**Heron** or **Hero of Alexandria** was an important geometer and worker in mechanics who invented many machines including a steam turbine. His best known mathematical work is the formula for the area of a triangle in terms of the lengths of its sides.

- Perhaps the first comment worth making is how common the name Heron was around this time and it is a difficult problem in the history of mathematics to identify which references to Heron are to the mathematician described in this article and which are to others of the same name.
- There are additional problems of identification which we discuss below.
- A major difficulty regarding Heron was to establish the date at which he lived.
- There were two main schools of thought on this, one believing that he lived around 150 BC and the second believing that he lived around 250 AD.
- The first of these was based mainly on the fact that Heron does not quote from any work later than Archimedes.
- The second was based on an argument which purported to show that he lived later that Ptolemy, and, since Pappus refers to Heron, before Pappus.
- Both of these arguments have been shown to be wrong.
- There was a third date proposed which was based on the belief that Heron was a contemporary of Columella.
- He gave measurements of plane figures which agree with the formulas used by Heron, notably those for the equilateral triangle, the regular hexagon (in this case not only the formula but the actual figures agree with Heron's) and the segment of a circle which is less than a semicircle ...
- However, most historians believed that both Columella and Heron were using an earlier source and claimed that the similarity did not prove any dependence.
- We now know that those who believed that Heron lived around the time of Columella were in fact correct, for Neugebauer in 1938 discovered that Heron referred to a recent eclipse in one of his works which, from the information given by Heron, he was able to identify with one which took place in Alexandria at 23.00 hours on 13 March 62.
- From Heron's writings it is reasonable to deduce that he taught at the Museum in Alexandria.
- Some are clearly textbooks while others are perhaps drafts of lecture notes not yet worked into final form for a student textbook.
- the ancients also describe as mechanicians the wonder-workers, of whom some work by means of pneumatics, as Heron in his Pneumatica, some by using strings and ropes, thinking to imitate the movements of living things, as Heron in his Automata and Balancings, ...
- or by using water to tell the time, as Heron in his Hydria, which appears to have affinities with the science of sundials.
- A large number of works by Heron have survived, although the authorship of some is disputed.
- We will discuss some of the disagreements in our list of Heron's works below.
- It contains a chapter on astronomy giving a method to find the distance between Alexandria and Rome using the difference between local times at which an eclipse of the moon is observed at each cities.
- In this work, Heron states that vision results from light rays emitted by the eyes.
- Let us examine some of Heron's work in a little more depth.
- A method, known to the Babylonians 2000 years before, is also given for approximating the square root of a number.
- The methods of dealing with these solids are, in view of their surprising character, referred to Archimedes by certain writers who give the traditional account of their origin.
- But whether they belong to Archimedes or another, it is necessary to give a sketch of these results as well.
- Heron begins with a theoretical consideration of pressure in fluids.
- Some of this theory is right but, not surprisingly, some is quite wrong.
- Although all this seems very trivial for a scientist to be involved with, it would appear that Heron is using these toys as a vehicle for teaching physics to his students.
- It seems to be an attempt to make scientific theories relevant to everyday items that students of the time would be familiar with.
- There is, rather remarkably, descriptions of over 100 machines such as a fire engine, a wind organ, a coin-operated machine, and a steam-powered engine called an aeolipile.
- Heron wrote a number of important treatises on mechanics.
- They give methods of lifting heavy weights and describe simple mechanical machines.
- It also examines the theory of motion, certain statics problems, and the theory of the balance.
- There is a discussion on centres of gravity of plane figures.
- Other works have been attributed to Heron, and for some of these we have fragments, for others there are only references.
- The works for which fragments survive include one on Water clocks in four books, and Commentary on Euclid's Elements which must have covered at least the first eight books of the Elements.
- Works by Heron which are referred to, but no trace survives, include Camarica or On vaultings which is mentioned by Eutocius and Zygia or On balancing mentioned by Pappus.
- Also in the Fihrist, a tenth century survey of Islamic culture, a work by Heron on how to use an astrolabe is mentioned.
- Finally it is interesting to look at the opinions that various writers have expressed as to the quality and importance of Heron.
- Some have considered Heron to be an ignorant artisan who copied the contents of his books without understanding what he wrote.
- Some scholars have approved of Heron's practical skills as a surveyor but claimed that his knowledge of science was negligible.

Born about AD 10, (possibly) Alexandria, Egypt. Died about AD 75.

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African, Ancient Babylonian, Ancient Chinese, Ancient Greek, Astronomy, Chinese, Geometry, Origin Egypt, Physics, Special Numbers And Numerals

Epochs: 1

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive