The Strongest Matthew For Whenever Options

[Dr Strum]

Back for it's third iteration, and still longer than any other.
You know what to do. Just post about stuff. Your life, your insanity, or even your favorite cardinal direction.

[Elnendil]

I'll be picking it up later, but after finding out a few things, I decided to finish up this half semester of this german intensive course and drop the second half. My semester is pretty heavy, and i'm in courses in which a lot of concepts are very new to me, and German isn't my major. It'll be something to consider, obviously, if I want to get a Ph.D, but right now I need to focus on whats important. Doesn't mean i'll slack off though, I want to pass the class with a grade that is as high as it possibly can be. It'll last until next week, after that things will be more relaxed. I've barely gotten any sleep, the only thing i'm running on is being entertained, be it listening to upbeat music in the morning like its my coffee or making mathematical observations.

Aside from that, things are starting to get better all round. Discussed some observation I made with my professor after class, got a slight refresher on Trigonometry too, because its one of my weak points. Next week i'll be catching up on my math homework so i'll understand all of these concepts better.

Oh. Yeah. Actually, the definition of divisible is that:
a|b iff \exists q s.t. b = aq.

Yep. If a|b, there has to be some integer q that, when multiplied by a, equals b. I've been throwing some other concept around recently, has to do with using arithmetic to find square roots. This isn't a theorem, just a plausible observation:

q=lim(x->1+) sqrt(b)/x

When solving, it makes sense in a way that well, if x=1, then q=sqrt(b). But the observation is that you can get an approximation if q is an integer, when sqrt(b)/x and x approaches 1 from the right. Like how sqrt(33)=5.744... So there is some sqrt(x) that you can multiply into 5 that will equal sqrt(33) [5*sqrt(x)=sqrt(33)]. Then I divided both sides by sqrt(x), and I noticed that every time I pulled out a new decimal place, sqrt(x) approached 1 from the right, hence the observation. I showed this to the professor and he mentioned some other theorem...Newtons...gah, I forget the name. Its in my calculus book, i'll look into it later; has to deal with constantly finding approximations to find roots. I'll also say from observation that 1<=x<2 and q is the greatest integer of the root. Anyways, what do you think Rai?

This post has been edited by Elnendil: Oct 7 2010, 08:02 PM