Wednesday, December 10, 2008

Pythagorean Theorem

For ASU students today is reading day, a day between the last day of class and the first day of finals. At UofA I think they call it dead day, maybe because you're dead if you haven't studied for finals yet. It turns out that I'm going to school anyway for a test review session but before I get myself lost in cramming I wanted to write out the Pythagorean Theorem proof I promised. This one will be much more coherent than my last post.

I did it in two parts, part 2 is the only part that is necessary but I wrote out part 1 anyway in case you wanted to follow my whole train of thought as I was on the bus trying to prove to myself that 'c' squared really does equal 'a' squared plus 'b' squared.

You might also notice that the distance formula d = sqrt[(y_2-y_1)^2+(x_2-x_1)^2] is essentially the same thing as the Pythagorean Theorem. It comes up again and again, the 3D version is d = sqrt[(y_2-y_1)^2+(x_2-x_1)^2+(z_2-z_1)^2]

We sometimes speak of magnitutes of vectors and really it's the Pythagorean Theorem again.
Useful stuff.
Now I've got to get back to Laplace transformations, which are also very useful however I won't be giving you a proof any time soon! If you need help with math you should check out Paul's Online Math Notes, a very good resource for Algebra, Trig, Calculus and Differential Equations.


Anne said...

Interesting -- today was our last day of classes. Dead day is tomorrow (it is officially called Reading Day here too, but I've never heard anyone say that). I wonder if it's called that because the buildings feel dead inside with no students rushing to their classes. I suppose the campus will be relatively dead, but I'm sure the library will be hopping.

Bev said...

Jon Thwaits,
What you are doing is Hyroglifics to me!
You are truly one amazing person! You use BOTH sides of your brain so efficiently, when I can barely use one! I am truly impressed!
Good luck with finals, but with you it will be skills, not luck!