The people who laid out the city of Philadelphia between the Delaware and the Schuylkill Rivers had visions of creating a great, orderly city. Chief in creating this order was a large grid of streets crossing each other at right angles at regular intervals. Before the Parkway was paved, cutting diagonally through these streets, and before hundreds of alleys and side streets disrupted the grid's evenness, this grid, it was dreamed, would provide regularity and structure to people's daily activities. It was the hope, manifested, for a prosperous city. In this setting, a city block becomes the natural measure by which to gauge distances. A pedestrian walking from Rittenhouse Square at 18th and Walnut to Franklin Square at 7th and Race travels eleven blocks east and four blocks north for a total distance of fifteen blocks. If, however, we could travel as the crow flies, Pythagoras tells us that the distance is shorter, only $\sqrt{11^2+4^2}=\sqrt{137}$, which is less than twelve city blocks. To bring this geometry to high school freshmen, I mixed a little of the old with a little of the new. I took an old map of Philadelphia's grid system and overlaid it with the locations of present-day landmarks, as if the city planners could imagine what would one day be built in their city. I asked them to imagine a helicopter flight over 17th-century Philadelphia and a rendezvous that could only happen years later. Why shouldn't a math lesson have a little history mixed in? Enjoy!
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About Me
I started this blog to share my transformation from math nerd to math nerd who loves to share math with young people. I teach high school in Hanoi, Vietnam. Your comments are always welcome. Archives
May 2021
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