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Roots of Unity

Graham’s Number Is Too Big for Me to Tell You How Big It Is

Behold, Graham's number!

I was going to write an April Fool’s Day post with the title “Mathematicians Declare Graham’s Number Equal to Infinity.” Graham’s number is really big, but of course, it’s precisely 0% as big as infinity. On the other hand, everything we touch is finite, so in some sense, Graham’s number is probably “close enough” to [...]

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Roots of Unity

We Only Need to Fill Out 425 Brackets Each to Win Buffett’s Billion

Will your bracket be a slam dunk? Image: Acid Pix, via flickr.

Warren Buffett’s Bracket Challenge* has put even more of a spotlight than usual on March Madness, the annual NCAA basketball tournament. Buffett has offered a billion dollars to anyone who correctly predicts the outcome of all 63 games in the tournament. There are 2 possible outcomes of every game and therefore 263— 9,223,372,036,854,775,808, or about [...]

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Roots of Unity

A Different Pi for Pi Day

Nope, not this kind of pi(e). Image: flickr/djwtwo

The symbol π is overloaded in math: depending on context and capitalization, π could be the constant we all know and love (or hate), a projection, a product, or a function. There’s plenty of stuff to read about the circle constant, so today I’m writing about one of those other π’s. Today’s π is the [...]

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Roots of Unity

Has Anyone Ever Flipped Heads 76 Times in a Row?

What are the odds? Image: Evelyn Lamb

Tom Stoppard’s absurdist play Rosencrantz and Guildenstern Are Dead begins with one of them, Guildenstern (or is it Rosencrantz?), flipping coins. “Heads,” Rosencrantz says, and takes the coin. Guildenstern flips again. “Heads,” Rosencrantz says, and takes the coin. Another flip. “Heads.” Again, “Heads.” Soon we find out that Guildenstern has flipped 76 coins, and all [...]

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Roots of Unity

Goldbach Variations

A letter from Christian Goldbach to Leonhard Euler

On Monday, Harald Helfgott of the École Normale Supériure in Paris posted a proof of one of the oldest open problems in number theory to the preprint repository arxiv. The ternary Goldbach conjecture, like so many questions in number theory, is easy to state but hard to prove. Every odd number greater than 5 can [...]

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Roots of Unity

Big Numbers Are Big

Today I have a piece in Slate about that pi meme that’s been going around. According to the meme, your life story is encoded in pi somewhere. My life story would probably include the word “Evelyn” at some point. (I’m going out on a limb, but stay with me.) In a code that assigns the [...]

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