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The hydraulic diameter is similarly defined as 4 times the cross-sectional area of a pipe A, divided by its "wetted" perimeter P. For a circular pipe of radius R, at full flow, this is = = as one would expect. This is equivalent to the above definition of the 2D mean diameter.
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 value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...
Using radians, the formula for the arc length s of a circular arc of radius r and subtending a central angle of measure 𝜃 is =, and the formula for the area A of a circular sector of radius r and with central angle of measure 𝜃 is A = 1 2 θ r 2 . {\displaystyle A={\frac {1}{2}}\theta r^{2}.}
Jung's theorem provides more general inequalities relating the diameter to the radius. [5] The isodiametric inequality or Bieberbach inequality , a relative of the isoperimetric inequality , states that, for a given diameter, the planar shape with the largest area is a disk, and the three-dimensional shape with the largest volume is a sphere.
If R is a regular polygon's radius and n is the number of its sides, then its perimeter is 2 n R sin ( 180 ∘ n ) . {\displaystyle 2nR\sin \left({\frac {180^{\circ }}{n}}\right).} A splitter of a triangle is a cevian (a segment from a vertex to the opposite side) that divides the perimeter into two equal lengths, this common length being ...
Risks of Using High-Strength Minoxidil. The risks of using high-strength minoxidil include an increased likelihood of side effects. When using it as a topical solution, side effects of minoxidil ...
The area of an annulus is the difference in the areas of the larger circle of radius R and the smaller one of radius r: = = = (+) (). As a corollary of the chord formula, the area bounded by the circumcircle and incircle of every unit convex regular polygon is π /4
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