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Roots of Unity

Roots of Unity


Mathematics: learning it, doing it, celebrating it.
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    Evelyn Lamb Evelyn Lamb is a postdoc at the University of Utah. She writes about mathematics and other cool stuff. Follow on Twitter @evelynjlamb.
  • Measure Yourself by the Standard of the Capybara

    Are you more or less of a fish than this capybara? Image: VigilancePrime, via Wikimedia Commons.

    We all know a lot of measurements about ourselves. You are some number of feet or meters tall. You weigh some number of pounds, kilograms, or stone. Your BMI is some number of kilograms per square meter, even though humans are not two-dimensional. You have some number of milligrams of cholesterol in each deciliter of [...]

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    The Slowest Way to Draw a Lute

    Man Drawing a Lute, by Albrecht Dürer. Public domain, via Wikimedia Commons.

    Last month, I went to a talk by mathematician Annalisa Crannell of Franklin and Marshall College called Math and Art: the good, the bad, and the pretty. She talked about how mathematical ideas of perspective show up in art and how it can help us create and appreciate art. One of my favorite parts of the [...]

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    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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    What T.S. Eliot Told Me about the Chain Rule

    T.S. Eliot, who probably never thought about the chain rule while he was writing poetry. Photograph by Lady Ottoline Morrell. Public domain, via Wikimedia Commons.

    “We shall not cease from exploration And the end of all our exploring Will be to arrive where we started And know the place for the first time.” —from Little Gidding by T.S. Eliot If you took calculus in high school or college, you might remember the chain rule. One of the main topics in calculus [...]

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    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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    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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    The Math Wars, Lewis Carroll Style

    Lewis Carroll in 1863, photographed by Oscar Gustave Rejlander. Image: Public domain, via Wikimedia Commons.

    In 1879, Charles Dodgson, better known as Lewis Carroll, published an odd little book called Euclid and his Modern Rivals (available for free at the Internet Archive). Though it takes the form of a play, it is a defense of Euclid’s Elements as the best textbook for geometry. Carroll’s introduction lays out his purpose and why [...]

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    Chasing the Parallel Postulate

    If you'd like to see these again, accept the parallel postulate. Image: Webber, via Wikimedia Commons.

    Euclidean geometry, codified around 300 BCE by Euclid of Alexandria in one of the most influential textbooks in history, is based on 23 definitions, 5 postulates, and 5 axioms, or “common notions.” But as I mentioned in my recent post on hyperbolic geometry, one of the postulates, the parallel postulate, is not like the others. [...]

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    Knotted Needles Make Knitted Knots

    A knitted (5,15) torus link. Image: sarah-marie belcastro.

    Step aside, infinity scarves, you aren’t infinite at all. The (5,3) torus knot cowl is where it’s at. For me, one of the highlights of January’s Joint Mathematics Meetings was the mathematical fiber arts session. You can view a slide show I put together from the session here. During the session, co-organizer sarah-marie belcastro gave a [...]

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    Hyperbolic Quotes about Hyperbolic Geometry

    This Hungarian postage stamp does not portray János Bolyai. For more information about finding the "real face of János Bolyai," click the picture to read Tamás Dénes's article on the subject.

    “The treatise itself, therefore, contains only twenty-four pages—the most extraordinary two dozen pages in the whole history of thought!” “How different with Bolyai János and Lobachévski, who claimed at once, unflinchingly, that their discovery marked an epoch in human thought so momentous as to be unsurpassed by anything recorded in the history of philosophy or of [...]

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