Your geographical misconceptions

[Chronos]

If you count mountain masses, then it depends on how deep you go.

[Railer13]

@eschereal

That must be a complicated calculation based on land area being equal in each primary direction.

If you want to learn how the National Geodetic Service calculated it, here you go.

GeoCenter_USA1.pdf

[Dorjan]

@eschereal

That must be a complicated calculation based on land area being equal in each primary direction. When I do a Q&D calculation based on NSEW extremes, being defined as the farthest one can go and stand on solid ground – a rock off the Washington coast, Pt Quoddy Maine, an Island near the Florida Keys, the top of the NW Angle – and find the raw mathematical intersection, I land on a point near Cotton Valley Oklahoma some 250 miles SE of Lebanon.

I assume the centerpoint is where, if you put the country on a needle, that is where it would theoretically balance, but if you count in topographical mass, it seems likely the balance point would be a ways west.

Believe it or not, in 1918 the National Geodetic Survey made a precisely cut cardboard cutout of the contiguous US (of uniform thickness), and found its balance point on a pin. That spot was 39°50′ N and longitude 98°35′ W, the closest town being Lebanon, KS.

[Chronos]

One of my professors told us that the way he did numerical integrals was to graph the function on paper, cut it out, and weigh it on an analytical balance.

[eschereal]

I used to use a bamboo Post for multplication, square roots and trig.

[DPRK]

Huh? You graph it, okay, but you do not need to cut it out:

Planimeter

However, if you are starting from a table of numbers, why graph it?

Simpson's rule

[CalMeacham]

@Chronos

One of my professors told us that the way he did numerical integrals was to graph the function on paper, cut it out, and weigh it on an analytical balance.

If you cut it out of a thick enough piece, you can then locate the centroid by hanging the cutout from several different points, with a plumbline. The centroid will be where all the plumblines intersect.

[LSLGuy]

Which even works for surfaces with voids or concavities. A little imprecise, but better than trying to support your hollow cutout by a pin in a “lake”.

[LSLGuy]

Avulsion is like that. Rivers move abruptly but borders don’t. Leaving bits of state A on the state B side of the newly moved river.

There’s a famous bit of Iowa on the Nebraska side of the Missouri river just north of Omaha Nebraska’s Epply Airport.

[Chronos]

I actually just learned, from a different thread here, that it’s not like that on the Rio Grande. By treaty, the US and Mexico actually exchange little pieces of land whenever the river changes course.

Given that it goes one way about as often as the other, and given that most of the land near the river isn’t worth much, that’s probably a sensible way to do it.

[eschereal]

It is not north of the airport, it is west of it, and you can see the remains of the original oxbow as the crescent-shaped Carter Lake. That is a big chunk of land.

Saw a story today about a map of Africa used by the US State department that was breathtakingly incorrect, but it seemed improper to post it here. It is in a Pit thread.