Hero of Alexandria
by Courtney Golterman
It is difficult to pinpoint the famous Greek mathematician, Hero, in history since there were at least eighteen Heros who published works in Greek. A few works can be specifically attributed to Hero of Alexandria, since they still exist to the present day either in Greek or in early translations. Most historians place Hero of Alexandria's birth in Egypt around 20 A.D. All agree that he was writing prior to 62 A.D., the year in which many historians place his death.
Five complete works of Hero of Alexandria survive. These are “Pneumatics” and “Automata” in the original Greek, and “Mechanics”, “Metrics,” and “Dioptra” in Arabic. Many of Hero's works were translated first into Arabic and then into Latin. A few partial works also survive. Hero's compiled works, while not all of them original ideas, formed the foundation of mechanics and related fields well into the 18th Century.
“Pneumatics” was a two-volume work which described machines operated by steam, compressed air or water. In fact, Hero's most important invention, was the aeolipile, a steam-powered engine. Although, some of Hero's predecessors worked with steam, the discovery of the steam engine is always attributed to Hero. His simple steam engine was put to use in several mechanisms, but was never developed to the point of the steam-powered piston engine of the 1600's, which helped start the Industrial Revolution.
“Automata” gives descriptions of mechanical toys that were used in temples to perform “miracles” for the believers. “Mechanics” was published in three volumes and describes various types of engines.
Hero of Alexandria's most important work came in “Metrics,” a three book work. Book One includes, among other things, Heron's formula for finding the area of a triangle given the length of the three sides. It is useful if the height of the triangle is difficult to find. It begins by determining the semiperimeter (or half of the perimeter).
s = 1/2(a + b + c)
_____________
A = Ö s(s-a)(s-b)(s-c)
Book Two of “Metrics” gives formulas for calculating the volumes of cylinders, cones, pyramids, prisms, spheres, etc. Book Three describes the relationships of volumes and areas of various shapes in set ratios. “Dioptra” includes a detailed description of an odometer. Hero's odometer was made with a set of toothed wheels to convert the movement of vehicle into units of length (Roman miles or about 1400 meters). Hero also described a variation of this device that could be used on ship. It consisted of a paddlewheel and a float fitted to the outside of the boat that would likewise record the distance traveled.
Hero was an expert in applied mathematics, especially in mechanics. Much of his work is based on that of his Greek predecessors, such as Archimedes and Ctesibius, who lived two or three hundred years before Hero. Hero did add much original thought and provided a view of the progress that had been made in those centuries of Greek civilization. That his work continued to be used in modern times is a testimony to its importance. Some of his works that did not survive are mentioned in his existing works. Who can say what was lost with these books that did not survive.
List of Resources
“Hero of Alexandria” www.tmth.edu.gr/en/aet/5/55.html
“Hero of Alexandria (c.62)” www.bbc.co.uk/history/historic_figures/hero_of_alexandria.shtml
“Heron of Alexandria” www.britannica.com/eb/article?eu=41048
“Hero of Alexandria” http://library.thinkquest.org/C006011/english/sites/heron_bio.php3?v=2
“Heron's formula” www.mathworld.wolfram.com/hom/kmath226.htm
Encyclopedia of Mathematics (Prentice-Hall, Inc., 1982) pp.28-29
Michael Grant, Greek and Latin Authors; 800 B.C.-A.D. 1000 , ( The H.W. Wilson Company, New York, 1980) pp. 193-194
“Invention; Ancient Greece” The World Book Encyclopedia Volume I (World Book, Inc. 1996) pp.358-359