Hero of Alexandria was a mathematician and engineer who lived in Alexandria, Egypt, during the Roman era. He lived around 10 AD to 70 AD. He is known as one of the greatest scientists of ancient times and represented the scientific traditions of ancient Greece. Hero wrote about a steam-powered device called an aeolipile, also called "Hero's engine." He also created a windwheel, which was the first known example of using wind power on land. In his book Mechanics, he described tools called pantographs. Some of his ideas were inspired by the work of another scientist named Ctesibius.

In mathematics, Hero wrote a detailed explanation of Euclid's Elements and a book on applied geometry called Metrica. He is best known for Heron's formula, which helps calculate the area of a triangle using only the lengths of its sides.

Many of Hero's original writings and designs are no longer available. However, some of his works were saved in manuscripts from the Byzantine Empire and, to a lesser extent, in Latin or Arabic translations.

Life and career

Little is known about Hero's life, including where he was born or his background. The earliest records of his work appear in Book VIII of Pappus's Collection, written in the 4th century AD. Scholars estimate Hero lived between 150 BC and 250 AD. Otto Neugebauer (1938) studied a lunar eclipse mentioned in Hero's Dioptra and found it matched an eclipse in 62 AD. Later, A. G. Drachmann suggested Hero might have observed the eclipse from Alexandria. However, Hero did not clearly state this, and his description of the eclipse is unclear. He may have used data from another observer or made up the example.

Alexandria was founded by Alexander the Great in the 4th century BC. By Hero's time, it was a city with people from many cultures, part of the Roman Empire. The intellectual community, centered around the Mouseion (which included the Library of Alexandria), used Greek as their main language. Greek and Egyptian people in the city often married. Some scholars believe Hero taught at the Mouseion because his writings resemble lecture notes or textbooks on mathematics, mechanics, physics, and pneumatics. Although the term "cybernetics" was not used until the 20th century, Hero's work on automated devices is considered some of the earliest research in this field.

Hero is credited with inventing several devices, including:

• The aeolipile: A steam-powered device, sometimes called "Hero's engine." Vitruvius mentioned a similar device earlier, but Hero's version is the first recorded steam engine. Another invention used heated air to move water, which opened temple doors. Some historians have combined these two ideas, but Hero's device may not have performed useful work.
• A vending machine: This machine released water for washing when a coin was inserted. The coin triggered a lever that opened a valve. A counterweight later reset the lever.
• A wind-powered organ: This was the first recorded use of wind to power a machine.
• Theater mechanisms: Hero designed systems for Greek plays, including a mechanical play that lasted nearly ten minutes. Sound effects, like thunder, were created by dropping metal balls onto a hidden drum.
• A force pump: Widely used in Rome, this device was applied to fire engines.
• A syringe-like tool: Used to control air or liquid flow.
• A self-contained fountain: Now called "Heron's fountain," it operated using water pressure.
• A cart: Powered by a falling weight and strings wrapped around its axle.
• A thermometer: Hero described how air expands and contracts, which is the basis of thermometers. He demonstrated this with a tube filled with air and water.
• A self-filling wine bowl: Used a floating valve to control liquid flow.

Hero also developed a method to calculate square roots, now called "Heron's method," in his book Metrica. He is best known for "Heron's formula," which calculates a triangle's area using its side lengths. He also described a method for cube roots. In geometry, the "Heronian mean" helps calculate the volume of a pyramid or cone's frustum.

Hero explained a shortest path algorithm: to find a point on a line that minimizes the distance between two points. This led him to propose that light travels the shortest path. Later, Ibn al-Haytham expanded this idea to include reflection and refraction. Pierre de Fermat later stated the principle in a modern form, emphasizing that the optical path is "stationary."