Pegs and Holes, Part II

I was going to go and prove this whole thing formally (in a way that would make Dr. Viswanath Ramakrishna -- my multivariable calculus professor at UTD whose IQ was probably in the quadruple digits -- proud), but I'm lazy. So I'll do the abbreviated version:

First, you know that the areas of the square and the circle are equal, so you know x² = π * r² are equal (where x is the length of any side of the square and r is the radius of the circle). Now you have a way to relate x with r.

Second, assume that the circle and square have the same center.

So to prove that a square peg can't fit in a round hole, you have to show that the distance from the center of the square to one of its corners is always greater than the radius of the circle. (You can do this because of our first assumption, from which you can relate x with r.) This makes sense because the corner is that stubborn part of the square that wouldn't fit into the round hole.

Likewise, to show that the round peg won't fit in the square hole, you need to show that the distance from the center of the square to the midpoint of one of its sides (so that it forms a right angle) is always less than the radius of the circle. Again, this makes sense because that's the stubborn part of the circle that wouldn't fit into the square hole.

So there you have it. Eat it, Co-Worker #1. :) Add some equations, inequalities, the Pythagorean theorem, and some fancy diagrams to the above paragraphs and you have the type of thing you would need on every (and I mean every) homework assignment I had in those college mathematics courses. It got old, let me tell you, but this type of thing is fun to think about on the rare occasion, especially for an over-analytical mind like mine.

(NOTE: for another, perhaps more interesting glimpse into the world of mathematics, see my earlier post on Pascal's triangle.)

Pegs and Holes, Part I

WARNING: If you have any shred of doubt left that I, Josh Allen, am not a dork, please discontinue reading my blog immediately.

As I so often do in order to spice up the work day a bit, I had a little debate with my co-workers earlier today. As we were defining a problem with a software application we're developing, I uttered one of those archaic idioms common to the English language: "It's like trying to fit a round peg in a square hole." My co-worker responded, "You mean 'a square peg in a round hole.'" It went on like this for a little bit... I could've sworn the former was the customary way to express this adage.

But, no, it didn't stop there. He told me authoritatively, "But you can fit a round peg in a square hole!" To which those nerdy-sounding alarm bells related to the part of my brain that made me become a math minor rang resoundingly. I repudiated that falsehood (or at least what I was moderately confident was a falsehood), and we consluted Co-Worker #2. He sort of agreed with both of us, not really able to decide.

But we dissected the situation even further. I insisted that, given the appropriate size, you could in fact fit a round peg into a square hole (if the peg is much smaller than the hole), and vice-versa. But, if they were the same size, you couldn't fit a round peg into a square hole OR a square peg into a round hole. So actually, I proclaimed, the idiom has the same meaning in both of its variations. Co-Worker #1 stubbornly maintained that, even if the peg and hole are the same size, the round peg would fit.

We left the topic alone for the day (argh, finally!), because we actually had lots of other important things to do (like, oh, a little 30-page business plan complete with scientific rationale of our product, etc., etc., all due at 5pm Tuesday). But, like a good little math minor, I did find out the answer AND proved it. My question to you (assuming you haven't collapsed in utter boredom or left for something more interesting like, say, C-SPAN 3): Who's right? Solution tomorrow.

Bravo

Especially starting at the 3:45 mark:

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Karma

I heard about this on NPR: Wall Street swindler, Ponzi schemer, and enemy-of-the-people Bernie Madoff was a source of good fortune for at least 501 lucky lottery contestants. His prison registration number contained the winning lottery numbers the Sunday after Madoff's guilty plea.

Click here for the full article.

I Don't Know Who the GrooGrux King Is, But...

Barely 4 weeks until the Dave Matthews Band dominates the stage here in Dallas, and barely 2 months until their new VERY highly anticipated album, Big Whiskey and the GrooGrux King (best album title ever), hits your friendly local record store, almost FOUR YEARS after their last studio release, Stand Up. Finally, they realized all those live albums -- while each one a gem, I'm sure -- does not count as new material.

Yes, there's lots of things for us Dave-heads to get excited about. Including a re-design of their website, which is entirely Flash-based.


Listen to any song from any album ever recorded by the band on-demand (pictured above), check out pictures from their tours (cool design by the way: love the clothesline idea), or just admire the trippy landscapes that adorn the site's background.

And oh, does it look like I'm gonna love me some GrooGrux King: