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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.
  • 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.

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    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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    Learn to Count like an Egyptian

    Count Like an Egyptian by David Reimer. Image: Princeton University Press.

    Last semester, I began my math history class with some Babylonian arithmetic. The mathematics we were doing was easy—multiplying and adding numbers, solving quadratic equations by completing the square—but the base 60 system and the lack of a true zero made those basic operations challenging for my students. I was glad that the different system [...]

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    Mathematics, Live: A Conversation with Amal Fahad and Rasha Osman, Part II

    Amal Fahad

    I had the pleasure of attending the 2nd annual Heidelberg Laureate Forum in September. Modeled after the Lindau Nobel Laureate Meetings, it brings together recipients of prestigious awards in mathematics and computer science and young researchers in those areas. A focus of the meeting was the role of mathematics and computer science in the developing world, [...]

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