A typical post from those 4years – Yeah. You read that right. Lack of conviction might possibly be the worst way to suffer. One of these days I am going to wake up, decide to have coffee and then just have tea instead. Oh the horror! So what do I mean by conviction? faith in […]
So, the previous post of this blog said – “Mathematical Dreams? … Thats just the happier side of it..” And That started off a period of depression/inefficiency/lack of fulfilling work and a revival from the dust to a normal standing – NOW. So. Back. After 4 year hiatus. Lets get this rolling. 🙂
Mathematical Dreams? … Thats just the happier side of it..
The stats helper monkeys at WordPress.com mulled over how this blog did in 2010, and here’s a high level summary of its overall blog health: The Blog-Health-o-Meter™ reads Fresher than ever. Crunchy numbers A helper monkey made this abstract painting, inspired by your stats. A Boeing 747-400 passenger jet can hold 416 passengers. This blog […]
Definition. For and , Then , we define say that is residue of nth-degree modulo m , If there exist integer solutions for – Otherwise, It is non-residue of nth-degree modulo m. For we call it as quadratic, cubic and bi-quadratic residues respectively. Theorem : There are quadratic residues in . Proof : Consider […]
And miles to go before i sleep, And miles to go before i sleep … .. .. ..
The Area Way Incases , where a relation with areas is possible, It is quite efficient to use it to solve the problem. Example – If are the altitudes of a triangle from A,B,C to the opposite sides and r is the inradius. Prove that – 1. 2. Proof Let I be the incentre. Note […]
With the on-going trend, Algebraic Inequalities are almost erasing the existence of Geometrical Inequalities . Nevertheless, They are equally beautiful (if not more) , although they seem a lot harder to me. Yes, they can mostly be proved by brute-force trigononmetry or complex (whatever it is , they are equally good solutions) , but I […]
Man, i just found out about Loreena Mckennit . She is such a brilliant singer !!!! no more words to describe.. this says it all – http://www.youtube.com/watch?v=S2CFM4ev-g8
Problem Prove that – P.S. It is straightforward holder, but what about a solution by Cauchy or AM-GM ? Solution By, AM-GM we have , Write up analogous inequalities, and add to get – which re-arranges to the desired question 🙂
Ram
Mathematical Dreams 