Category Archives: Study Notes

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 […]

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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$ , $ […]

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On Ramanujan's Nested Radicals

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 […]

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Calendar Formula: Finding the Week-days

This is the last month of the glorious prime year 2011. We are all set to welcome upcoming 2012, which is not a prime but a leap year. Calendars have very decent stories and since this blog is based on […]

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Equations- A Basic Introduction

Applied mathematics is one which is used in day-to-day life, in solving tensions (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 […]

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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 […]

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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 […]

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Fermat Numbers

Fermat Number, a class of numbers, is an integer 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$ , […]

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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 […]

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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 […]

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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$ =? […]

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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 […]

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