What is the largest possible number of acute angles

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  • #1
What is the largest possible number of acute angles that a 2001-gon (shape with 2001 sides) can have if no two sides cross each other [?]
 
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  • #2
Hurkyl
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Depends on how you measure the angles.

If the angle at a concave vertex is measured externally to the polygon, then I can give you 2000 acute angles, and can probably give you the 2001-st as well.

Hurkyl
 
  • #3
It is possible to make a 2001-gon with 1334 acute internal angles.
 

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