#how to find the shortest path between 2 points in a scalar field

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gilded granite
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if i have a scalar field given by $f(x,y)=x^2+y^2$ and i want to find the shortest path between $(-1,-1)$ and $(1,1)$ how would i go about doing this. I know i would have to minimize $\int_C f(x,y)ds$ and i think i have to use the Euler Lagrange equation but i have no idea about how to go about this

severe ironBOT
solemn fox
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Hey

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@gilded granite you still need help?

gilded granite
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ya

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i have a concussiion so my brain is kinda fried

solemn fox
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@gilded granite

severe ironBOT
solemn fox
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Any questions?

rancid bridge
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imagine using gpt for this answer

solemn fox
rancid bridge
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it's not cool to do that

solemn fox
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Better

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Btw what do you mean gpt

rancid bridge
solemn fox
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@rancid bridge

rancid bridge
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almost the exact same answer

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as you provided

solemn fox
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I'm confused

rancid bridge
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you shouldn't

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because you know you used it

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how disappointing

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society now relies on ai for maths

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and programming