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The metabidiminished icosahedron is a convex equilateral solid that is Johnson solid J_(62). The unit metabidiminished icosahedron has volume V=1/6(5+2sqrt(5)) (1) and Dehn ...

The metabidiminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(81). The unit metabidiminished rhombicosidodecahedron has volume ...

The pentagonal gyrocupolarotunda is a convex equilateral solid that is Johnson solid J_(33). The unit pentagonal gyrocupolarotunda has volume V=5/(12)(11+5sqrt(5)) (1) and ...

To find the minimum distance between a point in the plane (x_0,y_0) and a quadratic plane curve y=a_0+a_1x+a_2x^2, (1) note that the square of the distance is r^2 = ...

Squaring is the geometric construction, using only compass and straightedge, of a square which has the same area as a given geometric figure. Squaring is also called ...

Let CD be the altitude of a triangle DeltaABC and let E be its midpoint. Then area(DeltaABC)=1/2AB·CD=AB·DE, and ABFG can be squared by rectangle squaring. The general ...

Let a distribution to be approximated be the distribution F_n of standardized sums Y_n=(sum_(i=1)^(n)(X_i-X^_))/(sqrt(sum_(i=1)^(n)sigma_X^2)). (1) In the Charlier series, ...

The converse of Fisher's theorem.

If X and Y are independent variates and X+Y is a normal distribution, then both X and Y must have normal distributions. This was proved by Cramér in 1936.

Any bivariate distribution function with marginal distribution functions F and G satisfies max{F(x)+G(y)-1,0}<=H(x,y)<=min{F(x),G(y)}.