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The semiperimeter is used most often for triangles; the formula for the semiperimeter of a triangle with side ... The constant of proportionality is the number pi, ...
The number = was chosen because it is a semiprime and therefore can be arranged into a rectangular image in only two distinct ways (23 rows and 73 columns, or 73 rows and 23 columns). [ 9 ] See also
A triangle with sides a, b, and c. In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths , , . Letting be the semiperimeter of the triangle, = (+ +), the area is [1]
A semiperfect number that is not divisible by any smaller semiperfect number is called primitive. Every number of the form 2 m p for a natural number m and an odd prime number p such that p < 2 m+1 is also semiperfect. In particular, every number of the form 2 m (2 m+1 − 1) is semiperfect, and indeed perfect if 2 m+1 − 1 is a Mersenne prime.
where s, the semiperimeter, is defined to be = + + +. This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a ...
There exist an infinite number of primitive Heronian triangles with one side length equal to a given a, provided that a > 2. [ 1 ] The semiperimeter s of a Heronian triangle cannot be prime (as s ( s − a ) ( s − b ) ( s − c ) {\displaystyle s(s-a)(s-b)(s-c)} is the square of the area, and the area is an integer, if s were prime, it would ...
A triangle with sides <, semiperimeter = (+ +), area, altitude opposite the longest side, circumradius, inradius, exradii,, tangent to ,, respectively, and medians,, is a right triangle if and only if any one of the statements in the following six categories is true. Each of them is thus also a property of any right triangle.
According to T. A. Ivanova (in 1976), the semiperimeter s of a tangential quadrilateral satisfies where r is the inradius. There is equality if and only if the quadrilateral is a square. [13] This means that for the area K = rs, there is the inequality