Jul 012011

Jun 122011

My Birthday is Coming...

May 312011

via fnf

I’ll take a pair of these Vans Meets Hermes please. Send bitcoin donations to: 14gFPynCLAGmhhmZcPaaXPf6vBt7NKaY56

Binary Bard of Blood

Apr 112011

I’m not a huuuge fan of the bard but Throne of Blood (aka MacBeth) rulez…

MacBeth

Whence is that knocking?
How is’t with me, when every noise appalls me?
What hands are here? Hah! They pluck out mine eyes.
Will all great Neptune’s ocean wash this blood
Clean from my hand? No; this my hand will rather
Making the green one red.

Soooo metal.

Anyway, this post was supposed to be about the Shakespeare Programming Language, SPL. It lets you code in verse…

Proofs I: The Pythagorean Theorem

Dec 312010

The Pythagorean Theorem is a true classic in the history of math. Generally, peeps credit the Ionian mathematician, Pythagoras, with the first proof of this theorem back around 500 BC. The oldest proof on wikipedia is Euclid’s proof and it looks pretty complicated. This is because Euclid was working within the classical framework of Euclidean geometry. As modern mathematicians, we have more powerful and diverse tools at our disposal for this proof. However, this makes the setup for our proof somewhat more complicated. Where do we begin? How much do we assume before beginning? I guess I’ll assume a basic knowledge of modern geometry. In particular, I’ll assume a basic knowledge of angles, lengths and triangles. The theorem concerns the length of the sides of a right triangle. Recall that the two sides connected to the right angle are called legs and the third side, opposite the right angle, is called the hypotenuse. Here’s a statement of the theorem:

Theorem: The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

So, according to the labels on the picture to the left, this relationship can be written as [pmath]a^2 + b^2 = c^2[/pmath]1. The easiest proof involves putting four of these right triangles together to form a square. You can do this in two ways, as demonstrated at the left. If you put them together in the top square, then you get the following proof:

Top Proof: The large square has side of length c and therefore it has area [pmath]A = c^2[/pmath]. However, we can see that this square is also composed of four triangles and a tiny square inside them. The area of each triangle is [pmath]1/2 ab[/pmath] and the area of the square is [pmath](b-a)^2[/pmath]. So, the area of the big square can also be written [pmath]4( 1/2 ab ) + (b-a)^2 [/pmath]. We can use algebra to rewrite this as [pmath]2ab + b^2 – 2ab + a^2 = b^2 + a^2[/pmath]. Since we already discovered that the area of the big square was [pmath]c^2[/pmath], we deduce that [pmath]a^2 + b^2 = c^2[/pmath]. The sum of the squares of the legs is equal to the square of the hypotenuse.

The argument for the bottom construction is similar. Both of these are found on wikipedia, along with several other proofs if you’re interested. My favorite might be the following proof by animated gif:

1. I got pmath to work! And boy does it look crappy.

Biggie vs Homer

Dec 262010

As an undergraduate, I double majored in math and classics. Since classics covers the history and literature of Ancient Greece and Rome, I studied lyric and epic poems like the Illiad and the Odyssey of Homer and the Aeneid of Vergil. As a hip hop fan/artist, I was amazed at how similar these guys were to Biggie, Ghostface, Nas and other modern poetic legends. Both hip hop and classical poetry are designed to be spoken aloud in rhythm either with or without music. The themes are similar too, as both classical poets and rappers primarily write about wars and females. I don’t understand why there isn’t more cross-disciplinary research examining the relationship between Biggie and Homer. I’ll guess I’ll keep working on my genious grant application…

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