Euler and his number

Leonhard Euler was, in my opinion, one of the greatest mathematicians of all time, among names like Carl Frederich Gauss. He is most famous for his number. It is an irrational constant called 'e'. Its value is somewhere between 2 and 3(approximately 2.718..). It is the figure obtained on constantly compounding 1 unit of money and the value obtained at the end of the year is e units. It has several amazing properties, such as its formula being

. It can also be written in terms of sums of numbers divided by their factorials.

The constant e is most notable for appearing in Euler's formula, a thing of beauty in mathematics. It combines the Maclaurin series and trigonometry. It is perhaps the only formula which has i as a power and still makes sense.(After all, what is anything to the power of an imaginary number?). Despite its odd features, e features in numerous formulas and fields of science, economics, and of course math. In economics for example, it features in Pareto's law, which deals with the distribution of wealth in a economy among its population. It says that the people with a large amount of wealth is directly proportional to 1/W to the 'e'. W is a large number.

In physics, e appears in the formula for radioactive disintegration of materials. It says that the number of atoms in a substance decreases in a time 't', as,

Nnew=N(old).e to the -kt, where k is the disintegration constant. In math, of course, e is the base for all natural logarithms. 

Apart from his number, Euler excelled in many areas. He worked in hyperbolic geometry, where he tried to discover a perfect cuboid(the search for which goes on). He came close and someone else discovered an 'Euler brick', having whole numbers for its sides and diagonals but not body diagonals. Also, in geometry, Euler formulated his 'Euler characteristic', which is:

V-E+F. The EC of any solid is the number of edges subtracted from the sum of its vertices and faces. So, a torus would have an EC of 0 as it has no edges, no faces, and not a complete face.