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Let M subset R^3 be a regular surface and u_(p) a unit tangent vector to M, and let Pi(u_(p),N(p)) be the plane determined by u_(p) and the normal to the surface N(p). Then ...

Sinai billiards is the reflection of a ray of light by an arrangement of perfectly reflecting circles in the plane (Trott 2004, pp. 28-30). The path is extremely sensitive to ...

A spheroidal section is the curve formed by the intersection of a plane with a spheroid. A spheroidal section is either a circle (for planes parallel to an equator, i.e., ...

In the triangle DeltaABC illustrated above, side c subtends angle ∠C. More generally, given a geometric object O in the plane and a point P, let A be the angle from one edge ...

The two-point form of a line in the Cartesian plane passing through the points (x_1,y_1) and (x_2,y_2) is given by y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1), or equivalently, ...

Let S be a set of simple polygonal obstacles in the plane, then the nodes of the visibility graph of S are just the vertices of S, and there is an edge (called a visibility ...

That portion of geometry dealing with solids, as opposed to plane geometry. Solid geometry is concerned with polyhedra, spheres, three-dimensional solids, lines in ...

A plane curve given by the parametric equations x = cost (1) y = sintsin^m(1/2t). (2) The plots above show curves for values of m from 0 to 7. The teardrop curve has area ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. Analytic geometry ...