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There are several results known as the Morgado identity. The first is (1) where F_n is a Fibonacci number and L_n is a Lucas number (Morgado 1987, Dujella 1995). A second ...

The term Nasik cube can refer to a number of different sorts of magic cubes. In particular, a Nasik cube is a magic cube in which additionally 1. The broken space diagonals ...

A nonzero vector v=(v_0,v_1,...,v_(n-1)) in n-dimensional Lorentzian space R^(1,n-1) is said to be negative lightlike if it has zero (Lorentzian) norm and if its first ...

A vector field X on a compact foliated manifold (M,F) is nice if X is transverse to F and if X has a closed orbit C (called a nice orbit) such that the intersection C ...

The eighth proposition in the third book of the Elements is one of Euclid's most complex propositions. It shows that a segment through an outside point D and a circle is ...

A pentagonal pyramid is pyramid having a pentagonal base. The edge length e and slant height s of a pentagonal pyramid with regular base of side length a are given by e = ...

The permutation tensor, also called the Levi-Civita tensor or isotropic tensor of rank 3 (Goldstein 1980, p. 172), is a pseudotensor which is antisymmetric under the ...

A polyare is a polyform formed from a polyomino by removing of half of each square such that at least half of the original join between squares is retained. The first few ...

A general quintic equation a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 (1) can be reduced to one of the form y^5+b_2y^2+b_1y+b_0=0, (2) called the principal quintic form. Vieta's ...

A groupoid S such that for all a,b in S, there exist unique x,y in S such that ax = b (1) ya = b. (2) No other restrictions are applied; thus a quasigroup need not have an ...