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>>7750123

like, did you notice squares and hexagons have like an even numbers of sides, and triangles have an odd number of sides?

>>7750232
I was trying to be helpful. Please no bully.

>>7750123
Isn't this just a fancy way of saying that in taxicab geometry all the paths between two points are either all of even or all of odd length, and then the same for a hexagonal taxicab geometry and not the same for a triangular one?

You just used reasoning. Congrats OP. Graph theory, study that shit.

You can use it to prove that 0 is even.

>>7750232
I noticed this, but I was wondering if there is a more abstract notion of the type of thing I was talking about in the OP.

>>7750123
>a path connecting two points will contain an even number of points of the grid
>if and only if every other path connecting those points contains an even number of points.
I don’t think the last statement really is a constraint on the first statement. I think the first statement is true and therefore the second statement is also true.

Resulting in:
> a path connecting two points will ALWAYS contain an even number of points of the grid, no matter which route you take

But I could be wrong

>>7750365
>> a path connecting two points will ALWAYS contain an even number of points of the grid, no matter which route you take
No, for any given points there is either an even or odd number of points on the path between them irrespective of which path is chosen.
But you are right that the way he said it sounds backward:
>if any path between two points is an even number of points, then every path between those points covers an even number of points
is how it should be stated.

you can read this too OP
https://en.wikipedia.org/wiki/Taxicab_geometry

>>7750429
yes, that's better. thanks for improving

Isn't this the basis of the Prussian bridge problem? Euler never figured it out.

>>7751319
Is it?