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Airport Please - November 2, 2009Rating: 4/5 (10 votes cast)
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I believe that would be displacement?
Good thing he doesn't know topology
I remember when I first learned Manhattan distance. What a "fancy" term for something so simple.
Wow... I used to think about stuff like that all the time, but I never knew they actually defined such a thing!
When I was a kid, I would think... hmmmm, if I bike along a set of streets that form a zig-zag, then maybe it will be faster, cuz it's kinda like a hypotenuse? But then I realized that the zig-zag would still be the same exact distance, and that the shortest street-distance between two points is rarely a straight line. :-(
Then again, like Randall Munroe, I have always worried about the efficiency of my path...
http://xkcd.com/85/
In a discrete space, they are the same distance.
Taxi math.
As long as the roads are square, it doesn't matter. When there are diagonals, though...
But the taxi is being paid by the minute, not by the shortest route.
So, he wants to maximize the distance. Where is the maximin saddle point?
In this case he would actually want to maximize time, that may or may not be taking airport road. This thus entirely depends on the amount of traffic on each route (slow moving traffic jam vs blazing through the side routes).
Yes, I got rushed and mistyped... Max time v. min distance?
I think this may be refering to something a greek philiospher said to a student who was a prince who wanted a shortcut to learning geometry: "In geometry there are no shorcuts even for princes." (or something similar)
The correct response for the lady in this comic is:
"Ok, then take me by the airport road".
My vague high school memory serves me that Pythagoras says otherwise. Even if it was the same distance, it would not be faster. Taking airport road would be one direction of acceleration/inertia/braking. Having to accelerate then brake to turn 90 degrees then accelerate again then brake would inevitably take longer to travel.
it's pythagorean theorem, isn't it? it's the same distance, not the faster choice....