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The rectifiable sets include the image of any Lipschitz function f from planar domains into R^3. The full set is obtained by allowing arbitrary measurable subsets of ...

The root separation (or zero separation) of a polynomial P(x) with roots r_1, r_2, ... is defined by Delta(P)=min_(i!=j)|r_i-r_j|. There are lower bounds on how close two ...

A polyhedron constructed by ruling 2n equally spaced vertical lines along the surface of a cylinder together with 2n^3 circles around the cylinder at equally spaced heights. ...

A Cantor set C in R^3 is said to be scrawny if for each neighborhood U of an arbitrary point p in C, there is a neighborhood V of p such that every map f:S^1->V subset C ...

The general sextic equation x^6+a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 can be solved in terms of Kampé de Fériet functions, and a restricted class of sextics can be solved in ...

Measurements of a centered convex body in Euclidean n-space (for n>=3) show that its brightness function (the volume of each projection) is smaller than that of another such ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_4=f(x_4). Then Simpson's 3/8 rule ...

The maximal number of regions into which space can be divided by n planes is f(n)=1/6(n^3+5n+6) (Yaglom and Yaglom 1987, pp. 102-106). For n=1, 2, ..., these give the values ...

The space groups in two dimensions are called wallpaper groups. In three dimensions, the space groups are the symmetry groups possible in a crystal lattice with the ...

The square antiprism is the antiprism with square bases whose dual is the tetragonal trapezohedron. The square antiprism has 10 faces. The square antiprism with unit edge ...