Cutting a huge polygon

Geometry Level 3

Consider all polygons with 2017 2017 sides.

Is it possible to cut the polygon into 2014 2014 triangles?

Yes, in some cases Yes, always No, never

Áron Bán-Szabó by Áron Bán-Szabó , 17, Hungary

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1 solution

Áron Bán-Szabó
Jun 10, 2017

Suppose it is possible.

Then each angle of the polygon is part of at least one triangle. Since the amount of the polygon's angles is 2015 ∗ 180 ° 2015*180° , we get 2014 ∗ 180 ° ≥ 2015 ∗ 180 ° 2014*180°\geq 2015*180° , but this is not true.

So it is not possible.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

If you check the report, Marta offers a way to get 2 triangles for a concave pentagon.

Do you see the misconception that you made in your solution? In particular, a side of a triangle could contribute towards the sum of internal angles.

Calvin Lin Staff - 3 years, 10 months ago

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