
Monge's theorem - dimastopel
https://en.wikipedia.org/wiki/Monge%27s_theorem
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anonytrary
Reminds me of flatland: There are three circular buildings. There's a line
that all three people can be on such that each person thinks there are only
two buildings and no one can agree on which two buildings are present.

Edit: Nope, nevermind, two of the points both see the medium and small
circles!

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rossdavidh
However, it does seem like they all see only two buildings, though.
Interesting point!

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n4r9
They all see _at most_ two buildings. You can arrange the circles in a line so
that each sees only one.

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maxk42
Is this the start of a new approach to public-key cryptography?

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throwawaymath
I strongly suspect that any cryptographically suitable problem derived from
finding the intersection points of external tangent lines would reduce to the
closest vector problem on lattices.

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ur-whale
The wikipedia page has mostly geometric proofs. Are there algebraic proofs?

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fibo
I studied it at the University, it was introduced after Pappo's theorem and
other theorem demonstrated using Descriptive Feometry most of all.

On the other end it was a Projective Geometry course and at the end we used a
lot the General Linear Group, in particular 4x4 matrices for bilinear forms,
so it was like warming up with Geometry to arrive to the Algebra tools.

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pvg
He's Pappus in English, for what it's worth.

