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I am looking for the the method of constructing the midpoint of two points in spherical geometry. The only tools allowed for the construction are a pair of spherical compasses and a spherical ruler.

In Eclidean geometry constructing the midpoint is relatively easy. We are looking for the midpoint of points A and B. We construct two circles on A and B with the radiuses of AB. Then we construct two straight lines. One is through the two intersections of the two circles and one is through A and B. The intersection of these two lines will give the midpoint of A and B.

It is clear that the Euclidean method of construction does not work in Spherical geometry. The circles do not intersect when the distance of our two points exceeds 120°. There is also no solution when their distance is exactly 90°.

How would you construct the midpoint of two points in spherical geomerty?

Thank you

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I'm afraid I can't quite understand your second paragraph. Can you clarify? – Willie Wong Dec 17 2010 at 20:30
The question you have written doesn't make any sense. Please click the "edit" link and change your question into one that is more clear. Alternatively, you may try to ask this question at math.stackexchange.com – S. Carnahan♦ Dec 17 2010 at 20:36
Thank you for your comments, I have reviewed the text of the post. – erdos Dec 17 2010 at 20:55
1 
 Thank you for expanding your question - I think I understand it now. I think it would be better to ask this question on math.stackexchange.com, because MathOverflow is intended for research-level mathematics question. Please read the FAQ page (link at the top) for more explanation about the scope of questions we answer here. – S. Carnahan♦ Dec 17 2010 at 21:00
thank you for your answer – erdos Dec 17 2010 at 21:09

closed as not a real question by S. Carnahan♦ Dec 17 2010 at 20:34

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