# 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 $b$ are both integers relatively prime to each other and $b$ being non-zero. Following two

# 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 a line joining the center of disk and any point on the circumference of the

# 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 $a$ , $b$ and $c$ be the three sides of a

# 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 two categories: 1. Countable Numbers 2. Uncountable Numbers The numbers which can be counted in

# Derivative of x squared is 2x or x ? Where is the fallacy?

We all know that the derivative of $x^2$ is 2x. But what if someone proves it to be just x?

# Solving Ramanujan’s Puzzling Problem

Consider a sequence of functions as follows:- $f_1 (x) = \sqrt {1+\sqrt {x} }$ $f_2 (x) = \sqrt{1+ \sqrt {1+2 \sqrt {x} } }$ $f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} } } }$ ……and so on to \$ f_n