## Tuesday, December 30, 2008

### 50 State Quarters

We started collecting the commemorative state quarters quite a while ago and just before Christmas I got the last one we were waiting for, Alaska. When Arizona's was introduced this past summer we took the family to the state capitol building where Janet Napolitano spoke and then representatives from the mint passed out shiny new AZ quarters to all the kids. Then they gave out free mint ice cream drumsticks for everybody. We then walked through the free museum that is a permanent fixture of the capitol building, it was a good activity.

So here is our collection (worth at least \$12.50)

## Thursday, December 18, 2008

### Clare and the Reasons

Went to a show with Jon Stone over Thanksgiving and while I really enjoyed the headliner: My Brightest Diamond, for their inventive music I'm a real sucker for a poppy song so I also really liked Clare and the Reasons, the openers. Found this video posted on their myspace site and thought some of you would appreciate this classic 80's cover.

## 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.