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Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
Another simple method for calculating the area of a polygon is the shoelace formula. It gives the area of any simple polygon as a sum of terms computed from the coordinates of consecutive pairs of its vertices. Unlike Pick's theorem, the shoelace formula does not require the vertices to have integer coordinates. [28]
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.
This formula is also known as the shoelace formula and is an easy way to solve for the area of a coordinate triangle by substituting the 3 points (x 1,y 1), (x 2,y 2), and (x 3,y 3). The shoelace formula can also be used to find the areas of other polygons when their vertices are known.
One equation used to analyze biological exponential growth uses the birth and death rates in a population. If, in a hypothetical population of size N, the birth rates (per capita) are represented as b and death rates (per capita) as d, then the increase or decrease in N during a time period t will be
Physics – negentropy, stochastic processes, and the development of new physical techniques and instrumentation as well as their application. Quantum biology – The field of quantum biology applies quantum mechanics to biological objects and problems. Decohered isomers to yield time-dependent base substitutions. These studies imply ...
Kleiber's law, like many other biological allometric laws, is a consequence of the physics and/or geometry of circulatory systems in biology. [5] Max Kleiber first discovered the law when analyzing a large number of independent studies on respiration within individual species. [2]
The resistance to the motion of an approximately stream-lined solid through a fluid can be expressed by the formula: C fρ (total surface)V 2 /2, [19] where: V = velocity ρ = density of fluid C f = 1.33R − 1 (laminar flow) R = Reynolds number. The Reynolds number R is given by R = VL/ν, where: V = velocity L = axial length of organism