Joshua Ciappara
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 Feb12 revised Quotient of a category by equality in Grothendieck group edited title Feb10 asked Quotient of a category by equality in Grothendieck group Dec14 comment Is it possible to find the $n$th digit of $\pi$ (in base $10$)? If you believe that we are free to define the values of a function $\mathbb{N} \to \{ 0, \dots , 9 \}$, then you already believe the function exists. In fact, your belief in the function is implicit in the first indented equations. Just because you can't list the function's values (either because you don't know them or you don't have enough time) doesn't mean it doesn't exist. Dec14 comment Is it possible to find the $n$th digit of $\pi$ (in base $10$)? There's nothing wrong with defining a function using words, $f(n) = n$th digit of $\pi$. So certainly there is a function for what you want. Perhaps you're asking for a formula -- but then again you mentioned you don't mind whether we can "explicitly state it". So it's not clear what you're after. Dec10 awarded Popular Question Oct24 accepted Ext groups for fraction field and a module annihilated by an element Oct13 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 $1/\sqrt{2}$. Oct13 comment Infinite staircase to a circle (I'll award the bounty when it becomes possible to do so.) Oct13 accepted Infinite staircase to a circle Oct13 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. Oct12 comment Infinite staircase to a circle It's interesting that if you add those numbers up it's scary close to $\sqrt{2}$. Oct11 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? Oct10 awarded Nice Question Oct10 revised Infinite staircase to a circle edited tags Oct10 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. Oct10 revised Infinite staircase to a circle added 12 characters in body Oct10 comment Infinite staircase to a circle Sorry for the ambiguity. You just alternate between east and north. Oct10 revised Infinite staircase to a circle deleted 386 characters in body Oct10 asked Infinite staircase to a circle Sep30 awarded Explainer