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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]
Shoelaces are typically tied off at the top of the shoe using a simple bow knot. Besides securing the shoe, this also takes up the length of shoelace exposed after tightening. The common bow consists of two half-knots tied one on top of the other, with the second half-knot looped in order to allow quick untying.
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]
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.
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
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(The Center Square) – After millions of illegal foreign nationals were released into the country through new parole programs created by the Biden administration, at least one million were ...
Close-up of a shoelace knot. The shoelace knot, or bow knot, is commonly used for tying shoelaces and bow ties. The shoelace knot is a doubly slipped reef knot formed by joining the ends of whatever is being tied with a half hitch, folding each of the exposed ends into a loop and joining the loops with a second half hitch. The size of the loops ...
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