Search Results for ""

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.

Given a convex plane region with area A and perimeter p, A-1/2p<N<=A+1/2p+1, where N is the number of enclosed lattice points (Nosarzewska 1948). This improves on Jarnick's ...

A nowhere-neat dissection is a dissection of an area into polygons such that no two polygons have a side in common. A nowhere-neat dissection in which squares of the same ...

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 ...

Given a regular tetrahedron of unit volume, the mean triangle area of a triangle picked at random inside it is approximately A=0.1811+/-0.0012, and the variance is ...

A class of area-preserving maps of the form theta_(i+1) = theta_i+2pialpha(r_i) (1) r_(i+1) = r_i, (2) which maps circles into circles but with a twist resulting from the ...

A triangle with side lengths a, b, and c and triangle area Delta satisfies a^2+b^2+c^2>=4sqrt(3)Delta. Equality holds iff the triangle is equilateral.

A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersecting pairwise in three vertices. The spherical triangle is the ...

A convex polyomino (sometimes called a "convex polygon") is a polyomino whose perimeter is equal to that of its minimal bounding box (Bousquet-Mélou et al. 1999). ...

An equilibrium point in game theory is a set of strategies {x^^_1,...,x^^_n} such that the ith payoff function K_i(x) is larger or equal for any other ith strategy, i.e., ...