# Category Math

## A Problem (and Solution) from Bhaskaracharya’s Lilavati

I was reading a book on ancient mathematics problems from Indian mathematicians. Here I wish to share one problem from Bhaskaracharya‘s famous creation Lilavati. Problem A beautiful maiden , with beaming eyes, asks of which is the number that multiplied by 3 , then increased by three-fourths of the product, divided by 7, diminished by one-third of the quotient, multiplied…

## On World Math Day – Do A Simple Self-Test to Identify a Creative Mathematician in You

There are many mathematicians, chemists, musicians, painters & biologists among us. But they are unaware of their qualities. Only some small suggestive strokes are needed for them. Unless one tells them, they will not know how great they are. Here is a small self test. Do you enjoy music, drums and dance? Do you enjoy looking at the flowers, carpets,…

## The Collatz Conjecture : Unsolved but Useless

The Collatz Conjecture is one of the Unsolved problems in mathematics, especially in Number Theory. The Collatz Conjecture is also termed as 3n+1 conjecture, Ulam Conjecture, Kakutani’s Problem, Thwaites Conjecture, Hasse’s Algorithm, Syracuse Problem. Statement: Start with any positive integer. • Halve it, if it is even. Or • triple it and add 1, if it is odd. If you…

## Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem

Topic Beta & Gamma functions Statement of Dirichlet’s Theorem $\int \int \int_{V} x^{l-1} y^{m-1} z^{n-1} dx dy ,dz = \frac { \Gamma {(l)} \Gamma {(m)} \Gamma {(n)} }{ \Gamma{(l+m+n+1)} }$ , where V is the region given by $x \ge 0 y \ge 0 z \ge 0 x+y+z \le 1$ . Brief Theory on Gamma and…

## The Mystery of the Missing Money – One Rupee

Puzzle Two women were selling marbles in the market place — one at three for a Rupee and other at two for a Rupee. One day both of then were obliged to return home when each had thirty marbles unsold. They put together the two lots of marbles and handing them over to a friend asked her to sell then…

## Understanding Poincare Conjecture

In 1904, the french Mathematician Henri Poincaré (en-US: Henri Poincare) posed an epoch-making question, which later came to be termed as Poincare Conjecture, in one of his papers, which asked: If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere? Henri Poincare – 1904 So what does it really mean? How can a regular math reader…

## Largest Prime Numbers

What is a Prime Number? An integer, say $p$ , [ $\ne {0}$ & $\ne { \pm{1}}$ ] is said to be a prime integer iff its only factors (or divisors) are $\pm{1}$ & $\pm{p}$ . As? Few easy examples are: $\pm{2}, \pm{3}, \pm{5}, \pm{7}, \pm{11}, \pm{13}$ …….etc.…

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

## What is Real Analysis?

Real analysis is the branch of Mathematics in which we study the development on the set of real numbers. We reach on real numbers through a series of successive extensions and generalizations starting from the natural numbers. In fact, starting from the set of natural numbers we pass on successively to the set of integers, the set of rational numbers…