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Internal angles of a triangle

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Amadeus
592168.  Thu Jul 30, 2009 8:50 am Reply with quote

Hi everyone.

This is my very first post on these forums, although I sincerely hope it won't be my last. :)
I really want to see how many of you know the answer to this question:

What do the internal angles of a triangle always add up to?

 
Moosh
592178.  Thu Jul 30, 2009 8:57 am Reply with quote

That depends what you mean by triangle.

 
Amadeus
592188.  Thu Jul 30, 2009 9:03 am Reply with quote

A geometric shape with 3 distinct, straight sides.

 
Davini994
592195.  Thu Jul 30, 2009 9:12 am Reply with quote

Welcome to the forums Amadeus!

I'll give the answer less than 180 degrees. I've assumed that you are talking about in hyperbolic geometry, yes? ;)

 
Moosh
592202.  Thu Jul 30, 2009 9:17 am Reply with quote

Well you could equally say greater than 180 degrees, if the triangle is on a convex surface.

And welcome to Qi Amadeus.

 
Amadeus
592203.  Thu Jul 30, 2009 9:18 am Reply with quote

Davini994 wrote:
Welcome to the forums Amadeus!

I'll give the answer less than 180 degrees. I've assumed that you are talking about in hyperbolic geometry, yes? ;)


Thanks Davini!

I'll let this question simmer for a little bit before giving an explicit solution.

 
Susannah Dingley
592208.  Thu Jul 30, 2009 9:27 am Reply with quote

I prefer to say “π radians” (Euclidean geometry), “less than π radians” (hyperbolic geometry) or “more than π radians” (elliptic geometry).

 
CB27
592233.  Thu Jul 30, 2009 9:56 am Reply with quote

42

 
Amadeus
592245.  Thu Jul 30, 2009 10:05 am Reply with quote

(I just posted the answer but I just thought that maybe I should wait if more people want to come and have a go at the puzzle. What do you think?)

 
Jenny
592261.  Thu Jul 30, 2009 10:32 am Reply with quote

Welcome, Amadeus :-)

 
samivel
592282.  Thu Jul 30, 2009 11:49 am Reply with quote

Welcome :)

 
ColinM
592293.  Thu Jul 30, 2009 12:17 pm Reply with quote

I'm with Susannah; degrees are an unnatural heresy not worthy of inclusion in serious mathematics. Still, at least they're better than grads. Oh, and I'd add that the sum will in all cases be at least 0 and at most 2π.

 
Moosh
592297.  Thu Jul 30, 2009 12:21 pm Reply with quote

Not sure on your at most 2π Colin. Try drawing a triangle on the surface of a sphere, it's pretty easy to get one with interior angles greater than 2π.

 
ColinM
592305.  Thu Jul 30, 2009 12:52 pm Reply with quote

Sorry, yes. I guess the upper bound would be 6π.

 
Posital
592516.  Thu Jul 30, 2009 5:20 pm Reply with quote

ColinM wrote:
Sorry, yes. I guess the upper bound would be 6π.
I can imagine special cases where there would be no upper bound - but the geometry would be potentially discontinuous and/or require four dimensions.

 

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