Hero of Alexandria (pronounced "HEE-ron"; also called Heron of Alexandria; lived around 10 AD to 70 AD) was a mathematician and engineer who worked in Alexandria, Egypt, during the Roman period. He is known as one of the most important scientists of ancient times and helped advance the scientific traditions of the Hellenistic world. Hero wrote about a steam-powered device called an aeolipile, also known as "Hero's engine." He also created a windwheel, which was the first known machine to use wind power on land. In his book Mechanics, he described tools called pantographs, which were used to copy drawings. 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 about practical 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.

Most 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 smaller degree, 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 known 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 book, Dioptra, and found it likely matched an eclipse observed in 62 AD. Later, A. G. Drachmann suggested Hero may have seen 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 diverse city within the Roman Empire. The intellectual community centered around the Mouseion, which included the Library of Alexandria. Most people in the city spoke and wrote in Greek, though Greeks and Egyptians 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 field of cybernetics was not formally named until the 20th century, Hero's work on automated devices is considered some of the earliest research in this area.

Hero is credited with inventing several devices, including:

• The aeolipile, a steam-powered device often 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 could open temple doors. Some historians mistakenly claim the aeolipile could perform useful work.
• A vending machine that released water for washing when a coin was inserted. The coin triggered a lever that opened a valve, allowing water to flow. A counterweight then reset the machine.
• A wind-powered organ, the first known use of wind to operate a machine.
• Theater mechanisms, such as a mechanical play powered by ropes and gears. Thunder was created by dropping metal balls onto a hidden drum.
• A force pump used in Roman fire engines.
• A syringe-like tool for controlling air or liquid flow.
• A self-contained fountain, now called Heron's fountain.
• A cart powered by a falling weight and strings wrapped around an axle.
• A device that used air expansion and contraction to demonstrate temperature changes, possibly an early thermometer.
• A self-filling wine bowl using a floating valve.

Hero described a method for calculating square roots in his work Metrica. This method is now called Heron's method. He is also known for Heron's formula, which calculates the area of a triangle using its side lengths. Hero also wrote about methods for calculating cube roots. In geometry, the Heronian mean helps find the volume of a pyramid or cone's frustum.

Hero also developed an algorithm to find the shortest path between two points across a line. This led him to propose that light travels the shortest path between two points in the same medium. Later, Ibn al-Haytham expanded this idea to include reflection and refraction, and Pierre de Fermat later stated the principle as the "stationary optical path."