by Ashani Dasgupta

Cyclic Quadrilaterals are often important objects in a Geometry problem. Recognizing them can lead to a path to the solution. A case in point is this problem from Pre RMO 2017. How to recognize cyclic quadrilaterals? Opposite angles add up to \( \pi \) Two angles...
by Ashani Dasgupta

Geometry is perhaps the most important topic in mathematics as far as Math Olympiad and I.S.I. Entrance goes. The following list of results may work as an elementary set of tools for handling some geometry problems. ‘Learning’ them won’t do any good....
by Ashani Dasgupta

Advanced Mathematics Seminar 2 hours An Open seminar for Pre-RMO and I.S.I. Entrance 2019 aspirants. We will work on topics from Number Theory, Geometry and Algebra. Registration is free. There are only 25 seats available. Date: 29th June, Friday, 6 PM Online...
by Ashani Dasgupta

If a function is 'nice' (!), then for every secant line, there is a parallel tangent line! This is the intuition behind the Mean Value Theorem from Differentiable Calculus. The fifth problem from I.S.I. B.Stat and B.Math Entrance 2018, has a clever application of this...
by Ashani Dasgupta

The Problem Let \(f:(0,\infty)\to\mathbb{R}\) be a continuous function such that for all \(x\in(0,\infty)\), $$f(2x)=f(x)$$Show that the function \(g\) defined by the equation $$g(x)=\int_{x}^{2x} f(t)\frac{dt}{t}~~\text{for}~x>0$$is a constant function. Key Ideas One...