## Irrational Numbers and The Proofs of their Irrationality

"Irrational numbers are those real numbers which are not rational numbers!" Def.1: Rational Number A rational number is a real number which can be expressed in the form of where $a$ and $b$…

## The Area of a Disk

If you are aware of elementary facts of geometry, then you might know that the area of a disk with radius $R$ is $\pi R^2$ . The radius is actually the measure(length) of…

## Triangle Inequality

Triangle inequality has its name on a geometrical fact that the length of one side of a triangle can never be greater than the sum of the lengths of other two sides of the triangle.…

## Numbers – The Basic Introduction

If mathematics was a language, logic was the grammar, numbers should have been the alphabet. There are many types of numbers we use in mathematics, but at a broader aspect we may categorize them in…

## Everywhere Continuous Non-differentiable Function

Weierstrass had drawn attention to the fact that there exist functions which are continuous for every value of $x$ but do not possess a derivative for any value. We now consider the celebrated function…

## Free Online Calculus Text Books

Once I listed books on Algebra and Related Mathematics in this article, Since then I was receiving emails for few more related articles. I have tried to list almost all freely available Calculus texts. Here…

## D’ ALEMBERT’s Test of Convergence of Series

Statement A series $\sum {u_n}$ of positive terms is convergent if from and after some fixed term $\dfrac {u_{n+1}} {u_n} < r < {1}$ , where r is a fixed number. The…

## Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem

Topic Beta & Gamma functions Statement of Dirichlet's Theorem $\int \int \int_{V} x^{l-1} y^{m-1} z^{n-1} dx dy ,dz = \frac { \Gamma {(l)} \Gamma {(m)} \Gamma {(n)} }{ \Gamma{(l+m+n+1)} }$ , where V…