arutar

5 ms·

1. 1.▲
   by arutar 22d ago

   Here is some (adjacent, but relevant) context, which has been posted elsewhere but I think is worthwhile to mention again here: https://mathstodon.xyz/@tao/117237320796901560 Especially in recent years the mathematics
2. 2.▲
   The Martian Ideology(nplusonemag.com)

   2 points by arutar 3mo ago|0 comments
3. 3.▲
   by arutar 3mo ago

   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 also rather unwieldy. Essentially, bibliographic data has prov
4. 4.▲
   by arutar 5mo ago

   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, such that the 4 queens and the bishop attack all unoccupie
5. 5.▲
   by arutar 5mo ago

   Unfortunately there are none
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   by arutar 5mo ago

   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 reflection symmetry (already mentioned by an earlier commen
7. 7.▲
   by arutar 1y ago

   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 define: e.g. the Koch snowflake [1] or the graph of
8. 8.▲
   by arutar 1y ago

   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 unit square, we can associate x and y with binary coordina
9. 9.▲
   by arutar 2y ago

   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 are online: [1] [2]. Josh's talk (at least from my persp
10. 10.▲
    by arutar 2y ago

    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 include objects such as the Devil's staircase [
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    by arutar 4y ago

    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.
12. 12.▲
    by arutar 4y ago

    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. Especially in mathematics, having a personal site (that yo
13. 13.▲
    by arutar 4y ago

    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 algebraic numbers to be non-normal. I am pretty sure it
14. 14.▲
    by arutar 4y ago

    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 ergodic theorem, which states for a "nice
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    by arutar 4y ago

    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 + CSS.
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    by arutar 5y ago

    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 gives the (misleading) impression that somehow feature
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    by arutar 5y ago

    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 which is invariant under isometries.
18. 18.▲
    by arutar 5y ago

    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, this "proof" is nice because it converts a non-obvio
19. 19.▲
    by arutar 5y ago

    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) = (x/2, y/2) f2(x,y) = (x/2+1&#
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    Ask HN: Obtaining support for (paid) AWS services that are not working?

    1 points by arutar 5y ago|0 comments
21. 21.▲
    by arutar 6y ago

    Thanks for your comment - that is good to know. I should have looked more carefully into the article before commenting.
22. 22.▲
    by arutar 6y ago

    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 methods are very interesting, and the techniques used here essent