean refers to everything that can historically or logically be referred to Euclid's monumental treatise The Thirteen Books of the Elements, written around the ...

Euler conjectured that there do not exist Euler squares of order n=4k+2 for k=1, 2, .... In fact, MacNeish (1921-1922) published a purported proof of this conjecture (Bruck ...

Points, also called polar reciprocals, which are transformed into each other through inversion about a given inversion circle C (or inversion sphere). The points P and P^' ...

The point on a line segment dividing it into two segments of equal length. The midpoint of a line segment is easy to locate by first constructing a lens using circular arcs, ...

A nut graph is a graph on n>=2 vertices with adjacency matrix A such that A has matrix rank 1 and contains no 0 element (Sciriha 1998, 2008; Sciriha and Gutman, 1998; and ...

A figurate number which is the sum of two consecutive pyramidal numbers, O_n=P_(n-1)+P_n=1/3n(2n^2+1). (1) The first few are 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, ...

The Tschirnhausen cubic is a plane curve given by the polar equation r=asec^3(1/3theta). (1) Letting theta=3tan^(-1)t gives the parametric equations x = a(1-3t^2) (2) y = ...

An array is a "list of lists" with the length of each level of list the same. The size (sometimes called the "shape") of a d-dimensional array is then indicated as ...

The snub dodecahedron is an Archimedean solid consisting of 92 faces (80 triangular, 12 pentagonal), 150 edges, and 60 vertices. It is sometimes called the dodecahedron simum ...