Viewing profile — arutar

I think Zotero is an excellent tool and I used it for a long time. However, like the author, I also felt that Zotero was not the ideal tool for me. But a straight BibTeX file is al…

Thanks for sharing such an entertaining problem! Bonus problem: find an arrangement of 4 queens on the board such that: 1. There is exactly 1 square on which a bishop can be placed…

Unfortunately there are none

More fun facts: After identifying solutions up to rotation and reflection there are only 49 solutions. No solutions have rotational symmetry, and there is exactly one solution with…

Once one exists the realm of differentiable manifolds, it is not really reasonable to talk about a single notion of 'dimension'. Topological dimension is indeed something one can d…

Here's another way that I like to think about it. First, forget briefly about the Hilbert curve and just think about the unit square [0,1]^2. If you take any point (x,y) in the uni…

This is a very phenomenal result and everyone in the field is excited about this! Josh and Hong both gave talks about this at a conference 2 weeks ago in Berkeley, and the videos a…

This is a reasonable candidate for a notion of a "Fractal" but these days it is generally accepted that there is no universal definition. For instance, this definition would not in…

That's a fair point, more precise phrasing would be "If you prefer a command-line interface, ..." which should be sufficiently vague to make almost everybody happy.

It’s cool to see this on HN. I originally wrote this article for a “microcourse” I ran at the University of St Andrews—aimed at a non-tech background—on building a personal webpage…

You're absolutely correct---countable sets have probability zero (with probability 1 a uniformly random number in [0,1] will irrational), and it would not be contradictory for all …

Results like this are a lot of fun, and like many a reasonable number of cool results in number theory, are "surprisingly easy". There's a proof only using two ideas: 1) Birkhoff e…

https://rutar.org A site to host my research, and some miscellaneous blog posts. I also have a recipes site: https://food.rutar.org They're all made using Zola, "compiled" to HTML …

I'm not sure why this is not mentioned in the article, but there is nothing special about circles and squares (or 2 dimensions, for that matter). If anything, phrasing it like this…

Would you be able to elaborate a bit what you mean here? There is no version of Banach-Tarski in two dimensions - you can prove that there exists a finitely additive set function w…

This is fair - there are a decent number of details omitted here. However, a lot of the details are hidden inside the proof that an IFS has a unique fixed point. At least to me, th…

Here's a quick proof as to how it works. Suppose the triangle has endpoints (0,0), (1,0), and (1/2, sqrt(3)/2). Given a point (x,y), the three transformations then become f1(x,y) =…

What is the best way to resolve issues with AWS services that are not working properly? I am asking this question in general, though I am motivated by my following (hopefully repre…

Thanks for your comment - that is good to know. I should have looked more carefully into the article before commenting.

I had the privilege to take a linear programming course with Bill, back when he still taught at the University of Waterloo. He spent some time discussing the TSP. TSP solving metho…