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Outstanding problems, discussion and more

## I.S.I Entrance Solution – locus of a moving point

This is an I.S.I. Entrance Solution Problem: P is a variable point on a circle C and Q is a fixed point on the outside of C. R is a point in PQ dividing it in the ratio p:q, where p> 0 and q > 0 are fixed. Then the locus of R is (A) a circle; (B) an ellipse; (C) a...

## Why is it interesting to laminate a genus-2 surface?

Take a two holed torus. Draw some geodesics (simple, closed). You have found a lamination! But there is something deep going on, in the veil of this apparantly innocent exercise. Find out more.

## RMO 2018 Problems, Solutions

This post contains RMO 2018 solutions, problems, and discussions. Let $$ABC$$ be a triangle with integer sides in which $$AB < AC$$. Let the tangent to the circumcircle of triangle $$ABC$$ at $$A$$ intersect the line $$BC$$ at $$D$$. Suppose $$AD$$ is also an integer....

## Cheenta and Singapore Method – creating Mathematicians of the future

Recently, French mathematician Cedric Villani’s team came up with ’21 measures for the teaching of Mathematics’. I read through the report, with great curiosity. I happily noted that Cheenta’s Thousand Flowers program has already implemented some of his recommendations.

## Pythagoras Extended! – RMO 2008 Problem 6

Pythagoras theorem can be extended! What happens if the triangle is obtuse-angled (instead of right-angled?) We explore the idea by using a problem from Math Olympiad.