# I need an awesome topic relating to maps/geometry!

January 3, 2012 2:16 PM Subscribe

I'm looking for an awesome video/discussion topic that relates to street maps - something appropriate for a HS geometry course.

I'm teaching the first two units of an Honors Geometry course this winter, and I'm trying to integrate some random cool projects into the standard curriculum. The first unit I need to cover reviews the algebra for parallel lines, perpendicular lines, and finding intersections, distances, and midpoints algebraically. I'm trying to make the unit more interesting by focusing on an application: road maps. I've picked out sections of cities with fairly tame road maps, and am asking students to make an even simpler version of satellite images by approximating the lines of the roads. I still need to flesh out the details of this project /and/ I'd like to spend about half an hour at the beginning of one class discussing something that students will find very cool that's at least fairly related to maps and to the algebra/geometry. Have you seen any online videos or heard any good discussions that a class of 10th grade students would find interesting?

Thanks!

I'm teaching the first two units of an Honors Geometry course this winter, and I'm trying to integrate some random cool projects into the standard curriculum. The first unit I need to cover reviews the algebra for parallel lines, perpendicular lines, and finding intersections, distances, and midpoints algebraically. I'm trying to make the unit more interesting by focusing on an application: road maps. I've picked out sections of cities with fairly tame road maps, and am asking students to make an even simpler version of satellite images by approximating the lines of the roads. I still need to flesh out the details of this project /and/ I'd like to spend about half an hour at the beginning of one class discussing something that students will find very cool that's at least fairly related to maps and to the algebra/geometry. Have you seen any online videos or heard any good discussions that a class of 10th grade students would find interesting?

Thanks!

It's well-known that the appropriate way to measure distance in Manhattan is not by using straight lines. Show them a map (maybe kind of stylized) and explain that the distance between the points (x street, y avenue) and (x' street, y' avenue) is |x-x'|+|y-y'|, because you have to walk on the street and can't walk diagonally across blocks. Remind them about Pythagoras and Euclid by explaining that, if Manhattan were a plane, instead of what mathematicians call a "plane with the L_1 metric" (or just "Manhattan"), then the distance between the same points would be the square root of (x-x')^2 + (y-y')^2.

Now pick a bunch of landmarks in Manhattan, and get their addresses. Have the students calculate the distance between each pair of landmarks, with respect to the Manhattan distance. Now: can they draw a new map of Manhattan, featuring all of those landmarks, in such a way that the Pythagorean/Euclidean distance between landmark A and landmark B, on their new map, is the same as the Manhattan distance between landmark A and landmark B, for each pair of landmarks, in real Manhattan? In other words, can they draw Manhattan, projected onto an actual Euclidean plane? Start with a Manhattan consisting only of the Empire State building, the Statue of Liberty, and my friend's place in Washington Heights. What happens as more landmarks are added?

posted by kengraham at 3:03 PM on January 3, 2012 [1 favorite]

Now pick a bunch of landmarks in Manhattan, and get their addresses. Have the students calculate the distance between each pair of landmarks, with respect to the Manhattan distance. Now: can they draw a new map of Manhattan, featuring all of those landmarks, in such a way that the Pythagorean/Euclidean distance between landmark A and landmark B, on their new map, is the same as the Manhattan distance between landmark A and landmark B, for each pair of landmarks, in real Manhattan? In other words, can they draw Manhattan, projected onto an actual Euclidean plane? Start with a Manhattan consisting only of the Empire State building, the Statue of Liberty, and my friend's place in Washington Heights. What happens as more landmarks are added?

posted by kengraham at 3:03 PM on January 3, 2012 [1 favorite]

To people who have responded so far:

Thank you!

To future responses:

If you reference a video or article, linking to it would be much appreciated! :)

posted by ch3cooh at 3:23 PM on January 3, 2012

Thank you!

To future responses:

If you reference a video or article, linking to it would be much appreciated! :)

posted by ch3cooh at 3:23 PM on January 3, 2012

This article might give you some inspiration. It's good for a laugh at the very least.

posted by gueneverey at 4:20 PM on January 3, 2012

posted by gueneverey at 4:20 PM on January 3, 2012

There are lots of YouTube videos about the "Sacred Geometry" of Washington DC, which from what I gather refers to some crazy-ass conspiracy theory about the Illuminati. Not sure you want to go there with a bunch of high schoolers, but it would make for an interesting discussion.

Here are a few: 1, 2, 3

Here's a crazy-ass one on New York.

posted by desjardins at 7:09 PM on January 3, 2012

Here are a few: 1, 2, 3

Here's a crazy-ass one on New York.

posted by desjardins at 7:09 PM on January 3, 2012

You can probably find less woo-woo stuff about DC by looking for Pierre L'Enfant, who developed the plan for the city. This video seems to make the awesome urban planning incredibly dull, but it's a start.

posted by Homeboy Trouble at 10:02 PM on January 3, 2012

posted by Homeboy Trouble at 10:02 PM on January 3, 2012

You probably don't have time or inclination to get into GIS software, but there is endless discussion of points, lines and polygons in introductory texts. Also, things like buffers (circles or polygons around a point or line) are calculated geometrically. Sorry I can't link to specifics at the moment, but check out ESRI - I believe they have a specific site for educators.

posted by desjardins at 7:34 AM on January 4, 2012

posted by desjardins at 7:34 AM on January 4, 2012

This thread is closed to new comments.

posted by Wretch729 at 2:22 PM on January 3, 2012