Talk:Band model
Add topicLatest comment: 1 year ago by Tamfang in topic Shape of the geodesics?
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Shape of the geodesics?
[edit]What is the general shape of the geodesics, not just the middle horizontal one and the vertical ones? —Kri (talk) 00:15, 24 June 2025 (UTC)
- Is the second image in the article unclear or inadequate? I can say that those with both ends on the same boundary are not circular. —Tamfang (talk) 20:06, 24 June 2025 (UTC)
- Looking at my notes from 2008 (when I independently reinvented the band model, showed it to Vladimir Bulatov who made it more famous, and eventually lost interest). Here is the conversion to the hyperboloid model:
- |y0| < π/2
- y1 = sin(y0)
- y2 = sqrt((1+y1)/(1-y1))
- y3 = 1/y2
- y4 = (y2+y3)/2
- (u,v,t) = ( y4*cosh(x0), y4*sinh(x0), (y2-y3)/2 )
- A geodesic can be defined by au+bv-t = 0, for some (a,b). Hope that helps. —Tamfang (talk) 22:09, 26 June 2025 (UTC)