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The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a,b], ...

The ordered pair (s,t), where s is the number of real embeddings of the number field and t is the number of complex-conjugate pairs of embeddings. The degree of the number ...

An obelisk is a stone pillar erected as a monument that usually consists of a pyramid atop a tall square (or sometimes rectangular base). The elongated square pyramid can ...

A number which is simultaneously octagonal and hexagonal. Let O_n denote the nth octagonal number and H_m the mth hexagonal number, then a number which is both octagonal and ...

An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...

The catacaustic of a parabola (t,t^2) opening upward is complicated for a general radiant point (x,y). However, the equations simplify substantially in the case x=infty ...

A hypersphere S^n is parallelizable if there are n vector fields that are linearly independent at each point. There exist only three parallelizable spheres: S^1, S^3, and S^7 ...

The pedal circle with respect to a pedal point P of a triangle DeltaA_1A_2A_3 is the circumcircle of the pedal triangle DeltaP_1P_2P_3 with respect to P. Amazingly, the ...

A graphical plot with abscissa given by the number p of consecutive numbers constituting a single period and ordinate given by the correlation ratio eta. The equation of the ...

Polynomials P_k(x) which form the Sheffer sequence for g(t) = (2t)/(e^t-1) (1) f(t) = (e^t-1)/(e^t+1) (2) and have generating function ...