What is the largest possible number of acute angles

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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
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.
 

1. What is an acute angle?

An acute angle is an angle that measures less than 90 degrees.

2. What is the largest possible number of acute angles in a shape?

The largest possible number of acute angles in a shape is dependent on the number of sides the shape has. For example, a triangle can have a maximum of 3 acute angles, while a square can have a maximum of 4 acute angles.

3. Can a shape have an infinite number of acute angles?

No, a shape cannot have an infinite number of acute angles. As the number of sides of a shape increases, the size of each angle decreases, eventually becoming a straight line and no longer an acute angle.

4. What is the minimum number of acute angles a shape can have?

The minimum number of acute angles a shape can have is 0. A shape with 0 acute angles would be a straight line.

5. Are there any shapes that only have acute angles?

No, all shapes have a combination of acute, obtuse, and/or right angles. A shape with only acute angles would not have any sides longer than the others, which is not possible in a closed shape.

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