unapologetically one-sided

2 Responses to unapologetically one-sided

1. Anton says:

   Tuesday, 2014 June 24 at 12:58

   The formula is symmetrical enough that I thought the ‘best’ projection point — the point on the 3sphere farthest from the LK surface — would probably be one of the 80 points whose coordinates are permutations of

   • (0, 0, 0, ±1)
   • (0, 0, ±1, ±1) /√2
   • (0, ±1, ±1, ±1) /√3
   • (±1, ±1, ±1, ±1) /2

   i.e. the vertices of a hypercube, the midpoints of its edges and so on.

   I now think that ain’t necessarily so, but don’t know how to search efficiently for a better one.

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2. Anton says:

   Friday, 2014 December 26 at 21:41

   In stereographic projection from (0,0,0,1), the LK surface is asymptotic to
   

   x′ = 4w′y′/(w′²+y′²)
   which in turn is tangent to the planes x′=x/(1-z)=±2, which is the projection of a sphere centred at (0,±1,0,2)/√5; so I tried projecting from there, and am pleased with the result.

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