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Oct
13
comment Infinite staircase to a circle
I'm satisfied that $x_\infty$ is not a remarkable number with a simple closed form. Of course I'd welcome more information on its properties, and maybe the previous sentence is actually in error (despite my checks at the OEIS), but I think viewing things from the perspective of $1/k$ suggests it's just "some number" in a certain sequence converging to $1/\sqrt{2}$.
Oct
13
comment Infinite staircase to a circle
(I'll award the bounty when it becomes possible to do so.)
Oct
13
accepted Infinite staircase to a circle
Oct
13
comment Infinite staircase to a circle
This is a great answer, thanks. I guess heuristically it explains why we get so close to $\sqrt{2} = 2 \cdot \frac{1}{\sqrt{2}}$ when adding up the co-ordinates for the $k = 2$ case.
Oct
12
comment Infinite staircase to a circle
It's interesting that if you add those numbers up it's scary close to $\sqrt{2}$.
Oct
11
comment Infinite staircase to a circle
Hi guys, thanks for all your comments. I think the most concrete progress has been Paul's provision of the recurrence relations. Can anyone see if they might be solvable analytically?
Oct
10
awarded  Nice Question
Oct
10
revised Infinite staircase to a circle
edited tags
Oct
10
comment Infinite staircase to a circle
Not sure what you mean by rush the border... If you draw a picture it's visually apparent that you'll approach some point on the circle. The distances you travel in each step get shorter and shorter.
Oct
10
revised Infinite staircase to a circle
added 12 characters in body
Oct
10
comment Infinite staircase to a circle
Sorry for the ambiguity. You just alternate between east and north.
Oct
10
revised Infinite staircase to a circle
deleted 386 characters in body
Oct
10
asked Infinite staircase to a circle
Sep
30
awarded  Explainer
Sep
30
answered Ext groups for fraction field and a module annihilated by an element
Sep
24
comment $n$-th order derivatives of multivariable composites
I'm not sure who downvoted this, but if it was one of the answerers: I appreciate your response, but you haven't provided a complete answer in one way or another, so I haven't ticked you. Ending posts with "moral" or "overall" is not what I was looking for.
Sep
24
asked Ext groups for fraction field and a module annihilated by an element
Sep
17
asked $n$-th order derivatives of multivariable composites
Jul
2
awarded  Curious
Jun
3
revised Superharmonic functions, Barriers - Complex Analysis (Conway)
woops brief fix