3 ms·

It would have been interesting if the west was divided into hexagons which tessellate perfectly and don't have this particular problem. I am curious with the t

It would have been interesting if the west was divided into hexagons which tessellate perfectly and don't have this particular problem. I am curious with the technology available at the time, how much either method would have increased the surveying time, accuracy, and other generally important parameters?

dmurray 3y ago
It's not immediately obvious to me how you colour 50% of hexagons equally dispersed on an infinite grid without cutting some areas off, can you provide a picture?
- DavidPeiffer 3y ago
  Well shoot...yes, that part fails. Perhaps hexagons cut in half (causing 6-corner intersections) or the isosceles trapezoid pattern below would work. https://robertlovespi.net/2020/06/03/tessellation-of-isosceles-trapezoids/ https://robertlovespi.net/2020/06/03/tessellation-of-isoscel... Partly it'd be cool to have it look like Settlers of Catan.
- Kamq 3y ago
  You could have them spiral around each other (i.e. start with two hexagons next to each other, have the left one go up/right and the right one go down/left and keep wrapping clockwise). I think this is only having the areas not be "cut off" in the mathematical sense, though.
Enginerrrd 3y ago
This would be a huge PITA. See here: https://en.m.wikipedia.org/wiki/Public_Land_Survey_System https://en.m.wikipedia.org/wiki/Public_Land_Survey_System And in particular checkout the section titled: Survey design and execution. Now keep in mind errors happened a lot over large distances with difficult terrain and lines got skewed. But defining a chunk of land as the "Southwest quarter of the Northeast quarter", and then breaking it down from there by physical corners set in the ground is pretty sensical even when things get skewed. With hexagons, you COULD do the same thing, but I don't think the errors would come out so well. You'd have to be more careful to tie to more points/lines in order to not accidentally create conflicting definitions. It sounds like a nightmare honestly.
anon291 3y ago
Hexagons do not perfectly tesselate a sphere. That's why soccer balls have pentagons.

dmurray 3y ago

It's not immediately obvious to me how you colour 50% of hexagons equally dispersed on an infinite grid without cutting some areas off, can you provide a picture?

DavidPeiffer 3y ago
Well shoot...yes, that part fails. Perhaps hexagons cut in half (causing 6-corner intersections) or the isosceles trapezoid pattern below would work. https://robertlovespi.net/2020/06/03/tessellation-of-isosceles-trapezoids/ https://robertlovespi.net/2020/06/03/tessellation-of-isoscel... Partly it'd be cool to have it look like Settlers of Catan.
Kamq 3y ago
You could have them spiral around each other (i.e. start with two hexagons next to each other, have the left one go up/right and the right one go down/left and keep wrapping clockwise). I think this is only having the areas not be "cut off" in the mathematical sense, though.

Enginerrrd 3y ago

This would be a huge PITA. See here: https://en.m.wikipedia.org/wiki/Public_Land_Survey_System https://en.m.wikipedia.org/wiki/Public_Land_Survey_System And in particular checkout the section titled: Survey design and execution. Now keep in mind errors happened a lot over large distances with difficult terrain and lines got skewed. But defining a chunk of land as the "Southwest quarter of the Northeast quarter", and then breaking it down from there by physical corners set in the ground is pretty sensical even when things get skewed. With hexagons, you COULD do the same thing, but I don't think the errors would come out so well. You'd have to be more careful to tie to more points/lines in order to not accidentally create conflicting definitions. It sounds like a nightmare honestly.

anon291 3y ago

Hexagons do not perfectly tesselate a sphere. That's why soccer balls have pentagons.