Robin Houston

@robinhouston

Cofounder of . Also maths. Blogging sometimes at . My name is an anagram of “No enthusiasm or job”.

London
Vrijeme pridruživanja: travanj 2009.

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  1. Prikvačeni tweet
    27. ruj 2019.

    This tweet contains exactly four As, one B, three Cs, two Ds, thirty-two Es, six Fs, one G, five Hs, twelve Is, one J, one K, three Ls, one M, twenty-one Ns, sixteen Os, one P, one Q, five Rs, twenty-five Ss, twenty-one Ts, two Us, seven Vs, nine Ws, five Xs, six Ys, and one Z.

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  2. prije 24 sata

    One of those apt juxtapositions that Twitter occasionally throws up.

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  3. 31. sij

    I don’t agree – I think the 10,000 year clock is a better use of time than most of the things people do – but this article is well-written and thought-provoking.

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  4. proslijedio/la je Tweet
    30. sij

    Here it is!! To me this is so good

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  5. proslijedio/la je Tweet
    30. sij

    [1/2] Now that the ingenious has posted linkages that compute both squares and cubes, I thought it would be fun to reverse-engineer the squaring one. If you want to work through this in detail yourself, note that all lengths are multiples of 1/16. The magic here…

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  6. 30. sij

    I just found out that there’s a clever, fairly new algorithm for multiplying matrices by Karstadt and Schwartz that looks like it might be faster in practical situations. Sadly it looks as though they have patented it.

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  7. proslijedio/la je Tweet
    25. sij

    1961: Alan Whicker got lost in Northumberland.

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  8. proslijedio/la je Tweet
    27. sij

    The linkages that comes up with are amazing! Having animated some graphs myself, I know how tricky it can be to find nice paths through the configuration space … but keeps inventing new and delightful examples.

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  9. proslijedio/la je Tweet
    26. sij

    At the very least, I learned that the Fourier coefficients of (the natural parametrization of the boundary of) the Mandelbrot set are rational, which I think is wonderful.

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  10. proslijedio/la je Tweet
    27. sij
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  11. 26. sij

    So p is the sum of a square and four times a square – but four times a square is still a square!

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  12. 26. sij

    Now consider the transformation that rotates the windmill arms by 90°. This doesn’t change the area either. Since there are an odd number of windmills of area p, the arm-rotation transformation must also have a fixed point, i.e. there must be a windmill with square arms.

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  13. 26. sij

    So… if p = 4k + 1 is prime, there are an *odd* number of windmills with area p.

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  14. 26. sij

    There is at most one cross-shaped windmill with a given prime area, since the width of the arms must divide the total area (of a cross-shaped windmill). If p = 4k + 1 then there exists a cross-shaped windmill of area p (with four arms of width 1 and length k).

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  15. 26. sij

    The idea, briefly, is: The transformation illustrated transforms every windmill to a different windmill of the same area; cross-shaped windmills (whose arms are the same width as the central square) are mapped to themselves.

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  16. 26. sij

    This was posted to Math Overflow in 2018, but I just found it via a comment on ’s video , which also explains this proof.

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  17. 26. sij

    You know Zagier’s brilliant-but-baffling “one sentence proof” that every prime of the form 4k+1 is the sum of two squares? It turns out there’s a lovely intuitive explanation of it!

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  18. 24. sij

    I was wondering whether anyone has conducted an experimental test of the hypothesis that a rolling stone gathers no moss. It turns out have done more or less the experiment I was imagining, and confirmed the hypothesis.

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  19. proslijedio/la je Tweet
    24. sij

    [1/2] My new eBook, INSTANTIATION, has 11 stories: • “The Discrete Charm of the Turing Machine” • “Zero For Conduct” • “Uncanny Valley” • “Seventh Sight” • “The Nearest” • “Shadow Flock” • “Bit Players” • “Break My Fall” • “3-adica” • “The Slipway” • “Instantiation”

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  20. 23. sij

    An intriguing mystery I know nothing about – but maybe one of my clever & knowledgeable followers has some insight?

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  21. proslijedio/la je Tweet
    21. sij

    This, my Numberphile debut, is about van der Waerden's theorem, including a proof (presented informally of course) for the case of two colours and progressions of length 3. It was fun to do, and my interviewer added some beautiful graphics afterwards, as is his wont.

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