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Posts Tagged "mathematics education"

Roots of Unity

The Math Wars, Lewis Carroll Style

Lewis Carroll in 1863, photographed by Oscar Gustave Rejlander. Image: Public domain, via Wikimedia Commons.

In 1879, Charles Dodgson, better known as Lewis Carroll, published an odd little book called Euclid and his Modern Rivals (available for free at the Internet Archive). Though it takes the form of a play, it is a defense of Euclid’s Elements as the best textbook for geometry. Carroll’s introduction lays out his purpose and why [...]

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Roots of Unity

These Hypocycloids Will Make You Happy

A 2-cusped hypocycloid rolling inside a 3-cusped hypocycloid rolling inside a 4-cusped hypocycloid... Image: Greg Egan. Used with permission.

Unless you’re holding a baby or a scalpel, drop everything and read this blog post about hypocycloids by John Baez. (And if you’re holding a scalpel, please put away whatever device you’re reading this on and pay attention to your surgery!) In addition to a lovely exposition by Baez, the post features some gorgeous animations [...]

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Roots of Unity

How the Simpsons (And You) Can Multiply by Seven Using Your Fingers

3 times 7 is...25? What?

When I tutored elementary school math, one of my favorite things to show the kids was how to multiply by 9 using their fingers. (I apologize, but this trick assumes that you have five fingers on each hand. Later you’ll see how to adapt it if you have nonstandard hands.) Here’s how the finger rule [...]

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Roots of Unity

Carnival of Mathematics #103

Image: David Simmonds, via flickr.

Welcome to the 103rd Carnival of Mathematics! The number 103 is prime, and it’s the “older” twin of a pair of twin primes as well—or is it the “younger” twin because it comes later? Regardless, 101 and 103 are twin primes. According to Tanya Khovanova’s site Number Gossip, 103 is not only prime and happy [...]

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Roots of Unity

Can a Closed Set Be Open? Can an Open Set Be Closed? When Math and Language Collide

A set that is neither open nor closed. The solid arc on the top of the half circle indicates that the boundary is included in the set, while the dotted line at the bottom indicates that the boundary is not included in the set. This set could also be described as the set of all points (x,y) that are less than or equal to 1 unit away from the point (0,0) and have a strictly positive y-coordinate. Image: Evelyn Lamb.

I gave my first midterm last week. I’m teaching a roughly junior level class for math majors, one of their first classes that is mostly focused on proofs rather than computations or algorithms. It is more abstract than most math classes they’ve taken up to this point. I love teaching this class because a class [...]

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Roots of Unity

Step Right Up! It’s the Carnival of Mathematics!

Circles, radii, and angles in a ferris wheel at the Riley County 4-H Fair. Image: Judy Klimek, via Wikimedia Commons.

The Carnival of Mathematics is a monthly blogging round-up of fun math-related blog posts organized by the friendly folks of the Aperiodical. This month, Michelle Blair of My Summation is hosting Carnival #102. Head on over to find some gems you may have missed in the last month. (Hint: you should check out the sonnets [...]

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Roots of Unity

10 Secret Trig Functions Your Math Teachers Never Taught You

A diagram with a unit circle and more trig functions than you can shake a stick at. The familiar sine, cosine, and tangent are in blue, red, and tan, respectively.

On Monday, the Onion reported that the “Nation’s math teachers introduce 27 new trig functions.” It’s a funny read. The gamsin, negtan, and cosvnx from the Onion article are fictional, but the piece has a kernel of truth: there are 10 secret trig functions you’ve never heard of, and they have delightful names like “haversine” [...]

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Roots of Unity

Mathematics+Motherhood: An Interview with Constance Leidy

Mathematician Constance Leidy and her daughter. Image: Constance Leidy.

This is a guest post from Lillian Pierce, who has been doing an interview series for the Association for Women in Mathematics. Her series has focused on women who are balancing motherhood with their mathematical careers. I found her interview with Constance Leidy very interesting, and I am grateful to Drs. Pierce and Leidy for [...]

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Roots of Unity

Mathematics, Live: A Conversation with Laura DeMarco and Amie Wilkinson

"Concealed within his fortress, the lord of Mordor sees all. His gaze pierces cloud, shadow, earth, and flesh. You know of what I speak, Gandalf: a great Eye, lidless, wreathed in flame."

This year I’ve been co-writing “Mathematics, Live,” an interview series for the Association for Women in Mathematics newsletter. In my interviews I’m “listening in” on conversations between pairs of female mathematicians. The first interview appeared in the May/June issue of the newsletter (password required). In it, I talked with mathematicians Laura DeMarco of the University [...]

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Roots of Unity

Strumming the Lute of Pythagoras

A drawing by Joseph Koch incorporates the Lute of Pythagoras into a portrait of Pythagoras himself. Image copyright Joseph Koch. Used with permission.

When I was at the Joint Math Meetings in January, the evocative name “Lute of Pythagoras” jumped out at me in a talk by Ann Hanson of Columbia College in Chicago. Hanson teaches a course, Math in Art and Nature, that satisfies the general math requirement for Columbia College but comes with a healthy helping [...]

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