Mathematics

The topic of ‘Equations’ can be approached in several ways. The choice of approach has a strong impact on the conceptual image which a student builds about a given concept. Hence, the choice is crucial in helping a student in understanding the concept as well as in developing the procedure for solving the problems. However, every approach has its limitations and can be used only for solving certain types of problems. Its use is limited and it may become necessary to expose students to other approaches when the type or complexity of the problems alters.

It was during lunch on a pleasant day that I was told about this popular book on Mathematics called “Mathematician’s Delight.” I was chatting with a professor who said that his choice to become a mathematician was influenced by this book. The story went like this: When the professor was a teenager, just after high school, during the summer vacation, he found this book and wanted to give it a try. He could follow most of it without much difficulty, and solved most of the exercises which led him to ‘experiment’ with mathematical ideas on his own.

Some problems for the Senior School.

We know that Pythagorean triples are infinite in number, and the most common formula for generating triples is to take two relatively prime odd numbers s and t, where s > t ≥ 1, and produce the triple (st, (s²−t²)/2 , (s²+t²)/2 ). However, can we generate all possible triples from just one triple? Can we generate infinitely many triples from just one triple? These might be questions worth investigating.

There is another class of semi-regular 3D shapes - the Archimedian solids. In these the faces are again regular polygons but they are not all congruent, i.e. they differ in the number of sides. One such Archimedian solid is the truncated  icosahedron.