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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: Fat Cantor Sets

    The first three steps in the construction of the Volterra function. Image: Rocchini, via Wikimedia Commons.

    Last month, I wrote about the Cantor set, a mathematical space that is an interesting mix of small and large. It’s small in the sense that its length is 0. But it’s large in the sense that it’s uncountable. Once a mathematician get their hands on an object, one of their first instincts is to [...]

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    Mathematics, Live: A Conversation with Katie Steckles and Laura Taalman

    Katie Steckles (center) and friends work on a level 1 Menger sponge. Image: Manchester Science Festival.

    Katie Steckles is a math communicator based in Manchester, England. Laura Taalman is a Professor of Mathematics at James Madison University who has been on leave to work first as the Mathematician-in-Residence at the Museum of Mathematics in New York City, and now as Senior Product Manager for Education at the 3D-printer company MakerBot in Brooklyn. Both [...]

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    In Praise of Fractals and Poetry


    This year for Math Poetry month, I read Proportions of the Heart: Poems that Play with Mathematics, a collection of poems by Emily Grosholz. Grosholz is both a philosophy professor at Penn State and a poet. She does research in the philosophy of math, and her poems are peppered with references to both mathematics and [...]

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    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


    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.


    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)


    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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