Talk:Band model

	This article is rated Start-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects:
Mathematics This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks. ??? This article has not yet received a rating on the project's priority scale.

Shape of the geodesics?

Latest comment: 2 months ago3 comments2 people in discussion

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)Reply

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)Reply

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)Reply