[math-fun] {(x,y,z): x+y+z=0}
I’ve spent 10 minutes googling things like “triangular coordinates“ and “reduced barycentric coordinates“ but haven’t found what I’m looking for. So, apologies if you feel I should have googled longer instead of wasting funsters’ time, but maybe one of you will instantly know the name of the coordinate system in which points in the plane are represented by triples summing to zero (and more generally n-tuples summing to zero in higher dimensions). Actually, I might as well include a followup question, which is, where is the best place to look for translations of the standard high school formulas for coordinate geometry into this somewhat arcane coordinate system? I could spend an hour figuring them out for myself, but that’s an hour I’d rather spend figuring out something new, and more importantly, I might make mistakes! Thanks, Jim Propp
I think Shakespeare called it by saying: “A plane by any other name would lay as flat” and followed with another clever phrase about “slings and arrows” of extra dimensions, but I might be confused on the exact history. Why even worry what Shakespeare had to say? There is one linear transformation between normal vectors, and possibly another around the normal vector. In higher dimensions, there are more internal transformations to worry about, but they are all linear. —Brad
On Apr 25, 2020, at 5:23 PM, James Propp <jamespropp@gmail.com> wrote:
I’ve spent 10 minutes googling things like “triangular coordinates“ and “reduced barycentric coordinates“ but haven’t found what I’m looking for. So, apologies if you feel I should have googled longer instead of wasting funsters’ time, but maybe one of you will instantly know the name of the coordinate system in which points in the plane are represented by triples summing to zero (and more generally n-tuples summing to zero in higher dimensions).
Actually, I might as well include a followup question, which is, where is the best place to look for translations of the standard high school formulas for coordinate geometry into this somewhat arcane coordinate system? I could spend an hour figuring them out for myself, but that’s an hour I’d rather spend figuring out something new, and more importantly, I might make mistakes!
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Wouldn't it just be the plane? Given x, y, z must be -x - y. On Sat, Apr 25, 2020 at 4:23 PM James Propp <jamespropp@gmail.com> wrote:
I’ve spent 10 minutes googling things like “triangular coordinates“ and “reduced barycentric coordinates“ but haven’t found what I’m looking for. So, apologies if you feel I should have googled longer instead of wasting funsters’ time, but maybe one of you will instantly know the name of the coordinate system in which points in the plane are represented by triples summing to zero (and more generally n-tuples summing to zero in higher dimensions).
Actually, I might as well include a followup question, which is, where is the best place to look for translations of the standard high school formulas for coordinate geometry into this somewhat arcane coordinate system? I could spend an hour figuring them out for myself, but that’s an hour I’d rather spend figuring out something new, and more importantly, I might make mistakes!
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
Searching on ` Hexagonal Coordinate System ' turns up quite a few hits for the plane, mostly from amateur game programmers rather than mathematicians. I don't recall that crystallographers actually dignify the technique with a name at all. WFL On 4/26/20, Mike Stay <metaweta@gmail.com> wrote:
Wouldn't it just be the plane? Given x, y, z must be -x - y.
On Sat, Apr 25, 2020 at 4:23 PM James Propp <jamespropp@gmail.com> wrote:
I’ve spent 10 minutes googling things like “triangular coordinates“ and “reduced barycentric coordinates“ but haven’t found what I’m looking for. So, apologies if you feel I should have googled longer instead of wasting funsters’ time, but maybe one of you will instantly know the name of the coordinate system in which points in the plane are represented by triples summing to zero (and more generally n-tuples summing to zero in higher dimensions).
Actually, I might as well include a followup question, which is, where is the best place to look for translations of the standard high school formulas for coordinate geometry into this somewhat arcane coordinate system? I could spend an hour figuring them out for myself, but that’s an hour I’d rather spend figuring out something new, and more importantly, I might make mistakes!
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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I have always thought of them as "isometric coordinates", in analogy with "isometric graph paper". I can find no formal authority for this, though a lot of people on the web also use the phrase. On Sat, Apr 25, 2020 at 8:56 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Searching on ` Hexagonal Coordinate System ' turns up quite a few hits for the plane, mostly from amateur game programmers rather than mathematicians. I don't recall that crystallographers actually dignify the technique with a name at all.
WFL
On 4/26/20, Mike Stay <metaweta@gmail.com> wrote:
Wouldn't it just be the plane? Given x, y, z must be -x - y.
On Sat, Apr 25, 2020 at 4:23 PM James Propp <jamespropp@gmail.com> wrote:
I’ve spent 10 minutes googling things like “triangular coordinates“ and “reduced barycentric coordinates“ but haven’t found what I’m looking
for.
So, apologies if you feel I should have googled longer instead of wasting funsters’ time, but maybe one of you will instantly know the name of the coordinate system in which points in the plane are represented by triples summing to zero (and more generally n-tuples summing to zero in higher dimensions).
Actually, I might as well include a followup question, which is, where is the best place to look for translations of the standard high school formulas for coordinate geometry into this somewhat arcane coordinate system? I could spend an hour figuring them out for myself, but that’s an hour I’d rather spend figuring out something new, and more importantly, I might make mistakes!
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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One of the articles Fred is mentioning may be Red Blob Games' (Amit Patel's) Hexagonal Grids article at https://www.redblobgames.com/grids/hexagons/, which refers to this as cube coordinates, and the variant of leaving out one of the components (here the y coordinate) as axial coordinates, and includes methods for several algorithms on these coordinate systems. However, I'm guessing that these names are probably ambiguous when used outside the context of hexagonal coordinate systems. http://www-cs-students.stanford.edu/~amitp/gameprog.html#hex has a list of resources on these hexagonal grids, including a page including some correspondence on the coordinate system circa 1994-1999, where these are referred to as isometric cube coordinates: http://www-cs-students.stanford.edu/~amitp/Articles/Hexagon2.html Hope this helps, --Neil Bickford On Sat, Apr 25, 2020 at 6:33 PM Allan Wechsler <acwacw@gmail.com> wrote:
I have always thought of them as "isometric coordinates", in analogy with "isometric graph paper". I can find no formal authority for this, though a lot of people on the web also use the phrase.
On Sat, Apr 25, 2020 at 8:56 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Searching on ` Hexagonal Coordinate System ' turns up quite a few hits for the plane, mostly from amateur game programmers rather than mathematicians. I don't recall that crystallographers actually dignify the technique with a name at all.
WFL
On 4/26/20, Mike Stay <metaweta@gmail.com> wrote:
Wouldn't it just be the plane? Given x, y, z must be -x - y.
On Sat, Apr 25, 2020 at 4:23 PM James Propp <jamespropp@gmail.com> wrote:
I’ve spent 10 minutes googling things like “triangular coordinates“
and
“reduced barycentric coordinates“ but haven’t found what I’m looking for. So, apologies if you feel I should have googled longer instead of wasting funsters’ time, but maybe one of you will instantly know the name of the coordinate system in which points in the plane are represented by triples summing to zero (and more generally n-tuples summing to zero in higher dimensions).
Actually, I might as well include a followup question, which is, where is the best place to look for translations of the standard high school formulas for coordinate geometry into this somewhat arcane coordinate system? I could spend an hour figuring them out for myself, but that’s an hour I’d rather spend figuring out something new, and more importantly, I might make mistakes!
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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participants (6)
-
Allan Wechsler -
Brad Klee -
Fred Lunnon -
James Propp -
Mike Stay -
Neil Bickford