Archive for December, 2007

Reading some of the Lev Kourliandtchik books, I’ve found a tricky observation how to write this gigantic expression in an extremely simple, with number of square roots. It’s easy to checkĀ that and using that equality we have cool, huh? šŸ™‚ Advertisements


For , we do have \ Trigonometrics


Suppose that we have a grounded sphere made from a conductor and an electron far from the sphere. Let the radius of the sphere be and the beginning speed of the electron be orientated on the line in distance of from the center of the sphere. The smallest distance between electron and the center of […]


Reading R. Resnick – D. Haliday thermodynamics, I’ve found something well known me although it’s making me wonder every single time when I think about it. It’s the derivation of the thermodynamics law that goes like this: From first law of thermodynamics , but in the adiabatic process we have and instead of we put […]


The solutions can be found here http://www.om.edu.pl/zadania/om/om59_1r.pdf My solution for task number 9 is here: Solution for numberĀ 9


Lets calculate more compilated sum further, the last one equals to and now the first of the sums is equal to however the second one is easy, cause its a geometric sequence equal to under the law from previous post. Now we have , in the result of elementary algebraic transformation we recieve It’s easy […]


Asume that we want to calculate Of course, But the sum on the right side is equal to Therefore and so,


I sold my old N95 and I bought N95 8GB – Ninja as some say šŸ™‚ I haven’t written any review yet, but this phone is totally awesome. It takes everything to another dimension, although there are a few things that should be fixed. Here some of my +/- + Bigger screen great for watching […]


Experimental problemĀ 2 Experimental problemĀ 3 Theoretical problemĀ 1 Theoretical problemĀ 2 Theoretical problemĀ 3 Problems from Poland 59 MO 2007/2008 I level/II set. Problem 5 Problem 6 Problem 7Ā  Problem 8