It is easy to confuse Apollinius. Like the name ‘Jack’ or ‘Sarah’ today, Apollinius was a very popular name in the ancient Greek world and there is also famous poet, sculptor and grammarian called Apollinius.
The mathematician, however, was born in what is present day Turkey. He went from there to Alexandria to study and later teach at the famous academy set up by Euclid.
We know little else about his life, except for the fact that he also made a trip to Pergamum back in Turkey where a university similar to Alexandria had been built.
Contemporories called him the ‘Great Geometer’. Over time this nickname has prove correct and his work is now seen as the culmination of Greek geometry on a par with other famous names such as Euclid and Archimedes.
Unlike these two, much of Apollinius’ work has been lost. His most famous text ‘Conics’ consisted of eight books. This extensive work contains 400 propositions about these curves. It extends considerably the work of Euclid and others.
They examined only finite right circular cones, but Apollonius also looked at arbitrary double cones that extend indefinitely in both directions.
The book also introduced terms we commonly use today such as parabola, ellipse and hyperbola. Other works of his have been lost and we are left only with glimpses of them.
The basic tools that were the subject of his geometry were the point, the straight line and the circle. He regarded them as equivalent - a point is a circle of zero radius; conversely, a straight line is a circle of infinite radius.
So his geometry is about circles, interpreted in this generalised way. One of the problems that Apollonius investigated is the problem of constructing a circle tangent to the three given circles - this is not simple.
The most difficult version of this problem concerns three given (pure) circles and then constructing a circle that touches them all. It became known as the problem of Apollonius.
His work inspired much of the geometric advances made by Islamic mathematicians and his book on Conics was to drive much of the Scientific Revolution which happened in Renaissance Europe.