### Heron of Alexandria

## Biographical Background

Hero(n) of Alexandria is thought to have been a Greek inventor and mathematician, either of Egyptian, Phoenician, or Greek heritage, who lived sometime between 150 BC and 250 AD. Known also as Michanikos, or, the Machine Man, Heron’s inventions were more like novelties, intended to awe crowds (Lahanas). He is also thought to have lived in Alexandria, working at the Museum that also housed the famous Library of Alexandria.

O’Conner and Robinson (1999) outline three schools of thought about when Heron lived. One postulated the date 150 BC, based primarily on the fact that he does not quote anyone later than Archimedes. Another postulated the date 250 AD by attempting to show that he lived later than Ptolemy, but before Pappus who quotes Heron in his own work. The third notes a ‘recent’ eclipse that Heron made reference to, which is now dated at March 13th, 62 AD. It also attempts to show that he was a contemporary of Columella, who makes several compelling references to Heron’s mathematics.

So, the currently accepted timeframe during which Heron is thought to have flourished is between 10 and 85 AD (Papadopoulos, 2007).

Heron’s inventions range from vending machines that released a discrete amount of liquid once a coin is inserted to much more grand devices such as automaton theaters. But, he is also renowned for advances in mathematics and hydraulics.

## Inventions

Most of the inventions here can be found in Papadopoulos or Lahanas:

Aeolipile – Heron invented this early version of the steam engine, though he or at least his contemporaries did not imagine the applications. Had they understood that the steam engine could do mechanical work on a massive scale, the Industrial Revolution could have happened nearly 2000 years before it did. Heron’s version was a container of fluid, that when heated, pushed steam up through two tubes into a hollow ball. The ball had two opposing arms that extended outward in an ‘L’ shape. Thus, the steam propelled the ball around in circles.

Odometer – Heron is thought to have invented a mechanical odometer, though some attribute this to Archimedes. Either way, Heron developed one that would release a discrete number of marbles per every precisely tuned turn of gears. The gears were connected to the wheels of a cart, and thus, the pusher of the cart could count the number of marbles and then the distance those marbles represented.

Vending Machine – Heron invented a vending machine that, once a coin was inserted, released a discrete amount of liquid. This was accomplished by letting the coin drop onto one side of a lever that pivoted around its center, pulling up a stop that would release the liquid. Once the coin fell off because of the angle of the lever, the stop would gently plug the hole again.

Baroulkos – This device was a gear box intended to lift weights.

Cheiroballista – This was a variation of the ballista, which is a mounted crossbow where the arms are drawn back against torsion bundles. Torsion works by twisting bundles of ropes in the same direction with an arm in the middle of the bundle. To increase the amount of torsion possible, the Cheiroballista (and other ballistas) made use of a ratchet and crank system to draw the projectile back. He also invented a stone-thrower concept similar to this, called a Palintonon.

Dioptra – This was a surveying device that made use of triangulation methods not used until the 16th-century.

Automata – Heron developed many self-driven devices and apparatus. The word automata denotes something that performs some function without outside manipulation.

For temples, Heron built several mythological scenes that would act out. Also, he designed a system that would automatically open temple doors once a fire was lit as an offering. Obviously, many of his designs were applied by temples to instill faith and awe in prospective disciples.

For the theater, Heron built completely mechanical plays that operated off binary-like systems of pulleys. The pulleys were driven by a weight sitting atop sand that poured out slowly. The self-contained plays would roll themselves on stage, lift the curtains to the diorama, and proceed through the plot of the play with figures and scenery moving automatically.

## Ideas

Besides his mechanical novelties, Heron both explicitly and implicitly advanced fields such as hydraulics, pneumatics, and mathematics, most often anticipating innovations hundreds and thousands of years down the road. These are some notable ideas associated with Heron, most of which can be found in Lahanas and World of Mathematics on Heron found on Bookrags.com:

Area of a triangle – Heron developed a method used even to this day for calculating the area of any given triangle, no matter the angles, based solely on the sides. The formula is:

Division of geometrical shapes – Heron wrote a few books only recovered within the last century that focused on dividing various shapes into various parts mathematically. This was of particular use to land surveyors.

Roots – Heron developed a method of finding the square root of a given number. If one has an initial approximation of the square root (it doesn’t really matter how accurate it is – just that the less accurate the approximation, the more iterations of the formula one must perform), then one may iterate Heron’s formula to the desired accuracy. Furthermore, he developed a method of finding the cube root of a given number, although it is only thanks to the work of Deslauriers and Dubac that we have the formula Heron must have used.

Harnessing power – Heron provided several methods of utilizing principles of mechanics to do work, though not on the scale of an industrial revolution. He worked on cybernetic principles in the form of self-regulating systems. One such example is the goblet he designed to maintain a certain level of fluid, replenishing or draining itself until the level was reached.

## Influence

Heron of Alexandria amassed a fame in his own day, particularly for the awe he inspired in theater and temple crowds with his mechanical devices. He played an important role in developing war-machines, surveying instruments, and systems of pulleys and gears. For contemporary society, Heron’s influence in geometry has not been felt nearly as much as his formula for the area of a triangle. In fact, Heron’s formula can be extended even to impossible triangles, allowing calculations in advanced fields of physics such as relativity where other formulae fail. So, not only does Heron’s formula provide a method of finding the area of a triangle without need for angles, but it also provides promising future applications. Unfortunately, Heron’s mechanical work (especially the steam engine) went largely unused until reinvented and applied during the Industrial Revolution. Finally, Heron recorded advances in mathematics and mechanics that came before him, and thus provided a connection from one generation to the next for inventors and scholars who would otherwise have been forgotten.

## Sources:

http://www.mlahanas.de/Greeks/HeronAlexandria.htm

http://www-history.mcs.st-and.ac.uk/Biographies/Heron.html

http://www.mlahanas.de/Greeks/HeronsMath.htm

http://www.bookrags.com/biography/hero-of-alexandria-wom/

Papadopoulos, Evangelos. “Heron of Alexandria (c. 10-85 AD)” in the book, Distinguished Figures in Mechanism and Machine Science. Springer Netherlands, 2007 (217-45).