Search results
Results From The WOW.Com Content Network
In three-dimensional geometry, the girth of a geometric object, in a certain direction, is the perimeter of its parallel projection in that direction. [ 1 ] [ 2 ] For instance, the girth of a unit cube in a direction parallel to one of the three coordinate axes is four: it projects to a unit square , which has four as its perimeter.
In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. [1] If the graph does not contain any cycles (that is, it is a forest), its girth is defined to be infinity. [2] For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3.
The "girth" terminology generalizes the use of girth in graph theory, meaning the length of the shortest cycle in a graph: the girth of a graphic matroid is the same as the girth of its underlying graph. [1] The girth of other classes of matroids also corresponds to important combinatorial problems.
The math template formats mathematical formulas generated using HTML or wiki markup. (It does not accept the AMS-LaTeX markup that <math> does.) The template uses the texhtml class by default for inline text style formulas, which aims to match the size of the serif font with the surrounding sans-serif font (see below).
In functional analysis, the girth of a Banach space is the infimum of lengths of centrally symmetric simple closed curves in the unit sphere of the space. Equivalently, it is twice the infimum of distances between opposite points of the sphere, as measured within the sphere.
The Tutte (3,8)-cage.. In the mathematical field of graph theory, a cage is a regular graph that has as few vertices as possible for its girth.. Formally, an (r, g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has a length of exactly g.
The Crank–Nicolson stencil for a 1D problem. In mathematics, especially the areas of numerical analysis concentrating on the numerical solution of partial differential equations, a stencil is a geometric arrangement of a nodal group that relate to the point of interest by using a numerical approximation routine.
Girth is a measurement of the distance around the trunk of a tree measured perpendicular to the axis of the trunk. [18] Use of girth to arrive at an equivalent diameter is an older forestry measurement that is still used. In the United States girth is measured at a height of 4.5 feet above ground level.