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A Cute Dissection (Posted on 2004-08-06) Difficulty: 4 of 5

How can you guarantee that you can cut an obtuse triangle into smaller triangles, all of which are acute? An obtuse triangle is a triangle with one obtuse angle. An acute triangle is a triangle with three acute angles. A right angle is neither acute nor obtuse. If you can find such a dissection, what is the smallest number of acute triangles into which any obtuse triangle can be dissected?

The graphic shows how this obtuse triangle can be divided into almost all acute triangles except one - the blue one. What approach should be used when one must cut an obtuse triangle into acute triangles only?

No Solution Yet Submitted by SilverKnight    
Rating: 2.7500 (4 votes)

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Question re: Answer in seven | Comment 2 of 6 |
(In reply to Answer in seven by Old Original Oskar!)

Oskar,

That is a method to follow.

Would you care to explain why it works, or how you know it will work?  And how you know it's the smallest number of acute triangles that will work?
  Posted by Thalamus on 2004-08-06 16:47:22

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