Search results
Results from the WOW.Com Content Network
Heron's formula is a special case of Brahmagupta's formula for the area of a cyclic quadrilateral. Heron's formula and Brahmagupta's formula are both special cases of Bretschneider's formula for the area of a quadrilateral. Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one of the sides of the ...
Today, however, his name is most closely associated with Heron's formula for the area of a triangle in terms of its side lengths. Hero also reported on a method for calculating cube roots. [22] In solid geometry, the Heronian mean may be used in finding the volume of a frustum of a pyramid or cone.
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.
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 .
This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula.
Heron of Alexandria (c. 10 –70 AD) is credited with Heron's formula for finding the area of a scalene triangle and with being the first to recognize the possibility of negative numbers possessing square roots. [77] Menelaus of Alexandria (c. 100 AD) pioneered spherical trigonometry through Menelaus' theorem. [78]
Heron was the flag bearer for Team Panama at the Olympics opening ceremony. She is one of eight Panamanian athletes, and the only gymnast from the country, to participate in the 2024 Paris Olympics.
An illustration of Hero's aeolipile. An aeolipile, aeolipyle, or eolipile, from the Greek "Αἰόλου πύλη," lit. ' Aeolus gate ', also known as a Hero's (or Heron's) engine, is a simple, bladeless radial steam turbine which spins when the central water container is heated. Torque is produced by steam jets exiting the turbine.