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Let a sequence be defined by A_(-1) = s (1) A_0 = 3 (2) A_1 = r (3) A_n = rA_(n-1)-sA_(n-2)+A_(n-3). (4) Also define the associated polynomial f(x)=x^3-rx^2+sx+1, (5) and let ...

The sequence obtained from reversing the digits of a number n and adding the result to the original number. For n=1, 2, ..., this gives 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

When computing the sample variance s numerically, the mean must be computed before s^2 can be determined. This requires storing the set of sample values. However, it is ...

A simple polyhedron, also called a simplicial polyhedron, is a polyhedron that is topologically equivalent to a sphere (i.e., if it were inflated, it would produce a sphere) ...

A pathwise-connected domain is said to be simply connected (also called 1-connected) if any simple closed curve can be shrunk to a point continuously in the set. If the ...

A strongly binary tree is a rooted tree for which the root is adjacent to either zero or two vertices, and all non-root vertices are adjacent to either one or three vertices ...

The nth Suzanne set S_n is defined as the set of composite numbers x for which n|S(x) and n|S_p(x), where x = a_0+a_1(10^1)+...+a_d(10^d) (1) = p_1p_2...p_m, (2) and S(x) = ...

Taniguchi's constant is defined as C_(Taniguchi) = product_(p)[1-3/(p^3)+2/(p^4)+1/(p^5)-1/(p^6)] (1) = 0.6782344... (2) (OEIS A175639), where the product is over the primes ...