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Proofs of 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 
Following two statements are equivalent to the definition 1.
1. 
2. 
Gamma Function
If we consider the integral 
The Area of a Disk
[This post is under review.]
If you are aware of elementary facts of geometry, then you might know that the area of a disk with radius 
The radius is actually the measure(length) of a line joining the center of disk and any point on the circumference of the disk or any other circular lamina. Radius for a disk is always same, irrespective of the location of point at circumference to which you are joining the center of disk. The area of disk is defined as the ‘measure of surface‘ surrounded by the round edge (circumference) of the disk.
The area of a disk can be derived by breaking it into a number of identical parts of disk as units — calculating their areas and summing them up till disk is reformed. There are many ways to imagine a unit of disk. We can imagine the disk to be made up of several concentric very thin rings increasing in radius from zero to the radius of disc. In this method we can take an arbitrary ring, calculate its area and then in similar manner, induce areas of other rings -sum them till whole disk is obtained. (more…)
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. If 
- Triangle
Consider the triangle in the image, side
In modulus form, 
- Visual representation of Triangle inequality
For example, the distance of 
Triangle inequalities are not only valid for real numbers but also for complex numbers, vectors and in Euclidean spaces. In this article, I shall discuss them separately. (more…)
My Five Favs in Math Webcomics
Cartoons and Comics are very useful in the process of explaining complicated topics, in a very light and humorous way. Like:
(more…)
Progress Report of MY DIGITAL NOTEBOOK in 2011
The WordPress.com stats helper monkeys prepared a 2011 annual report for this blog.
Here’s an excerpt:
The concert hall at the Syndey Opera House holds 2,700 people. This blog was viewed about 53,000 times in 2011. If it were a concert at Sydney Opera House, it would take about 20 sold-out performances for that many people to see it.
