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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.
  • 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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    Mathematics, Live: A Conversation with Amal Fahad and Rasha Osman, Part I

    Rasha Osman

    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 [...]

    Keep reading »

    12 Things I Had Way Too Much Fun Writing This Year

    A knitted (5,15) torus link. Image: sarah-marie belcastro.

    It’s the season for family, hot chocolate, and year-in-review lists. Guess which one this is! Roots of Unity has been around for two years now, and I’m so glad I have a place to share some of the weird and wonderful math I think about. In chronological order, here are 12 of my favorite posts [...]

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    What We Talk about When We Talk about Holes

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

    For Halloween, I wrote about a very scary topic: higher homotopy groups. Homotopy is an idea in topology, the field of math concerned with properties of shapes that stay the same no matter how you squish or stretch them, as long as you don’t tear them or glue things together. Both homotopy groups and the [...]

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    Online Game Crowd-Sources Theorems

    So close! Can we just round this one up to success? Screenshot from Nice Neighbors by Chris Staecker.

    Now is your chance to prove some theorems without knowing what they mean! Chris Staecker, a mathematician at Fairfield University, created the game Nice Neighbors to get crowd-sourced solutions to problems from a field called digital topology. Whether that means anything to you or not, you might be able to help Staecker and his colleagues prove some [...]

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    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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