Associated Topics || Dr. Math Home || Search Dr. Math

### Who was Hero (or Heron)?

```
Date: 11/12/97 at 12:50:48
From: Jeff Kilgore
Subject: Who was Hero?

I have been trying to find information on the Greek mathematician Hero.
The encyclopedias that I have referenced either do not give any
information, or they just state that he was a Greek who found a
formula for the area of triangles. Any references would be helpful.
```

```
Date: 11/12/97 at 16:53:59
From: Doctor Wilkinson
Subject: Re: Who was Hero?

Heron of Alexandria

Born: about 65 in (possibly) Alexandria, Egypt

Sometimes called Hero, Heron was an important geometer and worker in
mechanics. Book I of his treatise _Metrica_ deals with areas of
triangles, quadrilaterals, regular polygons of between 3 and 12 sides,
surfaces of cones, cylinders, prisms, pyramids, spheres etc. A method,
known to the Babylonians 2000 years before, is also given for
approximating the square root of a number.

Heron also proves his famous formula:

if A is the area of a triangle with sides a, b and c and
s = (a+b+c)/2

then A = sqrt[s(s-a)(s-b)s-c)].

In Book II of _Metrica_, Heron deals with volumes of various
3-dimensional figures such as spheres, cylinders, cones, prisms,
pyramids etc. Book III of _Metrica_ deals with dividing areas and
volumes according to a given ratio.

_Dioptra_ deals with theodolites and surveying. 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 of these cities.

_Catoptrica_ deals with mirrors. In his study of light, Heron stated
that vision results from light rays emitted by the eyes. He believed
that these rays traveled with infinite velocity.

Heron wrote a number of important treatises on mechanics. They give
methods of lifting heavy weights and simple mechanical machines. There
is, rather remarkably, a description of a coin-operated machine and a
steam-powered engine called an aeolipile, which has much in common
with a jet engine. Heron's aeolipile is described as follows:

The aeolipile was a hollow sphere mounted so that it could turn
on a pair of hollow tubes that provided steam to the sphere from
a cauldron. The steam escaped from the sphere from one or more
bent tubes projecting from its equator, causing the sphere to
revolve. The aeolipile is the first known device to
transform steam into rotary motion.

_Pneumatica_, in addition to the aeolipile, gives designs for over 100
machines such as a fire engine, a wind organ etc.

If you can find a copy of Heath's _History of Greek Mathematics_, it
will probably give you a lot more.

-Doctor Wilkinson,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School History/Biography
Middle School History/Biography

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search