In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths a , {\displaystyle a,} b , {\displaystyle...

triangle. Other frequently used formulas for the area of a triangle use trigonometry, side lengths (Heron's formula), vectors, coordinates, line integrals...

as Heron's method, for iteratively computing the square root of a number. Today, however, his name is most closely associated with Heron's formula for...

Bretschneider's formula, can be used with non-cyclic quadrilateral. Heron's formula can be thought as a special case of the Brahmagupta's formula for triangles...

(and did the same with circumscribed polygons). Heron of Alexandria found what is known as Heron's formula for the area of a triangle in terms of its sides...

1960s Heron or Hero of Alexandria (c. 10 – 70), ancient Greek mathematician and engineer, creator of Heron's formula (area of triangle) and Heron's method...

formula reduces to Heron's formula for the area of a triangle. Another equivalent formula for the area, which more closely resembles Heron's formula,...

same area formula can also be derived from Heron's formula for the area of a triangle from its three sides. However, applying Heron's formula directly...

standard in Fortran 90 via the new keyword RECURSIVE. This program, for Heron's formula, reads data on a tape reel containing three 5-digit integers A, B,...

simplest form of Brahmagupta's formula for the area of a cyclic quadrilateral has a form similar to that of Heron's formula for the triangle area: K = (...

area Pick's theorem Heron's formula Mathologer video about Gauss' shoelace formula Bart Braden (1986). "The Surveyor's Area Formula" (PDF). The College...

the length D1 of either diagonal, then the area can be found from Heron's formula. Specifically it is K = 2 S ( S − B ) ( S − C ) ( S − D 1 ) {\displaystyle...

symmetry, calculations in exterior algebra, or algebraic manipulation of Heron's formula (for which see § Soddy circles of a triangle). The result also follows...

triple-quad rule and triple-spread rule contain sums of squares, similar to Heron's formula. Squaring the square is a combinatorial problem of dividing a two-dimensional...

their relation to Heron's formula which Heron demonstrated with the example triangle of sides 13, 14, 15 and area 84. Heron's formula implies that the...

was approximately given by Heron, a 1st-century engineer. He is credited with a number of formulae, all called "Heron's formula." As far as pottery is concerned...

number of other results can be derived from the law of cotangents. Heron's formula. Note that the area of triangle ABC is also divided into 6 smaller...

s − b , {\displaystyle s-b,} and s − c . {\displaystyle s-c.} See Heron's formula. Denoting the incenter of △ A B C {\displaystyle \triangle ABC} as...

triangle with sides a, b, c must be a real number greater than zero. Heron's formula for the area is 4 ⋅ area = ( a + b + c ) ( − a + b + c ) ( a − b +...

relations. These relations served multiple purposes such as generalising Heron's Formula, computing the content of a n-dimensional simplex, and ultimately determining...

with area 66 (13, 14, 15) with area 84 (13, 20, 21) with area 126 By Heron's formula, the extra condition for a triple of positive integers (a, b, c) with...

semi-perimeter of the trapezoid. This formula is analogous to Heron's formula to compute the area of a triangle. The previous formula for area can also be written...

which in turn generalizes Heron's formula for the area of a triangle. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the...

above readily simplifies to Heron's formula for the area. The sine rule can also be used in deriving the following formula for the triangle's area: denoting...

Triangle Acute and obtuse triangles Equilateral triangle Euler's line Heron's formula Integer triangle Heronian triangle Isosceles triangle List of triangle...

={\frac {1}{2}}ab\sin C} Heron's formula is another method that may be used to calculate the area of a triangle. This formula states that if a triangle...

}&d(BC)^{2}&0&1\\1&1&1&0\end{bmatrix}}=0.} This determinant is, by Heron's formula, equal to −16 times the square of the area of a triangle with side...

inform us that the familiar area formula for a triangle in terms of its three sides, usually known as Heron's formula — k = s ( s − a ) ( s − b ) ( s −...

Apollonius's theorem Other Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Law of sines Menelaus's theorem Pappus's area theorem...

Jiushao's formula" for finding the area of a triangle from the given lengths of three sides. This formula is the same as Heron's formula, proved by Heron of...