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Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one of the sides of the quadrilateral to zero. Brahmagupta's formula gives the area K {\displaystyle K} of a cyclic quadrilateral whose sides have lengths a , {\displaystyle a,} b , {\displaystyle b,} c , {\displaystyle c ...
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]
In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all positive integers. [ 1 ] [ 2 ] Heronian triangles are named after Heron of Alexandria , based on their relation to Heron's formula which Heron demonstrated with the example triangle of sides 13, 14, 15 and area 84 .
A Heronian tetrahedron [1] (also called a Heron tetrahedron [2] or perfect pyramid [3]) is a tetrahedron whose edge lengths, face areas and volume are all integers. The faces must therefore all be Heronian triangles (named for Hero of Alexandria ).
The lune of Hippocrates is the upper left shaded area. It has the same area as the lower right shaded triangle. In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle.
Heron's fountain is a hydraulic machine invented by the 1st century AD inventor, mathematician, and physicist Heron (or Hero) of Alexandria. [ 1 ] Heron studied the pressure of air and steam, described the first steam engine , and built toys that would spurt water, one of them known as Heron's fountain.
A tetrahedron is a disphenoid if and only if its circumscribed parallelepiped is right-angled. [9]We also have that a tetrahedron is a disphenoid if and only if the center in the circumscribed sphere and the inscribed sphere coincide.
The following are trigonometric quantities generally associated to a general tetrahedron: The 6 edge lengths - associated to the six edges of the tetrahedron.; The 12 face angles - there are three of them for each of the four faces of the tetrahedron.