Laurens Gunnarsen

@MathPrinceps

Mathematical physicist and mentor to mathematically talented youth. Talent is that which bridges the gap between what can be taught and what must be learned.

Vrijeme pridruživanja: lipanj 2012.

Medijski sadržaj

  1. 12. sij
    Odgovor korisniku/ci

    Nothing compares to this:

  2. 16. lis 2019.
    Odgovor korisnicima

    No woman aiming to compel the attention of the male should contort herself into a simpering push-over, nor should she suppose that a carefully cultivated saccharine neoteny will do the trick. She should rather apprentice herself to this incomparable master.

  3. 9. lis 2019.
    Odgovor korisniku/ci

    It's possible to do better, though -- by which I mean, to make the correspondence clearer between the terms of the series and the areas in the figure. For example, here's how I'd say it should go for r = 2/3. Note the ease of counting the thirds, the ninths, the twenty-sevenths.

    1 proslijeđeni tweet 3 korisnika označavaju da im se sviđa
  4. 8. lis 2019.
    Odgovor korisniku/ci

    Here's a starting point, showing how things go for r = 1/2:

    1 proslijeđeni tweet 6 korisnika označava da im se sviđa
  5. 11. kol 2019.
    Odgovor korisniku/ci

    1 reply 1 proslijeđeni tweet 1 korisnik označava da mu se sviđa
  6. 25. svi 2019.
    Odgovor korisnicima

    Perhaps by juxtaposing the previous picture with this one I can show what I meant (for surely it is clear that the pink equilateral triangles have side lengths equal to one-half the unit length.)

    1 reply 2 korisnika označavaju da im se sviđa
  7. 25. svi 2019.
    Odgovor korisnicima

    I think it might be simpler to focus on the pink equilateral triangles in this picture, which evidently may be shifted slightly so as to stellate the small central square whose area is the fraction required.

    1 reply 1 korisnik označava da mu se sviđa
  8. 22. svi 2019.
    Odgovor korisnicima

    Here's the best way to picture all the (interesting) Pythagorean triples. Also great fun to try to figure out how to extend this indefinitely.

    1 korisnik označava da mu se sviđa
  9. 14. svi 2019.
    Odgovor korisnicima

    "You do know how to whistle, don't you, Steve? You just put your lips together, and blow."

  10. 6. svi 2019.
    Odgovor korisnicima

    Here are some pictures that may be worth sharing with those who are first encountering geometric series. The last one, in particular, is likely, I think, to provoke some interesting conversations.

    6 proslijeđenih tweetova 21 korisnik označava da mu se sviđa
  11. 26. ožu 2019.
    Odgovor korisniku/ci

    This, I think, may be the most efficient means of solution. But the real question is: where does it come from?

    1 reply 18 korisnika označava da im se sviđa
  12. 24. ožu 2019.
    Odgovor korisnicima

    I wonder what your son will think of this picture:

    1 proslijeđeni tweet 11 korisnika označava da im se sviđa
  13. 24. ožu 2019.
    Odgovor korisniku/ci

    Just count:

    3 proslijeđena tweeta 32 korisnika označavaju da im se sviđa
  14. 13. ožu 2019.
    Odgovor korisniku/ci

    It is perhaps worth remarking, as Edward Gibbon once did, that things may go spectacularly awry, even when every conceivable pain has been taken to educate and enlighten one's offspring. Here is Gibbon on Aurelius and his irredeemably vicious son Commodus.

    1 korisnik označava da mu se sviđa
  15. 13. ožu 2019.
    Odgovor korisnicima

    Right: this picture should do the trick. The green triangle is now naturally divided into pieces whose area can be readily expressed in terms of the area of the smallest triangles in the picture. Since 24 of these make up the blue hexagon, this area is 1. Thus, 13 = 3*(6/2) + 4.

    1 proslijeđeni tweet 31 korisnik označava da mu se sviđa
  16. 12. ožu 2019.

    Sorry if the link accompanying my previous remark appeared suspicious; this is what it points to:

  17. 12. ožu 2019.
    Odgovor korisniku/ci

    Perhaps not so much happy as enthralled? I wonder if that counts.

    1 korisnik označava da mu se sviđa
  18. 13. velj 2019.
    Odgovor korisnicima

    A postscript, for those who feel I made the above picture rather more symmetrical than I should have: nothing essential changes in the more general case, as this picture shows.

    4 korisnika označavaju da im se sviđa
  19. 13. velj 2019.
    Odgovor korisniku/ci

    Again, I maintain: always symmetrize! I think this picture makes the whole thing clear.

    1 reply 7 korisnika označava da im se sviđa
  20. 5. velj 2019.
    Odgovor korisnicima

    Pity there's no hint he'll mention what Abel Prize winner Jacques Tits seems to consider the most wonderful thing about 6, namely, that S_6 alone among all the permutation groups has a non-trivial outer automorphism -- which can be visualized using this wonderful figure:

    1 korisnik označava da mu se sviđa

@MathPrinceps još nije poslao/la nijedan tweet s fotografijama ili videozapisima.

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