### A familiar Functional Equation

Cauchy’s functional equations are very simple. The most familiar one has a simple formula: f(x + y) = f(x) + …

Cauchy’s functional equations are very simple. The most familiar one has a simple formula: f(x + y) = f(x) + …

An Application of Cauchy’s Functional Equation Cauchy’s functional equation is a description of a function. $$ f(x + y) = …

In the given figure, \(ABCD\) is a square sheet of paper. It is folded along \(E F\) such that \(A\) …

Let \(ABC\) be triangle in which \(AB=AC\). Suppose the orthocentre of the triangle lies on the incircle. Find the ratio …

It is almost like deflating a balloon. But the effect is exponential. Today (29th January 2018, Monday), we have a …

Let ABC be a non-equilateral triangle with integer sides. Let D and E be respectively the mid-points BC and C …

The most beautiful equation in mathematics is: It is often attributed to Swiss Mathematician Leonhard Euler. Interestingly enough, …

We have indicated the source of these problems. Do not look up solutions. It is fun to try it yourself …

Sine of an angle, half chord and vertical projection Note that half chord corresponding to a half arc is same …

PROBLEM Suppose the earth is a perfect sphere. You are on its surface at point A. First, you walk 1 …