# Euler tour of Manhattan

## weblog/

I've had a mind to do an Euler tour of the bridges of New York, specifically those in and out of Manhattan. Yesterday a few friends and I made our attempt. Our tour was an Euler tour in the historical sense, not quite the mathematical sense (I guess a valid Euler tour would start and finish in the same place). The graph illustrating the bridges (at least those traversable on bicycle) looks something like this: The basic idea of an Euler tour is to traverse each edge (bridge) exactly once. Notice this can only happen in the above graph if you start in New Jersey and end in Manhattan. In order to cross all the bridges of Manhattan, we originally thought we'd take the Path to the New Jersey side of the George Washington Bridge, but we were dismayed that Hoboken (the highest stop on the path) wasn't so close to the bridge. Also my girlfriend and I had decided to rent a tandem bike: The rental shop was on W 104 st in Manhattan so we conceded to cross the GW twice, essentially invalidating or at least delaying our Euler tour. Here's the map we used to find our way from bridge to bridge: The ordering of the bridges was to be as follows:
1. George Washington
3. 207 St
4. 181 St
5. Macombs Dam
6. 145 St
7. 138 St
8. 3 Ave
9. Willis Ave
10. Triborough
11. Ward's Island Pedestrian
12. Queensborough
13. Williamsburg
14. Manhattan
15. Brooklyn
...which is almost how it was executed. Unfortunately the pedestrian walkway from Ward's Island to Manhattan is not open in the winter and we didn't find this out until we saw it statically gaping from Randall's Island. Thus we had to also cross the Triborough bridge twice. My girlfriend and I, on the tandem bike, crossed 11 of the 15 bridges above. We covered about 42.5 kilometers (≈26.4 miles ≈ 1 marathon) in total before we were getting too nervous about returning our rental in time. Here's a rough sketch of our route on the map: The rest of our group made it over 14 of the 15 (all but that pedestrian walkway).