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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]
Acoustic foam is an open celled foam used for acoustic treatment. It attenuates airborne sound waves, reducing their amplitude , for the purposes of noise reduction or noise control . [ 1 ] The energy is dissipated as heat . [ 2 ]
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...
The mechanical advantage or MA of a wedge can be calculated by dividing the height of the wedge by the wedge's width: [1] M A = L e n g t h W i d t h {\displaystyle {\rm {MA={Length \over Width}}}} The more acute , or narrow, the angle of a wedge, the greater the ratio of the length of its slope to its width, and thus the more mechanical ...
The result of these feedbacks is the stable angle of the wedge known as the critical taper. When natural processes (such as erosion, or an increase in load on the wedge due to emplacement of a sea or ice cap) change the shape of the wedge, the wedge will react by internally deforming to return to a critically tapered wedge shape. The critical ...
A wedge is a polyhedron of a rectangular base, with the faces are two isosceles triangles and two trapezoids that meet at the top of an edge. [1]. A prismatoid is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces are triangles, trapezoids, and parallelograms; [2] the wedge is an example of prismatoid because of its top edge is parallel to the ...
The elevation is the signed angle from the x-y reference plane to the radial line segment OP, where positive angles are designated as upward, towards the zenith reference. Elevation is 90 degrees (= π / 2 radians) minus inclination. Thus, if the inclination is 60 degrees (= π / 3 radians), then the elevation is 30 degrees ...
The chapter on areas includes both trigonometric formulas and Heron's formula for computing the area of a triangle from its side lengths, and the chapter on inequalities includes the Erdős–Mordell inequality on sums of distances from the sides of a triangle and Weitzenböck's inequality relating the area of a triangle to that of squares on ...
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