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Bridges 2014 — Math and Art

bridges 2014The 2014 Bridges Math and Art conference will be held August 14th through 19th in Seoul, South Korea.

The Bridges organization has been hosting this international conference highlighting the connections between art, mathematics, and computer science since 1994.  I have participated in several Bridges conferences, and my experiences there have greatly influenced me as a mathematician and a teacher.

I am proud to have two photographs in this year’s art exhibit.  You can see my work here, and you can peruse the entire 2014 Bridges Art Gallery here.

Related Posts

By MrHonner, ago

Exploring Fair Division

fair division triangleMy latest piece for the New York Times Learning Network is a math lesson exploring basic techniques of fair division.

Fair division is concerned with partitioning a set into fair shares.  “Fair” can take on different meanings in different contexts, but at its most basic level, a share is fair if someone is willing to accept it.

This lesson builds on an excellent article in the NYT about a technique in rent-splitting based on Sperner’s Lemma, an important result in Topology.  The author tells the story of how he and two roommates used the technique to settle on a fair division of rent for three different-sized rooms.

“The problem is that individuals evaluate a room differently. I care a lot about natural light, but not everyone does. Is it worth not having a closet? Or one might care more about the shape of the room, or its proximity to the bathroom.

A division of rent based on square feet or any fixed list of elements can’t take every individual preference into account. And negotiation without a method may lead to conflict and resentment.”

After reflecting on the article, students use the related NYT interactive feature to explore the algorithm and then research basic techniques in fair division like divider-chooser, sealed bids, and the method of markers.  The full lesson is freely available here.

By MrHonner, ago

Full Interview with Steven Strogatz Freely Available

strogatz smallMy complete interview with Steven Strogatz in the February 2014 issue of Math Horizons is now freely available.

Math Horizons makes one article from each issue freely available online, and I’m thrilled that for the February 2014 issue they chose my piece.  Professor Strogatz is an acclaimed mathematician, writer, and teacher, and I think this interview captures a small amount of his enthusiasm, insight, and brilliance in all these fields.

The full interview is available as a PDF here.  You can also find our conversation about math education in the Aftermath section of the magazine (posted online here), as well as some bonus material from our conversation here.

By MrHonner, ago

Teaching Math Through March Madness

ncaa bracket 2014My latest piece for the New York Times Learning Network leverages March Madness to explore some basic ideas in counting and probability.

Begin by having students explore how to count the number of possible brackets. Start by analyzing a four-team bracket, say, with Team A playing Team B and Team C playing Team D in the first round. Have the students directly list the eight possible tournament outcomes: For example, A beats B, D beats C, and then D beats A is one such outcome. The use of tree diagrams may be helpful in representing the possible brackets.

Then ask students to predict and explore how many brackets are possible with an eight-team tournament. There are 2 raised to the 7th power, or 128, such brackets. One way to see this is first by noting that eight teams in a single-elimination tournament will end up playing seven total games: Seven of the eight teams must be eliminated, which requires that they lose a game.

I’m glad I could make a small contribution to the Math Madness surrounding March Madness!  You can find the entire lesson here.

By MrHonner, ago

Pi Day 2014

I don’t usually celebrate Pi Day, but a variety of inspirations intersected at a fun project idea this time around.

Thanks to Math for America, I participated in a terrific workshop on Zometool earlier this year, led by George Hart.  We built, explored, conjectured, proved, and collaborated around a lot of rich mathematical ideas.  And this semester, Steven Strogatz is teaching a History of Math course at Cornell, and he has been generously sharing thoughts and resources online.  As a result, I have been reading up on the derivations of the volume and surface area formulas for Platonic and Archimedean solids.

So when I recently re-watched James Tanton’s brilliant video “What is Pi for a Square?“, the idea hit me:  for Pi Day, students could explore the value of “Pi” for various Zometool-constructible solids!

pi day combo

What makes James Tanton’s exploration so wonderful is that it highlights the invariance of Pi in circles (as circumference by diameter) while inviting students to play around with the notions of “diameter” “radius”, and “Pi” in regular polygons.  We’ll be taking the question “What is Pi?” up a dimension, and thanks to Zometool, we have a tangible context for our conversations and calculations.

We’ll be exploring properties of polyhedra, calculating areas, volumes and ratios, arguing about definitions, and comparing the sphereness of various things.  I’m looking forward to a great day of mathematics!  And perhaps discovering what the value of “Pi” is for a rhombic triacontahedron.

By MrHonner, ago
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