Comments on: Rotation numbers and the Jankins-Neumann ziggurat

By: Group Theoretic Origin of the Domino Height Functions « monsieurcactus

Group Theoretic Origin of the Domino Height Functions « monsieurcactus — Thu, 12 Apr 2012 15:32:52 +0000

[...] Rotation Numbers and the Jankins-Neumann Ziggurat [...]

By: Ziggurats and the Slippery Conjecture « Geometry and the imagination

Ziggurats and the Slippery Conjecture « Geometry and the imagination — Sat, 29 Oct 2011 12:41:55 +0000

[...] couple of months ago I discussed a method to reduce a dynamical problem (computing the maximal rotation number of a prescribed [...]

By: Danny Calegari

Danny Calegari — Wed, 24 Aug 2011 07:04:14 +0000

I should definitely put a better picture here at some stage. Let me explain in words for now: the r and s axes are “horizontal” in the picture, and R is “vertical”. Now, it turns out that R(r,s)=1 for r+s<1; those values of R should be represented by a "flat" triangle at the front of the figure (which has been omitted). The straight (horizontal) line at the front is r+s=1; note that R(p/q,(q-p)/q) = 1+1/q, so there is a vertical line of height 1/q at each point (p/q,(q-p)/q) (these end at the vertices of the "cubes"). There is an order 3 symmetry in the figure, coming from the order 3 symmetry of F_2 interchanging a,b,AB.

By: Ian Agol

Ian Agol — Wed, 24 Aug 2011 03:23:15 +0000

Maybe you could label the ziggurat diagram, explaining where the r and s axes are?

By: Walking Randomly » 80th Carnival of Mathematics

Walking Randomly » 80th Carnival of Mathematics — Sun, 14 Aug 2011 01:28:00 +0000

[...] Terence Tao gives us a geometric proof of the impossibility of angle trisection by straightedge and compass while the Geometry and the imagination blog discusses Rotation numbers and the Jankins-Neumann ziggurat. [...]