Anonymous
7/21/2025, 7:41:11 AM No.16729942
wtf is tropical geometry
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Thread 16729942 - /sci/ [Archived: 33 hours ago]
Anonymous
7/21/2025, 7:44:09 AM No.16729943
>>16729942 (OP)
Math subfields are like music genres, you don't need to be a fan of all of them
Math subfields are like music genres, you don't need to be a fan of all of them
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Anonymous
7/21/2025, 8:00:37 AM No.16729946
>>16729943
This one seems fascinating.
I can't know for sure because YouTube only returns about 4 videos on it.
Apparently a 'curve' isn't just continuous. It can be some kind of weird graph that looks like barbed wire.
This one seems fascinating.
I can't know for sure because YouTube only returns about 4 videos on it.
Apparently a 'curve' isn't just continuous. It can be some kind of weird graph that looks like barbed wire.
Anonymous
7/21/2025, 9:16:33 AM No.16729966
>>16729942 (OP)
Looks cool from the wikipedia article about it but this is my first time hearing about it. I doubt anyone who knows more is on this board unfortunately because it has devolved into /iq/
Looks cool from the wikipedia article about it but this is my first time hearing about it. I doubt anyone who knows more is on this board unfortunately because it has devolved into /iq/
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Q
7/21/2025, 12:18:18 PM No.16730056
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Anonymous
7/21/2025, 9:10:13 PM No.16730449
>>16730056
yes, and ...?
yes, and ...?
Anonymous
7/21/2025, 10:35:56 PM No.16730534
>>16729966
Tropical geometry has an unfortunate name in that the word tropical has nothing to do with the subject -- it just so happened to be named after a Brazilian/Hungarian computer scientist who pioneered the field.
Having said that, the core idea is very simple: in ordinary (algebraic) geometry we're often interested in the curves that describe zeroes of polynomials in some set, let's say. These things are called varieties. Well, what happens if you were to look at the same thing, but replaced the ordinary operations of addition and multiplication in the ring of polynomials by the minimum and ordinary addition, respectively? The barbed wires one anon mentions arise naturally because of these minimum operations. Now, you'll have tropical analogs of varieties, and tropical analogs of theorems about varieties, etc.
Why do we care? Well, I can only speak for myself, but in my area of expertise -- economic theory -- tropical geometry appears in allocation problems in the presence of indivisibilities (goods that cannot be sliced up in arbitrarily fine ways, like cars - you can only have integer multiples of cars, but not half a car). It has also found fruitful applications in auction theory.
I hope this helps.
Tropical geometry has an unfortunate name in that the word tropical has nothing to do with the subject -- it just so happened to be named after a Brazilian/Hungarian computer scientist who pioneered the field.
Having said that, the core idea is very simple: in ordinary (algebraic) geometry we're often interested in the curves that describe zeroes of polynomials in some set, let's say. These things are called varieties. Well, what happens if you were to look at the same thing, but replaced the ordinary operations of addition and multiplication in the ring of polynomials by the minimum and ordinary addition, respectively? The barbed wires one anon mentions arise naturally because of these minimum operations. Now, you'll have tropical analogs of varieties, and tropical analogs of theorems about varieties, etc.
Why do we care? Well, I can only speak for myself, but in my area of expertise -- economic theory -- tropical geometry appears in allocation problems in the presence of indivisibilities (goods that cannot be sliced up in arbitrarily fine ways, like cars - you can only have integer multiples of cars, but not half a car). It has also found fruitful applications in auction theory.
I hope this helps.
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Anonymous
7/22/2025, 4:03:49 AM No.16730730
>>16730534
I believe a lot of the early tropical geometers were from South America, and this influenced the name moreso. Funny enough, the one professor at my instution who does tropical stuff is South American himself.
I believe a lot of the early tropical geometers were from South America, and this influenced the name moreso. Funny enough, the one professor at my instution who does tropical stuff is South American himself.
Anonymous
7/22/2025, 4:29:20 AM No.16730735
>>16729942 (OP)
The study of polynomials over the min-max semiring
The study of polynomials over the min-max semiring