# Class 11-12

## Inequalities in Algebra & Geometry part 3

This article is the third in the ‘Inequalities’ series. In this part, we explore the validity and application of the AM-GM inequality for three numbers and four numbers respectively.

## Problems for the Senior School

Challenge your senior school students with these problems.

## Harmonic Triangular Triples

An article on Harmonic Triangular Triples

## Napolean's Theorem part 2

In an earlier issue of At Right Angles, we had studied a gem of Euclidean geometry called Napoleon's Theorem, a result discovered in post-revolution France. We had offered proofs of the theorem that were computational in nature, based on trigonometry and complex numbers. We continue our study of the theorem in this article, and offer proofs that are more geometric in nature; they make extremely effective use of the geometry of rotations

## There are Infinitely many Prime Numbers

Some theorems, it seems, are evergreen. New proofs keep turning up for them. One such is the theorem of Pythagoras (the current number of proofs stands at over 300). Another is the claim that the square root of 2 is irrational. A third example is the statement that there exist infinitely many prime numbers. This is the one on which we will dwell in this short article.

## Tonic Ambiguity

It has been found (right from Pythagorean times) that the frequency of the tonic and the frequencies of the rest of the tones and semi-tones form a simple ratio. A particular musical tone always has the same frequency ratio relationship with the tonic. The western solfege syllables corresponding to Sa, Ri, Ga, Ma, Pa, Dha, Ni are Do, Re, Mi, Fa, So, La, Ti respectively.

## The Exponential Series an Addendum

Here, we depict the same steps that of the article graphically and present the material in a different way. This article may thus be regarded as an addendum to it.

## How to discover the exponential function ex

If a function is such that its derivative is the function itself, then what would it be? Some interesting mathematical objects appear while trying to answer this question, including a power series, the irrational number e and the exponential function ex. The article ends with a beautiful formula that connects e, π, the complex number i = $\sqrt{\mathrm{-1}}$, 1 and 0

## Teaching Concepts of Calculus

The topic of calculus is an integral part of the senior secondary mathematics curriculum. The concepts of limits and derivatives, which form the foundation of Calculus, are often hard to teach. In this article, we suggest a dynamic way of teaching the concept of the derivative through practical examples which may be easily explored through GeoGebra applets available through the Internet.

## A Review of G H Hardy's A Mathematician's Apology

I shall ask, then, why is it really worth while to make a serious study of mathematics? What is the proper justification of a mathematician’s life?

G H Hardy tries to answer that question in this classic book he wrote some 70 years ago. Here's a review of it.

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