Math

All mathematics articles on Gaurav Tiwari.

Interesting Articles and Must Read Papers in Math

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 accurate in 1582 ,—as a correction to earlier Julian Calendar. Julian

Equations- A Basic Introduction

Applied mathematics is one which is used in day-to-day life, in solving troubles (problems) or in business purposes. Let me write an example: George had some money. He gave 14 Dollars to Matthew. Now he has 27 dollars. How much money had he? If you are familiar with day-to-day calculations – you must say that George had 41 dollars, and since he had 41, gave 14

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 nature are called Countable Numbers and the numbers which can not be counted are called Uncountable

Mathematical Logic – The basic introduction

What is Logic? If mathematics is regarded as a language, then logic is its grammar. In other words, logical precision has the same importance in mathematics as grammatical accuracy in a language. As linguistic grammar has sentences, statements— logic has them too. After we discuss about Sentence & Statements, we will proceed to further logical theories . Sentences & Statements A sentence is a collection of

Fermat Numbers

Fermat Numbers, a class of numbers, are the integers of the form $F_n=2^{2^n} +1 \ \ n \ge 0$ . For example: Putting $n := 0,1,2 \ldots$ in $F_n=2^{2^n}$ we get $F_0=3$ , $F_1=5$ , $F_2=17$ , $F_3=257$ etc. Fermat observed that all the integers $F_0, F_1, F_2, F_3, \ldots$ were prime numbers and announced that $F_n$

Three Children, Two Friends and One Mathematical Puzzle

Two close friends, Robert and Thomas, met again after a gap of several years. Robert Said: I am now married and have three children. Thomas Said: That’s great! How old they are? Robert: Thomas! Guess it yourself with some clues provided by me. The product of the ages of my children is 36. Thomas: Hmm… Not so helpful clue. Can you please give one more? Robert:

381654729 : An Interesting Number Happened To Me Today

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

Social Networks for Math Majors

Math or Mathematics is not as difficult as it is thought to be. Mathematical Patterns, Structures, Geometry and its use in everyday life make it beautiful. ‘Math majors’ term generally include Math students, Math professors and researchers or Mathematicians. Internet has always been a tonic for learners and whole internet is supposed to be a social network, in which one shares and others read, one asks

Do you multiply this way!

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

Just another way to Multiply

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

How Genius You Are?

Let have a Test: You need to make a calculation. Please do neither use a calculator nor a paper. Calculate everything “in your brain”. Take 1000 and add 40. Now, add another 1000. Now add 30. Now, add 1000 again. Add 20. And add 1000 again. And an additional 10. So, You Got The RESULT!  Quicker you see the answer, sharper you are!

A Problem On Several Triangles

A triangle $T$ is divided into smaller triangles such that any two of the smaller triangles either have no point in common, or have a vertex in common, or actually have an edge in common. Thus no two smaller triangles touch along part of an edge of them. For an illustration let me denote the three vertices of T by 1, 2 and 3.

Two Interesting Math Problems

Problem1: Smallest Autobiographical Number: A number with ten digits or less is called autobiographical if its first digit (from the left) indicates the number of zeros it contains,the second digit the number of ones, third digit number of twos and so on. For example: 42101000 is autobiographical. Find, with explanation, the smallest autobiographical number. Solution of Problem 1 Problem 2: Fit Rectangle: A rectangle has dimensions

How many apples did each automattician eat?

Four friends Matt, James, Ian and Barry, who all knew each other from being members of the Automattic, called Automatticians, sat around a table that had a dish with 11 apples in it. The chat was intense, and they ended up eating all the apples. Everybody had at least one apple, and everyone know that fact, and each automattician knew the number of apples he ate.

Fox-Rabbit Chase Problem [Solution & Math Proof]

Part I: A fox chases a rabbit. Both run at the same speed $v$ . At all times, the fox runs directly toward the instantaneous position of the rabbit , and the rabbit runs at an angle $\alpha$ relative to the direction directly away from the fox. The initial separation between the fox and the rabbit is $l$ . When and where

Everywhere Continuous Non-differentiable Function

Weierstrass had drawn attention to the fact that there exist functions which are continuous for every value of $x$ but do not possess a derivative for any value. We now consider the celebrated function given by Weierstrass to show this fact. It will be shown that if \$ f(x)= \displaystyle{\sum_{n=0}^{\infty} } b^n \cos (a^n \pi x) \ \ldots (1) \ = \cos \pi x +b