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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…
What Happens If We Drop a Ball Through a Tunnel in the Earth? Imagine creating a tunnel straight through the Earth and dropping a ball or any other object into it. How would gravity affect the ball, and would it emerge on the other side? If so, how long would it take? Tunnel through the…
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…
Ensembles in Chemical Sciences and Statistical Physics are a collection of a number of macroscopically identical but essentially independent systems. The System, here, is defined by the collection of a large number of particles and the term macroscopically identical means that each of the systems constituting an ensemble satisfies the same macroscopic conditions, like Volume,…
About This post is actually a summary of a research project I took under INSPIRE-SHE Scholarship Program by the 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…
“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 definition…
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 same is true for a geometric circle. The difference between a disk and a circle lies in dimensions, as the disk is a two-dimensional object and…
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$…
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…
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…
An old yet beautiful untabled listing of highly interactive mathematics related articles and papers available online.
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:
