Some things in the world never fail to evoke a deep sense of awe from the human mind. Among other things, they may be the miracle of life, the vastness of the universe, and the existence of an uncountable set with measure zero …

A group of friends, even in number, meet in a get together event. They start playing a game: they sit in a circular formation and shake hands …

So the other day I had a quiz on permutations and combinations. Easy stuff right? We have all heard the formula for the number of permutations of n objects around a circle; (n - 1)! of course! Let us first take a look at why this is so …

Here, at first I have presented a simple problem related to π, and then I have presented one generalised version of this, and at last presented some ideas and some interesting series related to π.

When learning Calculus or Analysis for the first time, it can feel as if the entire subject is only about computation; one can forget the forest for the trees so to speak, and it all seems a bit arbitrary. However, there is no subject in mathematics that is an island; and Analysis is one such branch which is at the heart of nearly all branches of mathematics. For this particular article, I want to show how basic geometry that one learns before 11th/12th is connected with the abstract analysis that comes afterwards.

The article explores a theorem that states that even dimensional spheres do not admit a smooth non-vanishing nowhere zero tangent vector field. The 3 dimensional analogue of this is called the Hairy ball theorem, or as the Europeans say, the Hedgehog theorem, in layman’s term which says that if you have a ball with hair sprouting out of every point, it cannot be combed without creating a bald spot or a cow-lick!

“This Table has truly exceptional and admirable properties; for besides concealing within itself the mysteries of Combinatorics, it is known by those expert in the higher parts of Mathematics also to hold the foremost secrets of the whole of the rest of the subject.” - James Bernoulli

When Carver asked, “What do we talk about when we talk about love?” Esther Klein replied, “Why, math riddles, of course!” While love at first sight has been omnipresent in the works of poets, writers and musicians, love at first math problem has always remained an understatement.

“Algebra is nothing more than geometry, in words; geometry is nothing more than algebra, in pictures.” – Sophie Germain. Here, we attack a familiar problem with geometry, linear algebra, and a splash of intuition.