königs-pittsburgh
In case you didn't already see greg's or alan's writeup, here i am to report on our success solving the Königs-Pittsburgh Bridge Problem last saturday.
The idea is that while the original problem is not solvable, pittsburgh's variant is, and it turns out to be a 35-mile hike. The rules are that you must cross every bridge with at least one endpoint in the city limits and you may not, of course, repeat bridges. Since the 31st street bridge currently has an enormous chunk missing for construction, there are 18 bridges, and the hike even complets on the same landmass that it starts on.
Intrepid topologists gregh1983, alanv, and I completed the hike, starting around 0530 and ending around 2200. (Several other topologists joined late or left early - owen and cbuckey met us in the strip and left at point state park; keith started with us and left after the 10th street bridge, and dan started with us and invested heroic effort to get as far as hazelwood before needing to part ways.)
Click above for route; cut below for photos.
compared to mine, Alan's photos documented the hike itself better; he made sure to take a shot of us on each of the 18 bridges (plus I especially like this one of me modeling my smithfield street bridge shirt in front of same).
Mural during mile 6. Shortly after passing this, we saw real estate signs that read "FOR SALE - ENTIRE CITY BLOCK". I felt the juxtaposition was quintessentially Pittsburgh.
View of 40th street bridge, children's hospital, etc from north shore trail.
view of the ketchup-coloured heinz apartments from the mustard-coloured 16th street bridge.
We solved a miniature koenigsburg problem in allegheney commons park by crossing these two bridges.
A t-shirt in a north side shop. I wasn't sure what "don't come across that bridge" meant.
this building in mexican war streets had mixed feelings about us
Intrepid heroes cross a street.
The mckee's rocks bridge is about a mile long (counting the bit that crosses over mckee's rocks bottoms). We spent a disheartening 6 miles getting out to it and back.
also, hey greg, sharpsburg is totally more north than brighton heights.
huge water treatment facility underneath the bridge
Inscription and logo on the bridge. Note "allegheney covnty".
view of west end bridge, downtown, etc from mckee's rocks bridge.
Intrepid heroes press onward into station square.
A site on the pj mcardle roadway, just east of the liberty bridge, hearkens back to pittsburgh's older public transit system.
The idea is that while the original problem is not solvable, pittsburgh's variant is, and it turns out to be a 35-mile hike. The rules are that you must cross every bridge with at least one endpoint in the city limits and you may not, of course, repeat bridges. Since the 31st street bridge currently has an enormous chunk missing for construction, there are 18 bridges, and the hike even complets on the same landmass that it starts on.
Intrepid topologists gregh1983, alanv, and I completed the hike, starting around 0530 and ending around 2200. (Several other topologists joined late or left early - owen and cbuckey met us in the strip and left at point state park; keith started with us and left after the 10th street bridge, and dan started with us and invested heroic effort to get as far as hazelwood before needing to part ways.)
Click above for route; cut below for photos.
compared to mine, Alan's photos documented the hike itself better; he made sure to take a shot of us on each of the 18 bridges (plus I especially like this one of me modeling my smithfield street bridge shirt in front of same).
Mural during mile 6. Shortly after passing this, we saw real estate signs that read "FOR SALE - ENTIRE CITY BLOCK". I felt the juxtaposition was quintessentially Pittsburgh.
View of 40th street bridge, children's hospital, etc from north shore trail.
view of the ketchup-coloured heinz apartments from the mustard-coloured 16th street bridge.
We solved a miniature koenigsburg problem in allegheney commons park by crossing these two bridges.
A t-shirt in a north side shop. I wasn't sure what "don't come across that bridge" meant.
this building in mexican war streets had mixed feelings about us
Intrepid heroes cross a street.
The mckee's rocks bridge is about a mile long (counting the bit that crosses over mckee's rocks bottoms). We spent a disheartening 6 miles getting out to it and back.
also, hey greg, sharpsburg is totally more north than brighton heights.
huge water treatment facility underneath the bridge
Inscription and logo on the bridge. Note "allegheney covnty".
view of west end bridge, downtown, etc from mckee's rocks bridge.
Intrepid heroes press onward into station square.
A site on the pj mcardle roadway, just east of the liberty bridge, hearkens back to pittsburgh's older public transit system.