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Of all convex n-gons of a given perimeter, the one which maximizes area is the regular n-gon.

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

A polynomial is called unimodal if the sequence of its coefficients is unimodal. If P(x) is log-convex and Q(x) is unimodal, then P(x)Q(x) is unimodal.

A condition in numerical equation solving which states that, given a space discretization, a time step bigger than some computable quantity should not be taken. The condition ...

A solid such that the area A_y of any section parallel to and a distance y from a fixed plane can be expressed as A_y=ay^3+by^2+cy+d. The volume of such a solid is the same ...

Define the minimal bounding rectangle as the smallest rectangle containing a given lattice polygon. If the perimeter of the lattice polygon is equal to that of its minimal ...

The tangram is a combination of plane polygonal pieces such that the edges of the polygons are coincident. There are 13 convex tangrams (where a "convex tangram" is a set of ...

A graph G is called d-polytopal if there exists a d-dimensional convex polytope P such that the vertices and edges of G are in a one-to-one incidence-preserving ...

The figure formed when the midpoints of the sides of a convex quadrilateral are joined in order is a parallelogram. Equivalently, the bimedians bisect each other. The area of ...

A function f(x) is said to be concave on an interval [a,b] if, for any points x_1 and x_2 in [a,b], the function -f(x) is convex on that interval (Gradshteyn and Ryzhik 2000).