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 
Died: about 125 

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/