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Somewhere on the Earth, there is a pair of antipodal points having simultaneously the same temperature and pressure.

A particular way of doing something, sometimes also called an algorithm or procedure. (According to Petkovšek et al. (1996), "a method is a trick that has worked at least ...

Let f be a nonnegative and continuous function on the closed interval [a,b], then the solid of revolution obtained by rotating the curve f(x) about the x-axis from x=a to x=b ...

The method of exhaustion was an integral-like limiting process used by Archimedes to compute the area and volume of two-dimensional lamina and three-dimensional solids.

Let R be a plane region bounded above by a continuous curve y=f(x), below by the x-axis, and on the left and right by x=a and x=b, then the volume of the solid of revolution ...

Let f and g be nonnegative and continuous functions on the closed interval [a,b], then the solid of revolution obtained by rotating the curves f(x) and g(x) about the x-axis ...

Given a metric g_(alphabeta), the discriminant is defined by g = det(g_(alphabeta)) (1) = |g_(11) g_(12); g_(21) g_(22)| (2) = g_(11)g_(22)-(g_(12))^2. (3) Let g be the ...

The middle levels conjecture, also known as revolving door conjecture, posits that the middle layer graph has a Hamilton cycle for every n>=1. The conjecture was proved by ...

A derived polygon with side ratios chosen as r=1/2 so that inscribed polygons are constructed by connecting the midpoints of the base polygon. For a triangle P, the ...

Given order statistics Y_1=min_(j)X_j, Y_2, ..., Y_(N-1), Y_N=max_(j)X_j with sample size N, the midrange of the random sample is defined by MR=1/2(Y_1+Y_N) (Hogg and Craig ...