A Construction Comes in Handy

One of my friends shared a geometry problem with me, already quite despondent after having tried it for long. The problem statement was : In the square below,  . Prove that . Unsurprisingly, I spent the first twenty minutes applying trigonometry and classical geometry to solve the problem. However, when the size of the calculations…

Number Theory : The Queen of Mathematics

The Prince of Mathematics, Carl Friedrich Gauss once famously said : Mathematics is the Queen of the Sciences and Number theory is the Queen of Mathematics. This statement though highly debatable, does find resonance in many of the great mathematicians of both the past and the present (and most probably this will be true of…