The geometry of a hyperbolic paraboloid makes it a good choice for a canopy. The posts of different heights create a natural path for rainwater to flow off the tarp, eliminating the chance of standing water collecting in puddles on top.
Except maybe for a single drop at the saddle point!
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My 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.
A recent delivery came with an unexpected bonus.
A diagram illustrating the geometric relationship between the length and the width of the box!
Of course, the equation 
I did a quick search and found the standard pallet size to be 48 inches by 40 inches. So my best guess is that 
We’ve been discussing center of mass in class recently. While this powerful idea extends well beyond its physical interpretation, it’s good to frame the conversation around the idea of balancing objects on their centroids.
One student was inspired by the claim that all physical objects have centroids, and that they can be found fairly easily. So he took a small plate of aluminum, drilled a bunch of random holes in it, and tried to find its center of mass.
He claimed he had done it. But how could we test his hypothesis? It seemed like there was only one way!
It took us a while, and a few attempts, but we were able to do it! It created a nice little challenge for us, and a nice physical experience with the center of mass.
Through Math for America, I am part of an ongoing collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here
Test Yourself — Math, April 2, 2014
This question refers to an article about how dynamic ticket pricing has put the musical The Lion King back on top of the Broadway box office. Approximately how many people see the musical each week?