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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.
  • Seeing Music: What Does the Missing Fundamental Look Like?

    The function y=f(x) is shown in black, and the function y=sin(2x)+sin(4x)+sin(6x)+sin(7x) is in orange.

    I wrote a post yesterday about the missing fundamental effect. It’s a startling auditory illusion in which your brain hears a note that is lower than any of the notes that are actually playing. I decided to go to Desmos, an online graphing calculator, and play around with sines to see whether the missing fundamental [...]

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    Your Telephone Is Lying to You About Sounds

    telephone

    Telephones lie about sounds because odd numbers aren’t even. Once again with those integers and sound perception! Telephones can only pick up frequencies above 300 or 400 Hertz (cycles per second, also called Hz), but most adults’ speaking voices are lower than 300 Hz (approximately the D above middle C). And yet every day, people [...]

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    The Saddest Thing I Know about the Integers

    This beautiful piano cannot be tuned. Image: Gryffindor, via Wikimedia Commons.

    The integers are a unique factorization domain, so we can’t tune pianos. That is the saddest thing I know about the integers. I talked to a Girl Scout troop about math earlier this month, and one of our topics was the intersection of math and music. I chose to focus on the way we perceive [...]

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    The Math Geek Holiday Gift Guide

    The perfect necklace for the special mathematician in your life. Image: Sarah Wood, used with permission.

    Looking for a gift that says, “Hey, I know you like math”? Look no further. There is an embarrassment of riches when it comes to wonderful mathematical things to give to people, but here are some of the coolest items I’ve seen this year. To read I wrote reviews of Jordan Ellenberg’s How Not to Be [...]

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    A Proof of the Math Fact of Rolle in Short Words

    A pic that shows the math fact of Rolle. Image: the.ever.kid, via Wikimedia Commons.

    This proof of the math fact of Rolle, I wrote it down; here was my goal: Use just words with one part. (So it won’t sound too smart.) Please tell me if you find a hole. The math fact of Rolle: Let f be a map from a closed length of the reals (the length [...]

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    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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