It’s been a while since the last update. Here’s a small update on what I’m thinking about various stuff.
Prototype
Gameplay is okay I guess. Nothing I would spent too much time on though. It looks a lot worse than GTA 4 though (same as Crackdown).
Resident Evil
Seems to be lots of fun and some nice graphics, too.
Red Faction: Guerrilla
Some weird texture filtering issues and the presentation doesn’t knock off my chair (terrain popping and other ugliness), but multiplayer is loads of fun with friends. Physics isn’t completely stable though. I played the game for one hour in MP with friends and there were quite a few cases where geometry dropped through the floor with enough pressure from above (after destroying a building).
Brüno
A bad and quite stupid movie (Ali G in Da House is probably the only movie I kinda like that stars Cohen). If you haven’t watched it already, don’t >_<
Shadow Complex
I bought shadow complex a few weeks ago and I have to say that it is an awesome game. I read somewhere that the developer used the Metroid series as inspiration and it shows. It’s really fun to play and quite addictive. The graphics are pretty awesome (it is using the Unreal 3 engine) and the whole presentation is pretty polished. It certainly is worth its 1200 gamerpoints
Summing Formulas
A month ago I was doing some exercises in an analysis book (Königsberger) and found a nice/interesting problem:
Prove that if we denote of the sum of the numbers 1 to n to the p-th power by \[ S_n^p = 1^p + 2^p + ... + n^p \], then the following equation by Pascal holds: \[ (p+1) S_n^p + \binom{ p + 1 }{ 2 } S_n^{p-1} + \binom{ p + 1 }{ 3 } S_n^{p-2} + ... + S_n^0 = (n+1)^{p+1} - 1 \]
It can be used to get recursively/iteratively get formulas for sums of higher powers of numbers.
This is interesting because the proof doesn’t need any advanced maths (like eg the Euler-MacLaurin formula, which can be used to show this, too).
You can download the proof and a few examples here.
Cheers