Dtjytyk

Does the Linux kernel need a file system to run?

How to explain what's wrong with this application of the chain rule?

Why does a simple loop result in ASYNC_NETWORK_IO waits?

Is aluminum electrical wire used on aircraft?

Does Doodling or Improvising on the Piano Have Any Benefits?

Moving brute-force search to FPGA

Can I visit Japan without a visa?

Fear of getting stuck on one programming language / technology that is not used in my country

Picking the different solutions to the time independent Schrodinger eqaution

Can the US President recognize Israel’s sovereignty over the Golan Heights for the USA or does that need an act of Congress?

Hero deduces identity of a killer

PTIJ: Haman's bad computer

Why does the Sun have different day lengths, but not the gas giants?

What are the advantages of simplicial model categories over non-simplicial ones?

Can a stoichiometric mixture of oxygen and methane exist as a liquid at standard pressure and some (low) temperature?

Can a Canadian Travel to the USA twice, less than 180 days each time?

Does malloc reserve more space while allocating memory?

Yosemite Fire Rings - What to Expect?

Why would a new[] expression ever invoke a destructor?

How to hide some fields of struct in C?

Is there a way to get `mathscr' with lower case letters in pdfLaTeX?

A social experiment. What is the worst that can happen?

How do apertures which seem too large to physically fit work?

How can "mimic phobia" be cured or prevented?

Giraud's Theorem [on hold]

Proof of an obvious fact about convex polygons.Geometry of spherical triangleConverse of the British Flag TheoremMethod for computing density of points within a polygonInterior angle of spherical polygon given the coordinates of vertices in spherical coordinatesVisualizing $3^3+4^3+5^3=6^3$Euler Characteristic of Spherical PolygonFind an equation for a sphere where a spherical polygon was removedPolygons defined by lengths of sidesCase for Pick Theorem?

-1

$begingroup$

I was wondering how Giraud's Theorem would work for spherical polygon

geometry

share|cite|improve this question

edited 2 days ago

LsPi1313

asked Mar 13 at 16:27

LsPi1313LsPi1313

79

$endgroup$

put on hold as off-topic by Saad, Shailesh, dantopa, darij grinberg, Lee David Chung Lin yesterday

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Shailesh, dantopa, Lee David Chung Lin

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  I presume you mean this and not that? It's always best to write your question so as to actually state the theorem.
  $endgroup$
  – Lee Mosher
  Mar 13 at 18:53
  

  
  
  
  

add a comment | 

-1

$begingroup$

I was wondering how Giraud's Theorem would work for spherical polygon

geometry

share|cite|improve this question

edited 2 days ago

LsPi1313

asked Mar 13 at 16:27

LsPi1313LsPi1313

79

$endgroup$

put on hold as off-topic by Saad, Shailesh, dantopa, darij grinberg, Lee David Chung Lin yesterday

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Shailesh, dantopa, Lee David Chung Lin

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  I presume you mean this and not that? It's always best to write your question so as to actually state the theorem.
  $endgroup$
  – Lee Mosher
  Mar 13 at 18:53
  

  
  
  
  

add a comment | 

$begingroup$

I was wondering how Giraud's Theorem would work for spherical polygon

geometry

share|cite|improve this question

edited 2 days ago

LsPi1313

asked Mar 13 at 16:27

LsPi1313LsPi1313

79

$endgroup$

share|cite|improve this question

edited 2 days ago

LsPi1313

asked Mar 13 at 16:27

LsPi1313LsPi1313

79

share|cite|improve this question

edited 2 days ago

LsPi1313

asked Mar 13 at 16:27

LsPi1313LsPi1313

79

asked Mar 13 at 16:27

LsPi1313LsPi1313

79

asked Mar 13 at 16:27

LsPi1313LsPi1313

79

1 Answer
1

active

oldest

votes

2

$begingroup$

The general theorem, which works for any $n$-gon on the unit sphere, is that the area is equal to $2pi$ minus the sum of the external angles, which can be rewritten as $(2-2n)pi$ plus the sum of the internal angles. I think it's possible to prove this by induction, cutting the polygon into some number of triangles and then using the triangle version in the induction step. It can also be proved as a simple application of the Gauss-Bonnet theorem.

share|cite|improve this answer

answered Mar 13 at 19:04

Lee MosherLee Mosher

51k33889

$endgroup$

add a comment | 

2

$begingroup$

The general theorem, which works for any $n$-gon on the unit sphere, is that the area is equal to $2pi$ minus the sum of the external angles, which can be rewritten as $(2-2n)pi$ plus the sum of the internal angles. I think it's possible to prove this by induction, cutting the polygon into some number of triangles and then using the triangle version in the induction step. It can also be proved as a simple application of the Gauss-Bonnet theorem.

share|cite|improve this answer

answered Mar 13 at 19:04

Lee MosherLee Mosher

51k33889

$endgroup$

add a comment | 

2

$begingroup$

The general theorem, which works for any $n$-gon on the unit sphere, is that the area is equal to $2pi$ minus the sum of the external angles, which can be rewritten as $(2-2n)pi$ plus the sum of the internal angles. I think it's possible to prove this by induction, cutting the polygon into some number of triangles and then using the triangle version in the induction step. It can also be proved as a simple application of the Gauss-Bonnet theorem.

share|cite|improve this answer

answered Mar 13 at 19:04

Lee MosherLee Mosher

51k33889

$endgroup$

add a comment | 

$begingroup$

The general theorem, which works for any $n$-gon on the unit sphere, is that the area is equal to $2pi$ minus the sum of the external angles, which can be rewritten as $(2-2n)pi$ plus the sum of the internal angles. I think it's possible to prove this by induction, cutting the polygon into some number of triangles and then using the triangle version in the induction step. It can also be proved as a simple application of the Gauss-Bonnet theorem.

share|cite|improve this answer

answered Mar 13 at 19:04

Lee MosherLee Mosher

51k33889

$endgroup$

share|cite|improve this answer

answered Mar 13 at 19:04

Lee MosherLee Mosher

51k33889

answered Mar 13 at 19:04

Lee MosherLee Mosher

51k33889

answered Mar 13 at 19:04

Lee MosherLee Mosher

51k33889