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Roots of Unity

Roots of Unity

Mathematics: learning it, doing it, celebrating it.

  • Grapefruit Math

    Grapefruit Math

    By Evelyn Lamb | May 19, 2015 |

    I taught a topology and geometry class this semester, and one of the topics we covered was spherical geometry. One of the interesting properties of spherical geometry is the fact that on a given sphere, the angles in a triangle completely determine the side lengths and area of the triangle. […]

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  • A Few of My Favorite Spaces: Fat Cantor Sets

    By Evelyn Lamb | April 30, 2015 |

    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 tweak it and see what happens. […]

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

    By Evelyn Lamb | April 24, 2015 |

    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. […]

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  • In Praise of Fractals and Poetry

    In Praise of Fractals and Poetry

    By Evelyn Lamb | April 20, 2015 |

    A portion of the Mandelbrot set, which may be the world's most famous fractal. Image: Wolfgangbeyer, via Wikimedia Commons. This year for Math Poetry month , I read Proportions of the Heart: Poems that Play with Mathematics , a collection of poems by Emily Grosholz. […]

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  • Lambert on Love and Hate in Geometry

    Lambert on Love and Hate in Geometry

    By Evelyn Lamb | April 13, 2015 |

      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. […]

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  • The Cantor Function: Angel or Devil?

    The Cantor Function: Angel or Devil?

    By Evelyn Lamb | March 31, 2015 |

    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 . […]

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  • A Few of My Favorite Spaces: The Cantor Set

    A Few of My Favorite Spaces: The Cantor Set

    By Evelyn Lamb | March 26, 2015 |

    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?

    What’s so Great about Continued Fractions?

    By Evelyn Lamb | March 17, 2015 |

    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. […]

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

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

    By Evelyn Lamb | March 11, 2015 |

    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 the Simpsons , we might use base 8. […]

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  • Uber, but for Topological Spaces

    Uber, but for Topological Spaces

    By Evelyn Lamb | February 28, 2015 |

    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 that. […]

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