Stories indexed with the term ‘mathematics’

Today marks the first day of classes for students in the Ann Arbor Public Schools and many other local districts.

So I’m taking advantage of the occasion to launch an occasional series that is meant to present math puzzles I’ve stumbled over “in the wild,” in the course of covering local government. It will appear only as time allows, so this could very well be the only installment of the series.

The puzzles are meant to be accessible to kids in high school, junior high, or elementary school – so for many Chronicle readers, they will be trivial.

But these puzzles might offer readers’ children a chance to apply what they’ve learned in math class to an actual, authentic real-life example – drawn from the municipal workings of the city in which they live.

Today’s puzzle has a geometric flavor. The basic question: How tall is the schoolhouse in Figure 1?

First, let’s please agree not to argue about the quality of the drawing. I admit that it may look more like a church than a schoolhouse. I took as my starting point a photograph included in a recent piece by local history columnist Laura Bien.

The drawing is not Laura’s fault, of course. The drawing differs from that photo in many ways. For example, the drawing lacks a belfry and an American flag on the roof. I left them out, because they make the math puzzle more complicated than necessary.

Another reason I left them out: The real-world example – on which the puzzle is based – was not a schoolhouse. I chose a schoolhouse for the drawing just to honor today as the first day of school. The real world-example is a two-building apartment complex called City Place, located on South Fifth Avenue, just south of William Street.  [Full Story]

Ann Arbor is home to the University of Michigan, which makes it different from other similar-sized Midwestern cities lacking a world-class research institution. You can’t swing a dead Greek philosopher without hitting someone in this town who can tell you how significant the connection is between Ann Arbor and UM.

In that way, at least, Ann Arbor is densely packed.

This is a story about that town-gown connection. It’s a story that connects a recent UM mathematics PhD thesis defense to the Ann Arbor planning commission – and takes a continuous path though topics like Klingons, grocery bags, affordable housing, yard waste collection and Valentine’s Day.

We begin with Elizabeth Chen, who successfully defended her PhD dissertation last Friday in East Hall on the UM campus. Her presentation included several hands-on assignments for those in the audience of around 30 people – several of whom assured The Chronicle that hers was an “unconventional” thesis defense.

Chen exhorted the assembled mathematicians to paste together plastic pyramid shapes with gummi putty to help them get an intuitive feel for the shapes: “It’s not so scary!” she admonished them. After half an hour, one member of her thesis committee prodded her to get to the mathematics part – he really had “better things to do.” The Chronicle, however, did not. [Full Story]