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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.
  • Lambert on Love and Hate in Geometry

    Johann Heinrich Lambert. Image: public domain, via Wikimedia Commons.

    The history of hyperbolic geometry is filled with hyperbolic quotes, and I came across a beautiful one earlier this semester in my math history class. Johann Heinrich Lambert, a Swiss mathematician who lived from 1728-1777, was trying to prove the parallel postulate and thereby establish beyond a shadow of a doubt the truth of Euclidean [...]

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    The Cantor Function: Angel or Devil?

    The Cantor function. Image: Theon, via Wikimedia Commons.

    When you’re looking at it, it just stays there, constant and still. But if you turn your back for just an instant at a point in the Cantor set, the function grows impossibly quickly. It’s not a Weeping Angel, it’s the Devil’s staircase, or, if you’re a little less whimsical, the Cantor function. One of the [...]

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    A Few of My Favorite Spaces: The Cantor Set

    200px-Cantor4.svg

    Last month, I wrote about the π-Base, a website that serves a similar function to the book Counterexamples in Topology. I’m teaching a topology class this semester, and it’s been fun to revisit some good counterexamples. As a new series on the blog, I’ll be writing about some of these strange and interesting mathematical spaces. [...]

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    What’s so Great about Continued Fractions?

    The continued fraction expansion for the number pi.

    The more I learn about continued fractions, the more enamored I am with them. Last week, when I wrote about how much better continued fractions are than the arbitrary decimal digits we usually use to describe numbers, I mentioned that continued fractions tell us the “best approximations” of irrational numbers. Continued fractions are just fractions [...]

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    Don’t Recite Digits to Celebrate Pi. Recite Its Continued Fraction Instead.

    zoidbergthumb2

    The digits of pi reciting contest is an all-too-common Pi Day event. And as this year is a once-in-a-century confluence of month/day/year with the first few decimal digits of pi, we might be in for more of those than usual. Our 10 fingers make decimal digits a natural choice, but if we were capybaras or [...]

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    Uber, but for Topological Spaces

    Cantor's Leaky Tent, one of the many lovely, perplexing, and colorfully named counterexamples available at the π-Base.

    So it’s cold and rainy, and you’re up a little too late trying to figure out why that one pesky assumption is necessary in a theorem. Wouldn’t it be nice if you could just order up a space that was path connected but not locally connected? You’re in luck, there’s an app a website for [...]

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    Things to Make and Do in the Fourth Dimension (Book Review)

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    Sometimes you want to learn a “new” multiplication algorithm from a general interest math book, sometimes you want to learn why voting systems are doomed to imperfection, and sometimes you just want to play with numbers, patterns, and pictures. Things to Make and Do in the Fourth Dimension by Matt Parker is the third kind of [...]

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    Gauss and Germain on Pleasure and Passion

    Portrait_Sophie_Germain

    Sophie German, who was not allowed to attend university, was the first woman to make significant original contributions to mathematical research. Today, her story is both inspiring and heartbreaking. What might this brilliant, creative mind have done if barriers had not been thrown in her way at every step? How many others like her do [...]

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    The Media and the Genius Myth

    Not many of us can be Serena Williams. Does that keep us from playing tennis? Image: Yann Caradec, via Flickr.

    I’ve been thinking a lot about the genius myth, the notion that in order to be a successful in certain disciplines, you need to have a special innate talent that can’t be learned. Last month, a study in Science found that fields whose practitioners buy into the genius myth, say, mathematics, have lower proportions of [...]

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    Understand the Measles Outbreak with this One Weird Number

    A man sneezes, possibly transmitting measles or other airborne diseases. Image: James Gathany, CDC.

    15. That’s all you need to know about the measles. OK, that’s not true at all. There’s no one weird trick that will give you a flat belly (besides lying face-down on something flat), and there’s no one weird number that explains measles epidemiology. But the basic reproduction number, or R0, of a disease does [...]

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