Perigal's dissection proof of the Pythagorean theorem

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Shown here is the famous dissection proof of the Pythagorean theorem by Henry Perigal.

It can be shown in animation form, and that is what we have done here. Please click on the link given below and follow the instructions.

Perigal's dynamic proof of the Pythagorean theorem

For some biographical details of Henry Perigal, it is best to look at the Wikipedia link: Henry Perigal

RMO 2016 – a few solutions

The Regional Mathematics Olympiad 2016 was held on October 9. The format followed was the usual one; it was a 3 hour paper, with 6 problems from the usual Olympiad topics: Algebra, Number Theory, Euclidean geometry, Combinatorics.

The problem in geometry was particularly challenging, though I think it was inaccurately framed.

Anyway, here are the solutions to four of the problems (problems 3, 4, 5 and 6). Do have a look!

Click on this link: solutions to some RMO 2016 problems

Problem concerning a rational number

Here's an interesting problem from number theory.

Which positive rational numbers have the property that the sum of the number and its reciprocal is an integer?

A little bit of experimentation will probably lead you to the answer. But it would be interesting to find one's own proof for that answer.

I have written up my analysis of the problem in the following PDF file: Problem about a rational number.

Do have a look at it. Your comments would be very welcome.