Mathematics

The late Shri P. K. Srinivasan had developed an approach to the teaching of algebra titled ‘Algebra – a language of patterns and designs’. I have used it for several years at the Class 6 level and found it to be very useful in making a smooth introduction to algebra, to the idea and usage of concepts such as variable and constant, to performing operations involving terms and expressions. This approach steadily progresses from studying numerical patterns to line and 2-D designs, finally leading to indices and identities.

This is a review of the book “Beautiful, Simple, Exact, Crazy” written by Apoorva Khare and Anna Lachowska. The authors write in the preface that this book arose out of an introductory course called Mathematics in the Real World which they co-designed (and taught at Stanford and Yale University, respectively). The target audience of that course consisted mainly of undergraduates of humanities and social sciences – students whose principal interests lay outside of mathematics and the sciences.

This is a 13 minute story set in a village of natural numbers. A thief appears and is clearly not a natural number. It turns out that he is a (positive) rational number. Since all the characters (and hence the numbers) are positive, it is fair to say that this video is about natural numbers and fractions and their relation! The part-whole model is invoked and is used to define a (positive) rational number, explain equivalent fractions and that any natural number is also a rational number.

LinkedIn reader Peter Lovasz asks: Among all triangles that share a given circle as incircle, which one has the smallest perimeter?

Some problems for the Senior School...

In this edition of ‘Adventures’ we study a few miscellaneous problems, some from past RMOs. As usual, we pose the problems first and give the solutions later in the article, thereby giving you an opportunity to work on the problems.

ne of the scarier words in a math student’s lexicon is the word locus! The definition (A path traced by a point when it moves under certain condition) seems amorphous, difficult to pin down and much too open-ended! This topic is usually introduced in high school; we are deliberately presenting problems on locus which will give students a gentler introduction to the same.

The topic of Cellular Automata lends itself to interesting investigations which are well within the reach of high school students. As we hope to illustrate in this article, the ideas are simple and yet powerful. We shall describe briefly our attempts to investigate this unique and interesting topic.

A recent paper by Bizony (2017) discussed the interesting golden ratio properties of a Kepler triangle, defined as a right-angled triangle with its sides in geometric progression in the ratio 1 : √φ : φ, where φ =  (1 + √5)/2

In this episode of "How To Prove It" we study a number of possible characterizations of a parallelogram...

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