Pappus, regarded as an important Greek mathematician, was born in Alexandria in Egypt. His interest in mathematics is said to have began from when he observed a solar eclipse on October 18, 320 and then since has focused his work on geometry. Everything associated with Pappus mathematical mind was included in the collection of books he wrote called "the synagogue". The purpose of the volumes were to revive geometry and restore it to a level of significance, usually by providing further explanations or supplements to the works of previous geometers. The knowledge of some mathematicians was only a result from his citation.
"The Synagogue" consisted of 7 books although the first 2 books are missing.
Book III distinguishes plane, solid and linear problems and a summary of finding two mean proportionals (a:x=x:y=a:y). He shows that given two of the numbers a, b, c and the type of mean the third can be calculated.
Book IV is an extension of Pythagoras" theorem for parallelograms constructed on the legs of any triangle. He also includes material on the Archemedian spiral (the shape of a screw), such as finding the area of one turn.
Book V reproduces the work of Zeodorus on isoperimetric figures. He also celebrates the hexagonal shape of bees honeycomb. They would necessarily think that the figures must be all adjacent one to another and have their sides in common, in order that nothing else might fall into the interstices and so defile their work. Now there are only three rectilineal figures which would satisfy the condition, I mean regular figures which are equilateral and equiangular, inasmuch as irregular figures would be displeasing to the bees, these being the triangle, the square and the hexagon, the bees in their wisdom chose for their work that which has the most angles, perceiving that it would hold more honey than either of the two others for the same expenditure of material.
Book VI determines the center of an ellipse in relation to the circle.
