Land for Sale: Flat, Perfectly Aligned Boundaries - Can Bob Buy in the U.S.?

[Icebreaker]

Bob wants to buy a piece of land which must be perfectly flat, with two of the boundary lines running perfectly north-south; the other two, perfectly east-west. And all boundary lines must measure exactly 100 meters.

Can Bob purchase such a piece of land in the U.S. and why?

 

[matthyaouw]

No he can't. the Earth is curved, so any piece of land he buys with north-south lines of 100m will be slightly wider at the south end than the north as the longditude lines converge towards the pole.[/color]

 

[ArielGenesis]

the curvature of the Earth is interesting, isn't`it ?

 

[Galileo]

You'd have to be at the equator.

 

[Berislav]

The land could be artificially leveled, but normally no. For the reasons stated above.

 

[Icebreaker]

You people are good. It took me hours before figuring this one out.

 

[vikasj007]

well, the piece of land can be flattened artificially, so that is not a problem.

but as far as the dimensions are concered, i think the radius of Earth is too large to have any measurable effect on the size of the land. i mean, whatever the effect may be on the dimensions as mentioned, it will be so small that it can practically be neglected. n i don't think that it will be possible to measure it in the first place.


please comment...

 

[RandallB]

WRONG – Of course he can!

Bob’s request was for FLAT land not LEVEL land.
If he’d wanted LEVEL land there would be no place on Earth he could do this even the equator. But flat, OK. Let's start on the equator – just excavate out the “high ground in the center until using Pythagoras's theorem 3 dimensionally you have “FLAT” ground. Now when slope is measured with a bubble level we will see from the corners it slopes down to the center of the borders and from the borders and corners it slopes down toward the center of our perfectly flat and square surface of land. We just need to move this surface AND it orientation north somewhere. Let's use the border of Kansas and Nebraska about 40 degrees north.

Now the DISK (not the cone) made by the 40 degree north line is a surface parallel with the disk created by the equator. Both perpendicular to the axis of Earths rotation but only the equators disk runs through the very center. This disk is already parallel to the north and south borders of our 100M square, and the east and west borders are already perfectly parallel with the Earth’s axis! All four of these orientations are maintained as the flat surface square description is moved to 40 degrees north. A quick evaluation of it tells us we are looking for ground that slopes down to the south by about 40 degrees!
Where to we find such steep ground? North side Bank of a large stream or river running east west.
Now the neat part for Bob once he found the perfect location is he learned that ground was recorded at the land office as the space taken up by LEVEL ground. Thus for his 10,000 sq. meter sloped piece of land, he only had to pay for about 7500 sq meters of surveyed level area!

Sold said BOB, I understand he’s got his garden hose out and is currently enjoying the most extreme slip and slide in the county!

 

[20questions]

What exactly does running north-south mean. A flat square area, I believe RandallB suggests, would have parallel sides, so they can't both extend out to meat at the same point (North Pole) as they would if the land area were warped along with the globe. I believe only at the equator, not in the US fits the original question.

Can Bob purchase such a piece of land in the U.S. and why?

My first answer is Yes- do it over the internet, because it's cheaper than visiting in person.

 

[RandallB]

I believe only at the equator, not in the US fits the original question.

I understand why you'd think that, but for it to work at the equator, in the way you want, it must be LEVEL land not FLAT. And then the sides would not be straight lines even at the equator. You can not have it both ways on a sphere.

For a flat section to work you must accept "running North South" as lines running parallel to the axis the Earth rotates on (a fair enough assumption given the problem as stated). Not the infinite number of triangles that point to a spot beyond the north star – none being parallel to any other.
Plus once you’d found a piece of ground as I’d described you would not be able to describe the directions of the edges as anything but N-S and E-W.