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Speaker: B V Rajarama Bhat, Professor, Indian Statistical Institute, Bangalore

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Abstract:  Here is a simple puzzle: Start with a rectangular  3cm x 5cm piece of paper. Cut it down into smaller rectangular pieces and re-arrange to have a square of size 4cm x  4cm. Without wasting any paper, a little bit of thought should tell you that this is impossible as the original area is 15 cm^2  and any rearrangement would have the same area whereas we are asked to get a square of area 16 cm^2.    Here  `area’  is an  `invariant’.  It is an obstruction to realize the transformation asked for. The notion of invariants is widely used in mathematics to classify objects and to detect obstructions in transforming systems from one state to another. It also has many practical applications. In this talk, we will describe the concept of invariants through various puzzles and some mathematical problems.

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