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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.
  • Higher Homotopy Groups Are Spooky

    A visualization of some points on the sphere and their fibers in the Hopf fibration. Image: Niles Johnson, via Wikimedia Commons.

    When I tell people I’m a mathematician, I get a lot of different reactions. Perhaps surprisingly, I mostly get positive responses. Many of them are of the “You go, girl” variety. Some people say, “I’m a [some other profession], but I always liked math” or, “I wish I had taken more math classes.” I get [...]

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    In Which Omar Khayyam Is Grumpy with Euclid

    A portrait of Omar Khayyam. Image: Atilin, via Wikimedia Commons.

    My math history class is currently studying non-Euclidean geometry, which means we’ve studied quite a few “proofs” of Euclid’s fifth postulate, also known as the parallel postulate. I’ve written about this postulate before. There are many statements that are equivalent to the parallel postulate, including the fact that parallel lines in a plane are equidistant. This [...]

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    Beyond Emmy and Sophie: Resources for Learning about Women in Math

    Emmy Noether has a posse. Created by Evelyn Lamb based on a public domain image of Emmy Noether, via Wikimedia Commons.

    Today is Ada Lovelace Day, an international celebration of women in science, technology, engineering, and math. If you’d like to read about women in math for the occasion, you’re in serious danger of coming across an article about Hypatia, Emmy Noether, Sophie Germain, or Sofia Kovalevskaya. Of course, these are inspiring women with compelling stories, [...]

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    Build Your Own Fractal with MegaMenger!

    A completed level 1 Menger sponge. Image: Manchester Science Festival.

    Later this month, people will be gathering at museums and schools around the world to build giant Menger sponges as part of a global fractal extravaganza called MegaMenger. A Menger sponge is a fractal that sits in three-dimensional space. To visualize one, imagine starting with a cube and splitting it into 27 sub-cubes, like a [...]

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    Another Reason to Love the Number Seven

    A seven of hearts. Image: Kiran Foster, via Flickr.

    The world’s favorite number is seven, at least if the result of a poll conducted by Alex Bellos is to be believed. Some people like it because it is prime, some because they have a lot of sevens in their birthdates. But I went to a talk by 2014 Fields Medalist Manjul Bhargava that gave [...]

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    Extrapolation Gone Wrong: the Case of the Fermat Primes

    Sorry, Pierre, but not all Fermat numbers are primes. Image: Public domain, via Wikimedia Commons.

    Samuel Arbesman recently wrote about incorrect mathematical conjectures. I wanted to add one of my favorites, which came up in my math history class a couple weeks ago. Unlike the disproven conjectures Arbesman wrote about, which fail only for very large numbers, this one fails at 5. Pierre de Fermat was an amateur number theorist [...]

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    A Computer Scientist Tells Mathematicians How To Write Proofs

    Leslie Lamport, clad in a t-shirt that says "You want proof? I'll give you proof!" gave a presentation at the Heidelberg Laureate Forum. Image: HLFF/Kreutzer.

    Believe it or not, I do have friends who would describe themselves as not liking math, and every so often one of them will share this meme on Facebook: And then Satan said, “Put the alphabet in math.” There are different background pictures each time the meme pops up, but the text is always the [...]

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    Mathematics, Live: A Conversation with Evelyn Boyd Granville

    Evelyn Boyd Granville in 1997. Image: Margaret Murray, via Mathematicians of the African Diaspora by Scott W. Williams.

    Evelyn Boyd Granville was one of the first African American women to earn a Ph.D. in mathematics. She recently turned 90, and I wrote a post here to celebrate. This more complete version of our interview originally appeared in the September-October 2014 issue of the Association for Women in Mathematics Newsletter. It is an edited transcript that [...]

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    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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