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The Manhattan Grid extended to every point on Earth

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Re: The Manhattan Grid extended to every point on Earth

#44

Post by T-hawk »

stouset wrote: post #33
T-hawk wrote: post #31

Very cool of course. Why do the avenue lines meet at an antipode? In Manhattan, they are parallel, they don't converge. I understand the difference between latitude and longitude lines. A meridian of longitude is a great circle centered at the Earth's center; a line of latitude is a small circle (the analogue of a chord in a 2D circle on a plane) whose center lies north or south of the Earth's center in three dimensi…

> Why do the avenue lines meet at an antipode? In Manhattan, they are parallel, they don't converge. Sure they do. Manhattan isn't a plane; it's a region on the surface of a sphere. From Wikipedia[1], "In the spherical plane, all geodesics are great circles. ...all great circles intersect each other." Clearly, it's the non-intersecting streets that are at fault here. They should intersect, but don't. [1]: http://en.w…

That the avenues converge is your assumption. The avenues may not be geodesics. They may be parallel small circles. Manhattan is of course a region on the surface of a sphere, but the avenues could behave either way.

Throwing together that promised trigonometry, with some approximations (using round numbers, ignoring the oblateness of the sphere, ignoring the skew of Manhattan's grid from due north-south):

  40° = approx latitude of Manhattan's south end
  40.27° = approx latitude of Manhattan's other end 30 km north
  40000 km * cos(40°) = circumference of the 40° parallel
  40000 km * cos(40.27°) = circumference of the 40.27° parallel
  0.996 = ratio of the distance between avenues at the north end compared to the south
  300 m = assumed approximate distance between avenues at the south end
  298.8 m = expected distance between avenues at the north end
If the avenues are geodesics, they should be 1.2m closer to each other at the north end of Manhattan than the south end. Unfortunately a difference that small is probably essentially noise and below statistical significance to actually measure; the width of a sidewalk or a bicycle lane.

Re: The Manhattan Grid extended to every point on Earth

#47

Post by rquantz »

Bobby_Tables wrote: post #29

This doesn't make a lot of sense for Manhattan, because the grid doesn't have a center point; there's no numbering convention for streets south of Houston or avenues east of York/A. It would make more sense for cities like Miami or Salt Lake City, where there is a quadrant system and (for the most part) consistent spacing of streets

Yes, but Miami and Salt Lake City aren't the center of the world.

Re: The Manhattan Grid extended to every point on Earth

#49

Post by mdda »

mcantor wrote: post #41
jbooth wrote: post #26

The whole world? Like it extends out to Brooklyn and up to the Bronx?

Yeah, maybe even Jersey! I know , I know ! Right?!

Whatever you say about the rest of the world, New Jersey is definitely not part of Manhattan... I'm surprised there isn't some kind of grey fuzzing-out on that part of the globe.
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