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Rubik's Cube is a 3×3×3 cube in which the 26 subcubes on the outside are internally hinged in such a way that rotation (by a quarter turn in either direction or a half turn) ...

A square matrix U is a unitary matrix if U^(H)=U^(-1), (1) where U^(H) denotes the conjugate transpose and U^(-1) is the matrix inverse. For example, A=[2^(-1/2) 2^(-1/2) 0; ...

If an n-sided Poncelet transverse constructed for two given conic sections is closed for one point of origin, it is closed for any position of the point of origin. ...

The third prime number, which is also the second Fermat prime, the third Sophie Germain prime, and Fibonacci number F_4. It is an Eisenstein prime, but not a Gaussian prime, ...

A Cartan matrix is a square integer matrix who elements (A_(ij)) satisfy the following conditions. 1. A_(ij) is an integer, one of {-3,-2,-1,0,2}. 2. A_(ii)=2 the diagonal ...

A Chen prime is a prime number p for which p+2 is either a prime or semiprime. Chen primes are named after Jing Run Chen who proved in 1966 that there are infinitely many ...

The Golay code is a perfect linear error-correcting code. There are two essentially distinct versions of the Golay code: a binary version and a ternary version. The binary ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

A transformation of the form w=f(z)=(az+b)/(cz+d), (1) where a, b, c, d in C and ad-bc!=0, (2) is a conformal mapping called a linear fractional transformation. The ...

A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...