Hero's Steam Turbine

Hero (c. 10–70 AD) was an ancient Greek mathematician and engineer who lived in Alexandria, Egypt. He is considered the greatest experimenter of antiquity and his work is representative of the ancient Greek scientific tradition.

Hero published a well recognized description of a steam-powered device called an aeolipile (hence sometimes called a "Hero engine"). Among his most famous inventions was a wind wheel, constituting the earliest instance of wind harnessing on land. He is one of the earliest scientists that believed all matter was made up of tiny invisible particles that the ancient Greeks named atoms. Some of his ideas were derived from the works of Ctesibius.

Much of Hero's original writings and designs have been lost, but some of his works were preserved in Arab manuscripts.

The aeolipile was History's first known steam turbine. It was created almost two thousand years before the industrial revolution. The History Channel created a full size model and surprise, the aeolipile not only worked but turned 5,000 RPM. The aeolipile could have been developed further and been used to power ships and machinery but it was only used as a grown up toy. The industrial revolution could have started 2,0000 years earlier. The Roman World 2000 years ago was awash in slaves, who were mostly prisoners of war,  and no one saw the need for labor saving devices.

Another one of Hero's engines used air from a closed chamber heated by an altar fire to displace water from a sealed vessel; the water was collected and its weight, pulling on a rope, opened temple doors

The first known coin operated vending machine was also one of his inventions, when a coin was introduced via a slot on the top of the machine, a set amount of water was dispensed. This was included in his list of inventions in his book, "Mechanics and Optics". When the coin was deposited, it fell upon a pan attached to a lever. The lever opened up a valve which let some water flow out. The pan continued to tilt with the weight of the coin until it fell off, at which point a counter-weight would snap the lever back up and turn off the valve.

    Hero's wind-powered organ, a wind wheel operating an organ, marking the first instance of wind powering a machine in history.

    Hero also invented many mechanisms for the Greek theater, including an entirely mechanical play almost ten minutes in length, powered by a binary-like system of ropes, knots, and simple machines operated by a rotating cylindrical gear. The sound of thunder was produced by the mechanically-timed dropping of metal balls onto a hidden drum.

    In optics, Hero formulated the Principle of the Shortest Path of Light: If a ray of light propagates from point A to point B within the same medium, the path-length followed is the shortest possible. It was nearly 1000 years later that Alhacen expanded the principle to both reflection and refraction, and the principle was later stated in this form by Pierre de Fermat in 1662; the most modern form is that the path is at an extremum.

Hero described a method of iteratively computing the square root of a number. Today, though, his name is most closely associated with Hero's Formula for finding the area of a triangle from its side lengths.