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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 calculations involve some basic trigonometry but these calculations can easily be done on any inexpensive scientific calculator. Sine height measurement. Situations where the top of the tree being measured is above eye level and the base of the tree being measured is below eye level is the most common situation encountered in the field.
An Excel spreadsheet can be used to determine the rate the apparent size of the scale changes with distance, and that value can be used to calculate the diameter of the tree given that the tree is circular in cross section and the distance to the front side of the tree is known. Girth then is calculated by multiplying the diameter by pi.
To calculate trunk volume, the tree is subdivided into a series of segments with the successive diameters being the bottom and top of each segment and segment length being equal to the difference in height between the lower and upper diameters, or if the trunk is not vertical, the segment length can be calculated using the limb length formula ...
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.
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 matroid theory, a mathematical discipline, the girth of a matroid is the size of its smallest circuit or dependent set. The cogirth of a matroid is the girth of its dual matroid . Matroid girth generalizes the notion of the shortest cycle in a graph, the edge connectivity of a graph, Hall sets in bipartite graphs , even sets in families of ...
Body roundness index (BRI) is a calculated geometric index used to quantify an aspect of a person's individual body shape.Based on the principle of body eccentricity, it provides a rapid visual and anthropometric tool for health evaluation.