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 Post subject: Sum of internal angles of triangle in Poincare HPPosted: Fri, 10 Feb 2012 04:20:56 UTC
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I just went through the calculations for finding the internal angles of triangle ABC in the Poincare Half-Plane where A(1,1), B(1,2), and C(2,1). I found the sum of the internal angles to be approximately 176.65 degrees.

I'm just looking for confirmation that I did the calculations correctly. Thank you in advance.

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 Post subject: Re: Sum of internal angles of triangle in Poincare HPPosted: Fri, 10 Feb 2012 04:24:37 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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bejou102 wrote:
I just went through the calculations for finding the internal angles of triangle ABC in the Poincare Half-Plane where A(1,1), B(1,2), and C(2,1). I found the sum of the internal angles to be approximately 176.65 degrees.

I'm just looking for confirmation that I did the calculations correctly. Thank you in advance.

That looks right, just a hair short of is usually what you'll get with something like that.

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 Post subject: Re: Sum of internal angles of triangle in Poincare HPPosted: Fri, 10 Feb 2012 04:35:51 UTC
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Joined: Tue, 6 Sep 2011 04:11:20 UTC
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Thank you. Do you know of any website that would have a calculator for working in the halfplane?

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 Post subject: Re: Sum of internal angles of triangle in Poincare HPPosted: Fri, 10 Feb 2012 04:45:25 UTC
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bejou102 wrote:
Thank you. Do you know of any website that would have a calculator for working in the halfplane?

I doubt it.

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 Post subject: Re: Sum of internal angles of triangle in Poincare HPPosted: Fri, 10 Feb 2012 10:34:44 UTC
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bejou102 wrote:
I just went through the calculations for finding the internal angles of triangle ABC in the Poincare Half-Plane where A(1,1), B(1,2), and C(2,1). I found the sum of the internal angles to be approximately 176.65 degrees.

I'm just looking for confirmation that I did the calculations correctly. Thank you in advance.

That is definitely incorrect. The angular defect is , since the angles at A,B,C (assuming you are using the upper half-plane rather than the right half-plane) are respectively.

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 Post subject: Re: Sum of internal angles of triangle in Poincare HPPosted: Fri, 10 Feb 2012 18:17:20 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Location: Austin, TX
outermeasure wrote:
bejou102 wrote:
I just went through the calculations for finding the internal angles of triangle ABC in the Poincare Half-Plane where A(1,1), B(1,2), and C(2,1). I found the sum of the internal angles to be approximately 176.65 degrees.

I'm just looking for confirmation that I did the calculations correctly. Thank you in advance.

That is definitely incorrect. The angular defect is , since the angles at A,B,C (assuming you are using the upper half-plane rather than the right half-plane) are respectively.

And that's why it's good to actually check, in spite of heuristics.

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