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Roots of Unity

Roots of Unity


Mathematics: learning it, doing it, celebrating it.
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The First Root of Unity


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This is what I look like standing on a tilted post near Cayuga Lake in Ithaca, New York.

Welcome to Roots of Unity! I’m Evelyn Lamb, and I am a mathematician. You can read more about me here. I got my Ph.D. in math in May 2012 and started writing for Scientific American in June through an AAAS Mass Media Fellowship. My journey into science communication has been thrilling, and I’m excited to be part of the Scientific American blog network now.

I love math, but I didn’t always, and I know that not everyone shares my feelings. I hope my posts will give you a taste of what I find fun, exciting, and beautiful about the wide world of numbers, shapes, and patterns. Here are some pieces from the past few months that might give you an idea of what I write about:
Deep Spaces: Geometry Labs Bring Beautiful Math to the Masses
How Much Pi Do You Need?
A Presidential Pythagorean Proof
5 Sigma—What’s That?
Bridging the Gap Between Math and Art
Abandoning Algebra is Not the Answer
Fractal Kitties Illustrate the Endless Possibilities for Julia Sets. This is probably my favorite piece so far. It has fractals and a picture of a cat. What more could you want?

I love to hear from readers in the comments section, on Twitter, or via email. Scientific American requires that you register in order to comment. It’s pretty painless, and you can do it with Twitter or facebook if you want. When leaving a comment, please remember that your fellow commenters and I are human beings. Let’s treat each other that way. This blog is my space, and I reserve the right to delete comments that are offensive or off-topic. My Twitter handle is @evelynjlamb, and if you’d like to email me about a math question that has always interested or frustrated you, you can find that under the “Contact” tab at the top of the page. I look forward to hearing from you.

If you already love math, welcome. If you were traumatized by a math class years ago, welcome. If your relationship with math is complicated, welcome. I hope there will be something here for everyone.

Evelyn Lamb About the Author: Evelyn Lamb is a postdoc at the University of Utah. She writes about mathematics and other cool stuff. Follow on Twitter @evelynjlamb.

The views expressed are those of the author and are not necessarily those of Scientific American.





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  1. 1. Raja48 5:32 pm 01/7/2013

    Good stuff!

    Link to this
  2. 2. rloldershaw 9:24 pm 01/7/2013

    Hi Evelyn,

    I am interested in conformal geometry and its application in modeling nature. I have a conceptual grasp of most aspects of conformal invariance properties, but the special conformal transformations have always been something of a mystery to me.

    In the math/physics literature there are sometimes statements that it provides the conformal invariance of accelerated motions, or involves combinations of translations and rotations, but I have never seen a conceptual explanation using a concrete physical example, i.e., a way to picture what is going on in the transformations.

    Dilation invariance has a simple conceptual description. Why not the special conformal transformations?

    I have asked this question in several math and physics forums and never got a straight answer- usually complete silence.

    Any help you might offer would be most appreciated.

    Robert L. Oldershaw
    Discrete Scale Relativity
    http://www3.amherst.edu/~rloldershaw

    Link to this
  3. 3. evelynjlamb 9:55 pm 01/7/2013

    I’m not sure exactly what you’re after, but there is a beautiful video about Möbius transformations on Youtube here: http://www.youtube.com/watch?v=JX3VmDgiFnY
    I think it explains visually how these conformal transformations are created from simple rotations and translations. (And the Schumann soundtrack is very relaxing.)

    Link to this
  4. 4. notscientific 2:34 am 01/8/2013

    Evelyn,

    Welcome to SciAm! Hope to read some stats on the blog (:

    Link to this
  5. 5. rloldershaw 10:21 am 01/8/2013

    Thanks, Evelyn.

    I’ll watch that video.

    Link to this
  6. 6. M Tucker 4:42 pm 01/9/2013

    Evelyn I look forward to reading your new blog. I really enjoyed the “How Much Pi Do You Need?” post (Pi is one of my favorite numbers) because I had never heard of Pi Approximation Day. I had always liked using the 3/14 “Pi day” date to help me remember Einstein’s birthday. When I saw the date of your post I was confused at first until I remembered the European dating convention and, being a pie lover, I thought it a wonderful excuse to eat more pie. Now I have two Pie Approximation Days and my own birthday so I thank you for that.

    Link to this
  7. 7. Andrés 5:49 pm 01/16/2013

    Hi Evelyn. Thank you very much for your new project on this blog and I am expectant for stuff that you can share. I would ask you some comments, or web reference, about what inspired you to choose the name of Roots of Unity as a title, as well as the logo on the blog. Greetings.

    Link to this
  8. 8. Evelyn Lamb in reply to Evelyn Lamb 11:27 pm 01/16/2013

    Thanks for asking, Andrés. I have been so busy immediately following the launch that I haven’t had a chance to write about what the heck a root of unity is. I will be writing about the topic, probably next month, but for now, here is a link to a worksheet on complex roots, which mentions roots of unity: http://www.adeptscience.co.uk/products/mathsim/maple/powertools/precalc/html/P09-ComplexRoots.html
    It is designed to help people both learn about a topic in complex analysis and learn about how to use Maple, so it might be a bit much to take in if you’re new to either of those things. But if you scroll partway down the page, you will see the blog logo. That’s is where I got it.
    Both wikipedia and Wolfram MathWorld (http://mathworld.wolfram.com/RootofUnity.html) have pages on roots of unity, and you can surf over to more basic complex analysis pages if you’re curious. The MathWorld page linked above has a neat animation. I like animations.

    Link to this
  9. 9. dogspies 8:51 pm 01/29/2013

    Your blog will be VERY helpful to me. Looking forward to it!

    Link to this

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