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An affine isoperimetric inequality.

The square root inequality states that 2sqrt(n+1)-2sqrt(n)<1/(sqrt(n))<2sqrt(n)-2sqrt(n-1) for n>=1.

If 0<=g(x)<=1 and g is nonincreasing on the interval [0, 1], then for all possible values of a and b, int_0^1g(x^(1/(a+b)))dx>=int_0^1g(x^(1/a))dxint_0^1g(x^(1/b))dx.

The p-adic norm satisfies |x+y|_p<=max(|x|_p,|y|_p) for all x and y.

There are a number of attractive polyhedron compounds consisting of six octahedra. The two illustrated above can be constructed as the duals of cube 6-compounds. These ...

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...

Let Omega be an open, bounded, and connected subset of R^d for some d and let dx denote d-dimensional Lebesgue measure on R^d. In functional analysis, the Friedrichs ...

Ono (1914) conjectured that the inequality 27(b^2+c^2-a^2)^2(a^2+c^2-b^2)^2(a^2+b^2-c^2)^2<=(4K)^6 holds true for all triangles, where a, b, and c are the lengths of the ...

Let Omega be an open, bounded, and connected subset of R^d for some d and let dx denote d-dimensional Lebesgue measure on R^d. In functional analysis, the Poincaré inequality ...

Let x and y be vectors. Then the triangle inequality is given by |x|-|y|<=|x+y|<=|x|+|y|. (1) Equivalently, for complex numbers z_1 and z_2, ...