# Math

The Math Blog by Gaurav Tiwari. Contains articles, study notes, book suggestions and career advises in addition to how-to guides, tutorials and much more.

## Complete Elementary Analysis of Nested radicals

This is a continuation of the series of summer projects sponsored by department of science and technology, government of India. In this project work, I have worked to collect and expand what Ramanujan did with Nested Radicals and summarized all important facts into the one article. In the article, there are formulas, formulas and only…

## Hopalong Orbits Visualizer: Stunning WebGL Experiment

I just discovered Barry Martin’s Hopalong Orbits Visualizer — an excellent abstract visualization, which is rendered in 3D using Hopalong Attractor algorithm, WebGL and Mrdoob’s three.js project. Here is a demo video: Hop to the source website using your desktop browser (with WebGL and Javascript support) and enjoy the magic. Hopalong Attractor Algorithm Hopalong Attractor…

## Study Notes on Real Sequences (Definitions and Examples)

In this study note, I have discussed and explained about real sequences — a very important topic in Real Analysis and Calculus. I will cover the topic, definitions and examples under the following headings: Real Sequence: A sequence of real numbers A sequence of real numbers (or a real sequence) is defined as a function…

## Euler’s (Prime to) Prime Generating Equation

The greatest number theorist in mathematical universe, Leonhard Euler had discovered some formulas and relations in number theory, which were based on practices and were correct to limited extent but still stun the mathematicians. The prime generating equation by Euler is a very specific binomial equation on prime numbers and yields more primes than any…

## 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 statements are equivalent to the…

## 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 disk or any other circular…

## 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 triangle, then neither $a$…

## Welcome 2012 – The National Mathematical Year in India

I was very pleased on reading this news that Government of India has decided to celebrate the upcoming year 2012 as the National Mathematical Year. This is 125th birth anniversary of math-wizard Srinivasa Ramanujan (1887-1920). He is one of the greatest mathematicians India ever produced. Well this is ‘not’ the main reason for appointing 2012…

## Interesting Math Articles and Must Read Research Papers for Students

An old yet beautiful untabled listing of highly interactive mathematics related articles and papers available online.

## Claim for a Prime Number Formula

Dr. SMRH Moosavi has claimed that he had derived a general formula for finding the $n$ -th prime number. More details can be found here at PrimeNumbersFormula.com and a brief discussion here at Math.SE titled  “Formula for the nth prime number: discovered?” SOME MORE EXCERPTS ARE HERE:

## Find the Day of a Date using this Calendar Formula

Calendars have very decent stories and since this blog is based on mathematical approach, let we talk about the mathematical aspects of calendars. The Calendar We Use The international calendar we use is called Gregorian Calendar, said to be created by Pope Gregory XIII. Gregorian calendar was introduced in 80s of 16th century, to be…