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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.
  • Look Ma, No Zero!

    Babylonian numerals are surprisingly easy to decipher. Image: public domain, via sugarfish and Wikimedia Commons.

    As I told my class on Thursday, the theme of the first week of our math history course was “easy algebra is hard in base 60.” We started the semester in ancient Mesopotamia, trying to understand Babylonian* mathematical notation and decipher Plimpton 322, an enigmatic tablet from about 1800 BCE. The Babylonian number system uses [...]

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    In Praise of Proofs by Contradiction that Aren’t

    Opposing arrows, a common conclusion to a proof by contradiction.

    If you don’t know what to do, do something. That’s one of my mottos when I teach math (and it’s probably good life advice too). Last year, I taught introductory analysis (basically calculus with the juicy bits left in), one of the first proof-oriented classes students take. Writing proofs is hard, and sometimes the hardest [...]

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    What Is the Goal of a Math History Class?

    An illustration from Oliver Byrne's 1847 edition of Euclid's Elements. Image: Public domain, via Wikimedia Commons.

    I’ll be teaching a math history class for the first time this semester. I’m excited to be teaching it, but I’ve noticed that preparing for this class has been very different from preparing for other classes I’ve taught, which have all been math content courses. I know how to teach a math content course. I [...]

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    How to Talk About the Fields Medal at Your Next Cocktail Party

    The profile of Archimedes on the front of the Fields Medal Grigori Perelman did not accept. The medal was designed by Robert Tait McKenzie Image: Stefan Zachow.

    On Wednesday, four mathematicians will receive the prestigious Fields Medal at the International Congress of Mathematicians (ICM) in Seoul. If you go to the kinds of parties I do, the Fields Medal will probably come up at the next party you attend, so here’s your guide for conversing about the medal with aplomb. First, a [...]

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    Math Twitter Bots, Reviewed and Rated

    Math+Twitter Image: Design Shack.

    In the course of being a math person on Twitter, I have run across some math-related Twitter bots and feeds. It would just be mean to grade my human tweeps, but I have no qualms about rating the bots! Taking a page from the Aperiodical’s integer sequence reviews, I’m rating them on a scale of [...]

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    The Shocking Failure of British Rail Travel to Respect the Triangle Inequality

    A British train approaches a station. Image: Ingy the Wingy, via flickr.

    I spent about a month in the UK earlier this summer, and that meant I took a lot of train trips. I love riding trains: the feeling of endless possibility I get when I look at the departure boards, the countryside rolling by, the fantastic people-watching, the two-hour delay between Edinburgh and Manchester because a [...]

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    Some Infinities Are Bigger than Other Infinities, and Some Are Just the Same Size

    How to count potatoes by pairing them with numbers. Image: Yen Duong.

    Warning: contains minor spoilers for The Fault in Our Stars. I recently read The Fault in Our Stars by John Green, now a major motion picture that has led to theft in Amsterdam and a shortage of dry eyes in movie theaters around the world. One of the ideas that resonates with Hazel, the 16-year-old narrator [...]

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    British Objects of Constant Width

    Several British objects of constant width. Image: Evelyn Lamb.

    As I wrap up a trip to the UK, I reflect on the many objects of constant width I encountered here. I’ll let Numberphile tell you a little more about objects of constant width. Almost immediately after getting off the plane at Heathrow, I got some breakfast and some change in the form of metal [...]

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    Really Big Numbers (Book Review)

    Really Big Numbers by Richard Schwartz, will be published by the American Mathematical Society on July 3, 2014.

    “Now and then we pluck numbers from the blur…numbers which have no names except the ones we might now give them…souvenirs from alien, unknowable worlds.” -Really Big Numbers by Richard Evan Schwartz Really Big Numbers by Richard Schwartz, a mathematician at Brown University, is the first children’s book published by the American Mathematical Society. (Disclosure: [...]

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    The Most Mathematically Perfect Day of the Year

    Paley9-perfect.svg

    Whether you write it 6/28 or 28/6, today is a perfect day. A perfect number is a number that is the sum of its factors besides itself, and 6 (1+2+3) and 28 (1+2+4+7+14) are the first two perfect numbers. Hence, June 28 is a perfect day. Perfect numbers are few and far between, so don’t [...]

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