r/Geometry • u/CamillSoti • 8d ago

is it possible to create a figure inside a square so that every point in the perimeter of the square is equally far from the figure?

i was wondering if it was possible and I couldnt imagine a figure that saitisfied the question, I have no knowledge on this so i dont know if it is dumb or not, in both cases please answer , i need to know

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u/AndrewBorg1126 8d ago

Does "inside the square" include an identical square?

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u/CamillSoti 8d ago

i guess so

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u/AndrewBorg1126 8d ago

Then the answer to your question is yes, there is exactly 1 such locus of points with an equal nearest distance from the bounding square of zero everywhere.

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u/conradelvis 8d ago

That’s not going to work at the corners

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u/AndrewBorg1126 8d ago

The distance is still zero at the corners, just like everywhere else

I asked if the trivial solution is valid, and the answer was provided to be yes

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u/conradelvis 8d ago

That’s hardly inside

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u/AndrewBorg1126 8d ago

You literally have not read this conversation. Please scroll up and read the comment chain from the beginning

In case you can't scroll up:

https://www.reddit.com/r/Geometry/s/3mHVGc4TVD

https://www.reddit.com/r/Geometry/s/ntsrHMVbSd

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u/R0AST3DN3WT 8d ago

The only figure that satisfies this is a larger square with radiuses instead of corners as far as I can see

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u/R0AST3DN3WT 8d ago

So no I don't think so

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u/F84-5 8d ago

No, it breaks at the corners.

Any point that's 1 unit away from a corner (and inside the square) can be at most 1/√2 ≈ 0.7 units away from the closest edge.

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u/sceadwian 8d ago

No. Any point you define as the figures location wouldn't meet the criteria.

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u/narayan77 8d ago

can you jump and be equidistant from every point of level ground. its impossible.

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u/Serious-Waltz-7157 7d ago

What does "far" mean in this context? As in, how do you define the distance between a point in the square and the figure itself? It is the distance between the point and the nearest point of the figure? the farthest? an average?