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Omni-MATH / A set of points of the plane is called [i] obtuse-angled[/i] if every three of…

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problem

A set of points of the plane is called [i] obtuse-angled[/i] if every three of it's points are not collinear and every triangle with vertices inside the set has one angle >91o >91^o. Is it correct that every finite [i] obtuse-angled[/i] set can be extended to an infinite [i]obtuse-angled[/i] set? (UK)
Plain-text mathematical notation (without MathML)
A set of points of the plane is called [i] obtuse-angled[/i] if every three of it's points are not collinear and every triangle with vertices inside the set has one angle >91^(o). Is it correct that every finite [i] obtuse-angled[/i] set can be extended to an infinite  [i]obtuse-angled[/i] set?

(UK)
Original LaTeX notation
A set of points of the plane is called [i] obtuse-angled[/i] if every three of it's points are not collinear and every triangle with vertices inside the set has one angle $ >91^o$. Is it correct that every finite [i] obtuse-angled[/i] set can be extended to an infinite  [i]obtuse-angled[/i] set?

(UK)

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Source and history

task_id
865edb32-cd0a-5516-9473-13f1b8b27cd0
task_key
test--865edb32-cd0a-5516-9473-13f1b8b27cd0
task_revision_id
1
config / split
/ test

Official source

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