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.

So Quadradical Dude!

Lorin seems to think that I'm some kind of math whiz because I've been getting good grades in Calculus, while in reality it's a real struggle for me to understand all of the amazing math that other people have figured out. Through all the formulas and proofs I first try to understand why it works, sometimes I can and sometimes it's beyond me so in those cases I just try to understand how to use it properly so I can get the right answers!

One basic formula that I first learned before I cared about "why it works" is the quadratic formula. I just accepted it at the time and have used it since then. Now that I'm thinking more deeply about such things, I feel a little guilty every time I use it, like I'm copying someone else's homework. Well today I put a stop to the guilt, I decided to derive it without looking at a proof.

I know most of you probably don't care too much about this but Lorin was asking if my blog is about math, no it's not a math blog but I'll do this one post for him. So here it is Lorin, an old favorite and a standard of elementary Algebra: The Quadratic Formula. Use it to impress people at parties!

First factor out the coefficient of the x^2 term, you can immediately eliminate it by dividing both sides by it (for some reason I kept it around till the next step in my work). Then you must do the dreaded "complete the square" technique, I was feeling a little bold today so I did a few steps in my head on this one. Then it's just a matter of isolating x, get rid of the square by taking the square root of both sides (don't forget your plus/minus) and simplify. My circuits teacher recently used the quadratic equation in a different form as noted in the figure, the reason why he likes it is because of the repeated b/2a term. I had never seen it like that before but now I see where it comes from.

going back in time

Jon Stone spearheaded a memorial for Only Anything in the form of a new blog with added mp3 downloads and photo albums. He set it up the framework and then opened it up to the group (band members and close friends) to add content at our liberty. The whole premise is that we just can't let go of the good old days so we are going to relive them by sharing our memories with each other (and whoever else will listen). It came together as planned and is still growing.

Shortly after its conception, a new spark was ignited as Jon Stone saw an upcoming Thanksgiving trip to Arizona as an opportunity to have not only a digital memorial but an actual flesh and blood Only Anything revival. It is not a total flashback as it won't be the original 5 together again with guitars in hand, we have some substitutes lined up. In fact, Jon and I will be the only original members participating but we are doing it in the spirit of old times. Any input from the other members is appreciated.

The events include playing a lot of music (old and new) and getting some recordings of it. In trying to decide what to play we have both picked some old songs and agreed to finish an old song idea and come up with a completely new one. The problem for me is that I have many new song ideas that are promising but all incomplete and time is ticking away. When I told Jon that I was planning on pitching 4 or 5 snippets of song ideas to him he got pretty excited and suggested that we instead raise the bar to do a whole new Only Anything album. Clearly this would be a long term project as we are both doused in schoolwork.

We quickly dismissed this idea as impractical and reverted our focus back to the few songs that we want to do this Thanksgiving. We really try to keep our feet on the ground but as an example of our stubbornness let's look at the new blog and call it what it really is: evidence of our inability to let things go. So, I wouldn't be surprised if in some time down the road there is an announcement of the new Only Anything album (limited release).

Don't hold me to that but feel free to browse www.onlyanything.com to experience music, photos, artwork and other artifacts from the greatest band that ever was. Some of those old songs are better than others, we just put it all out there though. Good or bad, it's history. Eventually we will get some better video up there, I know it exists.

little kid media rocks!

Generally, I don't really like going to the movies. There's a lot out there that I'm not interested in. I find myself enjoying books and movies geared towards a younger audience. I tried reading Love in the time of Cholera because we got it from the library and some people have recommended it, but I hated it and after forcing myself to get half way, I realized I was wasting my time.
I now recommend to you 3 movies that aren't so "mature"; I have watched each one twice and I count none of that time as wasted. So here it goes, 3 movies that you should watch for a good time!

Son of Rambow - Totally liked it. Especially how Will says "Lee Carter". Watch it and you'll see.

Little Manhattan - A 10 year old in love, but it resonates with this 31 year old.

Millions - Good movie, Strange at parts but still refreshingly different. (the band Muse in soundtrack!)

We are complete

It turns out that when I said in the last post "it may have been a dress rehearsal, a week before.." I was pretty much dead on. We were back at the hospital exactly a week later and Sophie came shortly after that!

shuffle

I got a surprise package in the mail, an ipod shuffle. Apparently my friends love me a lot. Jon, John and Mat all went in on it. It is a must have for every cool college student. An ipod wasn't on my wishlist but, as I was setting it up I couldn't get over how something so small could play so many songs. It's my first mp3 player and I can say already that it's going to get a lot of use.
Thanks guys.

the limit of y as t approaches infinity

This time she's not so early, but we still have some time. She just may be a little early yet; not as early as her previous babies but at least we got another ultrasound out of our false alarm trip to the hospital. Baby was probably not much more than 6 pounds as of Friday Sept 5. Contractions every five minutes for about 5 hours doesn't necessarily mean you're in labor. Who knew? It may have been a dress rehearsal a week before the actual debut. As we get closer to the due date, my classes have been getting harder. Physics is attempting to take over my world. The first exams are coming up next week.