Hippocrates of Chios

He is the most famous mathematician in the fifth century BC. The name of Hippocrates is drawn in everyone's minds. The reason for this name's popularity is Hippocrates of Kos. Hippocrates of Chios was born in the city of Chios. Hippocrates tried to solve the following problems that confused the minds of mathematicians at that time:

1. Squaring a circle is any drawing of a square with a known area of a circle, using the compass and the ruler that without grading.

2. Triangulation of the angle, i.e. dividing the angle into three equal sections, also using the compass and the ruler that without grading.

3. Doubling the cube, i.e, drawing a cube has twice the volume of a given cube.

We note that solving the first equation leads to the length of the side of the square

The second equation leads to ( sin3x = 3sinx - 4sin³x )

( h = 3u – 4u³ )

As for the third equation, it leads to ( x³ = 2L³ ) where L: the side of the known cube and the straight edge (the ruler is not graded) and the compass do not solve more than one equation of the second degree, so these equations cannot be solved previously. However, the Greek mathematicians in the fifth century BC were created theoretical solutions to these issues.

(In 1760 Johann Heinrich Lambert proved that pi is an irrational number)

(In 1794 Joseph Lagrange proved that (pi) 3 is an irrational number)

(In 1882 Ferdinand Lindemann proved that pi is a transcendental number)

Hippocrates revealed three of the five types of crescents that can be squared in a simple way. His revelation was exciting and the simplest example of Hippocratic crescents:

In addition, Hippocrates' solution to the problem of doubling the cube showed that Hippocrates had a clear understanding of the compound ratio.