Hero of Alexandria | Biography

Hero(or Heron) of Alexandria was a Greek mathematician and engineer whose major contributions to mathematics were Hero's formulaand the first approximation in Greece of a number's square root. He also wrote a number of books on mathematics, including Metrica, is a treatise on geometry. While much of his writings in mathematics and mechanics stem from earlier authors, Hero is credited as being one of the earliest and most comprehensive and detailed recorders of ancient technology, especially through such works as Penumaticaand Automata. Hero also designed many mechanical instruments, which earned him the name "the mechanic" or "the machine man."

Other than his writings, nothing is known about the life of Hero, who is sometimes referred to as Heron. The date of his birth is unknown, and estimates of when he lived vary by 150 years. However, Hero mentions an eclipse of the moon visible from Alexandria in his book Dioptra. Modern astronomers date this eclipse as having occurred in 62 A.D., thus providing the major clue as to the era when Hero lived. Scholars agree that Hero probably lived and worked in Alexandria. However, there is some question as to his nationality, which may have been Egyptian.

Despite the lack of historical records on Hero's life, the breadth of his writings on mathematics and mechanics leave little doubt that he was well educated. Hero was strongly influenced by the writings of Ctesibius of Alexandria and may even have been a student of the ancient mechanical engineer. His works draw on a wide range of sources, including, Greek, Latin, and Egyptian. Unlike most of his contemporaries, Hero makes no mention of working for a Roman patron.

Hero's writings in mathematics and especially in mechanics reveal that he was practical by nature, often using ingenious means to attain his goal, like his design for a steam engine, catapults for war, and various machines for lifting that used compound pulleys and winches. Hero was also precise in dictating the types of materials to be used to make the machine function properly. Interestingly, Hero designed several mechanical devices to simulate "temple miracles," including a device attached to the temple door which made a trumpet play when the door was opened.

Compiles Encyclopedic Works on Geometry

Hero's background in mechanical engineering is clearly evident in his practical rather than theoretical approach to mathematics and geometry. Although credited with the first approximations of square roots and his famous formula for calculating the area of a triangle, Hero's primary contribution to geometry stem from a series of treatises in which he freely incorporated the writings and findings of others to compile a coherent body of work on the subject.

The most famous of these works is Metrica, which consists of three books focusing on the calculation of areas and volumes and their division. This book was lost until the last century, and scholars knew of its existence only through a 6 A.D. commentary by Eutocius. Then, in 1894, historian Paul Tannery discovered a fragment of the book in Paris. A completed copy was found by R. Schöne in Constantinople (Istanbul) in 1896. Book I of Metrica contains the famous Hero's formula, which he used to calculate the area of a triangle when the sides are given and provided surveyors of his day with a formula for determining the area of land lots. Like most of Hero's work, this formula may came from an earlier source. Although an ancient Islamic manuscript credit's Archimedes with developing the famous equation, no writings of Archimedes are known to contain the formula.

Hero's other works include Definitions, basically a catalogue of geometrical terms; Geometrica, an introduction to geometry, and Sterometrica, which focuses on solid geometry for spheres, cubes, pyramids, and other figures. He is also believed to have written a commentary on the famous Greek mathematician Euclid. Hero's emphasis on the practical use of geometry is evident in the types of problems he tackles. For example, he provides a method for calculating a theater's seating capacity and for determining the number of jars that could be stored in a ship. In the theoretical realm of mathematics, Hero is credited as the first Greek mathematician to use systematic geometrical terminology and symbols. Although the Babylonians had developed a formula for approximating square roots nearly 2,000 years before Hero, he was the first Greek to develop methods for finding approximate numerical square and cube roots.

Advances the Principles of Mechanics

Hero's contributions to the field of mechanics are wide ranging, and he achieved considerable fame in his own day for some of his inventions. For the most part, these inventions focused on the practical, like keeping time with a water clock and developing a compressed air catapult for war. His most famous mechanical design was for the aeolipile, which used steam to rotate a sphere and has been compared to the modern-day jet engine.

Much of Hero's fame today lies in the fact that most of his treatises on mechanics have survived throughout the centuries. As a result, he is considered the definitive source on ancient Greek and Roman technology. His design for the aeolipile appear in his Penumatica, which focuses on designs for machines powered by compressed air, siphons, and steam pressure. Although the treatise contains some theoretical components, the most important aspect of the book is Hero's ability to combine different schools of mechanical thought into a cohesive treatise. In Mechanica, Hero focuses on basic mechanics and their application, including the levers, pulleys, screws, and various tools. Hero was also interested in mechanical "gadgets," primarily used to produce "miracles" in a religious context. He describes these devices in both Pneumatica and Automata, which includes designs for making miniature mechanized puppet theaters. A book on machines for lifting heavy objects, Baroulkos , is also lost.

The wide range of Hero's interests are evident in his other works, which include Dioptra, at treatise on surveying. In Catoptrica, Hero discusses mirrors, including the theory of refraction and the various kinds of mirrors, such as flat, concave, and complex. He also wrote lost works on topics like large and hand catapults (Baelopoeica and Cheiroballistra), time keeping devices, and vault construction.

Hero's stature as a historical figure in mathematics and mechanics has grown with the rapid advance of technology in the last two centuries. Hero was more than a mere chronicler of ancient devices and how they should be built, he also exhibit scrupulous attention as to their construction and the materials to be used. Although Hero never built many of his models, they presented interesting design problems that grew in importance with the industrial revolution.

Hero is not without his critics for a number of reasons. First and foremost, his works contain some notable errors, primarily in the area of mathematics. Hero is also known to have gathered much of his knowledge from previous writers. Despite these criticisms, Hero revealed an advanced understanding of harnessing power, especially in the form of wind and steam. As a scholar, he conducted comprehensive research and took a systematic approach to revealing the basic of many useful devices, including a coin-operated machine. As with his birth, the date of Hero's death is unknown.