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Heron of AlexandriaAnd his formula for the area of a triangle
By Miguel Navarro Martínez – IES Saavedra Fajardo
Biography
Heron of Alexandria was born in 10 and died in the year 70. He was a Greek mathematician and engineer who was active in his native city of Alexandria.
Hero published a well recognized description of a steam-powered device called an aeolipile (sometimes called a "Hero engine"). Among his most famous inventions was a wind wheel, constituting the earliest instance of wind harnessing on land.
Besides this, and some of his published works, little is known about his life. His contrubutions to mathematics are mainly his formula for the area of a triangle and a method to find out or approximate square roots.
Aspects of maths he was interested in
He was interested in geometry and the following books written by him talk about geometry: Geometrica, Stereometrica, Mensurae, Geodaesia,Definitiones, and Liber Geëponicus.
Besides geometry he was also interested in Mechanics, he wrote some books about it: Pneumatica, Automatopoietica,Belopoeica, and Cheirobalistra
In Maths I curriculum
Mainly, Heron’s formula for the area of the triangle is related to trignonometry. This formula, can help you find out the area without using sin, cos and tan for example, but trigonometry is faster. This formula can also be used to find the area of a triangle that has a circle in it, because it uses s(semiperimeter).
Formula of the area of the triangle
Heron’s famous area formula appeared as Proposition I.8 of his Metrica. It states that if A is the area of a triangle with sides a, b, and c, and s = (a + b + c)/2 (called semiperimeter)
A = √ s(s – a)(s – b)(s – c) With this formula Heron calculated the area of a triangle in terms of the semiperimeter
s of the triangle. Some may question why one should use this formula to find the area of a triangle when there is a far simpler formula for area of a triangle given in terms of the base b and height h of the triangle, A = (bh)/2.
But remember that Heron was a practical mathematician. His formula could be used in measuring the area of a real triangular region where the boundaries were known but it was not possible to enter the region to determine its height.
Bibliography and sources
http://www.robertnowlan.com/pdfs/Heron.pdf
https://en.wikipedia.org/wiki/Hero_of_Alexandria
http://www.ugr.es/~eaznar/heron.htm
Bibliography and sources
http://www.robertnowlan.com/pdfs/Heron.pdf
https://en.wikipedia.org/wiki/Hero_of_Alexandria
http://www.ugr.es/~eaznar/heron.htm
