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.
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]
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.
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.
