Research

My Own

Today, the average cost of a research paper is roughly around $30. This is because of the present model, which has publicly funded research locked behind paywalls established by publishers, who don’t really add much extra value by themselves. As a result, many researchers and other people who are aware of this issue have been looking for a better alternative to this existing system. In fact,

I woke up today (29th June 2021) with a piece of news that the Riemann Hypothesis has been solved. But looks like that was all just a fuss. Indian newspapers, The Hindu, The Quint, Hindustan Times, etc., everyone reported that a Hyderabad-based mathematician has succeeded in solving this $1 million question. Riemann Hypothesis is one of the unsolved problems in mathematics and it has a bounty

Citation is the process in which you cite (refer, quote or pronounce) sources of the particular information you have added to your content. In this way, you tell the reader that your information belongs to that particular site. By doing this, your readers can seek help from the site you have cited. They can check the references for many purposes like: Information about the author Name

Our reader Eswar Chellappa has sent his work on the solution of ‘3X+1’ problem, also called Collatz Conjecture. He had been working on the proof of Collatz Conjecture off and on for almost ten years. The Collatz Conjecture can be quoted as follow: Let $\phi : \mathbb{N} \to \mathbb{N}^+$ be a function defined  such that: $$\phi(x):= \begin{cases} \frac{x}{2}, & \text{if } x \text{ is even } \\

Online communities are groups of web savvy individuals who share communal interests. A community can be developed with just a single topic or by a bunch of philosophies. A better community binds its members through substantial debates. Mathematics is a very popular communal interest and there are hundreds of online communities formed in both Q&A and debate styles. Some mathematical communities are so immense that they

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 formulas — I think this is exactly what Ramanujan is known

About This post is actually a summary of a research project I took under INSPIRE-SHE Scholarship Program by Dept. of Science and Technology, Govt. of India. My plan was to make the content open-source on the web that faults could be corrected by time. The language is simple and very easy to understand and the ease of understanding is focused on A-level (10+2) students and beyond. Abstract

Ramanujan (1887-1920) discovered some formulas on algebraic nested radicals. This article is based on one of those formulas. The main aim of this article is to discuss and derive them intuitively. Nested radicals have many applications in Number Theory as well as in Numerical Methods . The simple binomial theorem of degree 2 can be written as: $ {(x+a)}^2=x^2+2xa+a^2 \ \ldots (1)$ Replacing $ a$ by

You might be thinking why am I writing about an individual number? Actually, in previous year annual exams, my registration number was 381654729. Which is just an ‘ordinary’ 9-digit long number. I never cared about it- and forgot it after exam results were announced. But today morning, when I opened “Mathematics Today” magazine’s October 2010, page 8; I was brilliantly shocked. 381654729 is a nine digit

Before my college days I used to multiply this way. But as time passed, I learned new things. In a Hindi magazine named “Bhaskar Lakshya”, I read an article in which a columnist ( I can’t remember his name) suggested how to multiply in single line (row). That was a magic to me.  I found doing multiplications this way, very faster – easier and smarter. There may be

Multiplication is probably the most important elementary operation in mathematics; even more important than usual addition. Every math-guy has its own style of multiplying numbers. But have you ever tried multiplicating by this way? Exercise: $ 88 \times 45$ =? Ans: as usual :- 3960 but I got this using a particular way: 88            45 176          22 352           11 704  

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 (x) = \sqrt {1+\sqrt{1+2 \sqrt {1+3 \sqrt {\ldots \sqrt {1+n \sqrt {x} } } } }