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Given N dots uniformly spaced (the arc distance between any two adjacent dots is the same) on the surface of a sphere of radius R, find that distance in terms of N and R. (Assume N is greater than 10.)

R.W. Bird
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  • "Adjacent dots" on a sphere is ambiguous. What would you do with a triangle? Please [edit] to clarify. Include an example. – Ethan Bolker Aug 11 '20 at 14:14
  • @EthanBolker as per the plain statements by OP, you can assume any equilateral triangle on a sphere, For 4 points, you'd need tetrahedral – Anindya Prithvi Aug 11 '20 at 14:17
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    @AnindyaPrithvi Put $4$ points at random on a sphere. Is each then "adjacent" to all three others? If so the the OP wants the tetrahedron to be regular. Put $5$ points on a sphere. How do you specify which pairs are "adjacent"? The OP really must clarify. – Ethan Bolker Aug 11 '20 at 14:21
  • Probably you're looking for this https://qphs.fs.quoracdn.net/main-qimg-8976c3f781fba407affa2bc2809d6c5e.webp – Anindya Prithvi Aug 11 '20 at 14:22
  • The diagrams in the reference from Anindya Prithvi illustrate the uniform distribution. For my question, each triangles would be part of the spherical surface (one per dot) and I want the arc length separating two nearest centers. – R.W. Bird Aug 11 '20 at 16:40

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