30 January 2007 - My little corner of reality (original) (raw)

Teaching and useless skills

Jan. 30th, 2007 | 12:19 pm

mood: accomplished
location: work

So last night, as we were finishing up a TA meeting for a lab class for which I am middle management, one of the TAs noticed that the filing cabinet with the labs in it was locked, and none of us had a key for it. It needed to be open, and everybody who might have a key was gone for the day.

So I resorted to going out to the street, and finding a street sweeper bristle, and making a set of lockpicks to open the lock. Never mind that I haven't picked a lock since I was in college. And I'll be damned to say it, but it only took around 20 seconds to open that lock!

*buffs fingernails*

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Pythagarus, and odd number addition

Jan. 30th, 2007 | 12:40 pm

location: still work
mood: geeky

Kathryn reminded me a few weeks ago about a simple fact: the sum of the first n odd numbers is n2, but then she said she didn't have a good proof for it.

So I gave her two, one recursive, and one based on sum equations. The recursive one is nice; it points out the relationship between the binomial distribution and perfect squares. Hell, here it is.

For n=1, it's obvious.

Assume true for n. (Note, the nth odd number is 2n-1.)

Show it's true for (n+1): (n+1)2 =? n2 + 2n - 1 + 2 = n2 + 2n + 1, which checks out. Cool.

Pythagoras came into the discussion when I pointed out that 2n+1 can also be a perfect square. so you get a set of Pythagorean triples whenever it is. So 3,4,5 comes out, as does 5,12,13; hell, an infinite number do, since there's infinitely many odd squares.