F or those who don’t know him, Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University in the US. He is a passionate educator who spends considerable time and energy trying to communicate the intricacies of mathematics to the lay audience.


Pose these problems to the Senior School students...

The Pythagorean equation x^2 + y^2 = z^2 (to be solved over the positive integers N) is a much-studied one; many articles have appeared in this magazine alone, devoted to this equation. A close relative to this is the equation 1/x + 1/y = 1/z (which can be written as x^−1 + y^−1 = z^−1 ; in this form, its similarity to the Pythagorean equation is readily seen), and this too has been studied many times in At Right Angles.

On the Facebook page (AtRiUM: At Right Angles, Us and Math) linked to this magazine, one of our contributors, Arsalan Wares, has been astonishingly prolific in posting problems. A good many of these have had to do with regular hexagons; more specifically, with the areas of polygonal regions drawn within such hexagons. It is both astonishing and pleasing to see such a rich diversity of problems arising from this simple and familiar structure.

The history of Mathematical Olympiad (MO) activity in India is not available anywhere. Hence, while recording this history, we also mention the people who initiated and nurtured this activity. However, before we talk about it, we first highlight a few aspects of the International Mathematical Olympiad (IMO).

In this edition of ‘Adventures’ we study a few miscellaneous problems, mostly from the Pre-Regional Mathematics Olympiad (PRMO; this year’s PRMO was conducted on August 19 in centres all over the country). As usual, we pose the problems first and present solutions later.

The Pigeonhole Principle (PHP) or the Dirichlet Principle is perhaps the easiest theorem that exists in all of Mathematics. It states that if n + 1 pigeons are put into n pigeonholes, then there is at least one pigeonhole with more than one pigeon. The proof is as easy as the statement.

Factors and multiples, tables and long division – students who are relieved at mastering these in numbers are confounded when the same topics rear their head in algebra. Here is a nice collection of problems that allow students to play with algebraic expressions and study them through the lens of divisibility.

For the middle school student, the transition from arithmetic to algebra is often quite daunting. In grade VI, the concept of a ‘variable’ is encountered for the first time. This is the stage where either a child embraces the newly introduced ‘Algebra’ or gets overwhelmed with the idea of numbers being replaced by letters of the alphabet. This is also the stage where the students learn to solve equations and find the value(s) of the unknown(s).


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