William Rose

@dodecahedra

Washington, DC
Vrijeme pridruživanja: listopad 2009.
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  1. Prikvačeni tweet
    2. lip 2019.

    Something that is very difficult to find anywhere else on the internet -- a clear and precise geometric definition of a limaçon, with explanations of the meaning of each parameter and a description of a polar coordinate system so that one may prove the well-known formula.

    1 reply 14 korisnika označava da im se sviđa
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  2. prije 2 sata

    Homemade 3D-printed and hand-painted snub cube earrings by !!

    12 korisnika označava da im se sviđa
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  3. proslijedio/la je Tweet
    prije 16 sati
    Odgovor korisnicima i sljedećem broju korisnika:

    Yep, that's a really good point. One of the reasons to *choose* a particular codomain is to actually do mathematics on the complement of the image. (Which, as you say, is the entirety of the topology & geometry of knots!)

    1 reply 1 proslijeđeni tweet 4 korisnika označavaju da im se sviđa
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  4. proslijedio/la je Tweet
    2. velj
    Odgovor korisniku/ci

    The time when it should come up, but doesn’t, is during the construction of inverse functions. For f: A→B, modify it to make f’: A’→range(f) (A’⊆A) so that f’ is a bijection. Then f⁻¹ is just f’ with domain and codomain swapped and order within each ordered pair reversed.

    1 proslijeđeni tweet 3 korisnika označavaju da im se sviđa
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  5. proslijedio/la je Tweet
    2. velj
    Odgovor korisnicima

    when i’m reading other people’s work, i interpret equality of functions being defined by having equal domains and codomains, and the images of their domains being equal. this is the only way we could have a notion of a function being intrinsically surjective.

    1 reply 1 proslijeđeni tweet 4 korisnika označavaju da im se sviđa
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  6. proslijedio/la je Tweet
    4. kol 2019.

    Finest curves in geometry: the Astroid ✨

    12 proslijeđenih tweetova 22 korisnika označavaju da im se sviđa
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  7. 2. velj

    Are f: ℝ→ℝ f(x)= x² and g: ℝ→[0,∞) g(x)= x² the same function (only the ordered pairs matter; codomains are not real) or different functions (sorry, but this is how it has to be; non-surjections are a thing)

    35 replies 13 proslijeđenih tweetova 38 korisnika označava da im se sviđa
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  8. 2. velj

    The Sooty Empiric: Truth in the Culture War

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  9. proslijedio/la je Tweet
    30. sij

    Dividing a quadrilateral into two equal areas

    17 proslijeđenih tweetova 58 korisnika označava da im se sviđa
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  10. proslijedio/la je Tweet
    31. sij

    Thanks to an email from a reader, I found a compass and straightedge "angle trisection" online. Spoiler alert: it doesn't. But, I was amazed by how close it was to an actual trisection. The person's construction was pretty complicated, but I distilled it

    8 proslijeđenih tweetova 17 korisnika označava da im se sviđa
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  11. proslijedio/la je Tweet
    30. sij

    one of the best parts of the impeachment process is watching people be like "Republicans think you can win a trial by lying and blocking relevant evidence!" like yes you absolutely can do that, literally every trial is like this, there is no justice and there is no god

    Trumps lawyers should give every lawyer in the country confidence. Know you can simply walk into court and just make shit up!
    31 reply 1.257 proslijeđenih tweetova 8.263 korisnika označavaju da im se sviđa
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  12. proslijedio/la je Tweet
    30. sij

    この機構のある1つの点はアステロイドを描いています アステロイドの媒介変数表示は x=cos(θ)^3 y=sin(θ)^3 これでなんとなく仕組みがわかった方もいらっしゃるかも

    10 proslijeđenih tweetova 41 korisnik označava da mu se sviđa
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  13. proslijedio/la je Tweet
    29. sij

    Dodacedra growing until they fill the hyperbolic space. Each has an inscribed cube. While these cubes do not fill the hyperbolic space (only 40%), the rest can be filled with the same cubes (12-hedron = cube + 6 quartercubes). (Observed by MagmaMcFry in the HyperRogue discord.)

    1 reply 20 proslijeđenih tweetova 66 korisnika označava da im se sviđa
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  14. 29. sij

    It may just not even be possible to clearly state what the range of a function is. Take some 8th degree polynomial which has an absolute maximum at x= (the solution of some 7th degree equation, not expressible in terms of radicals...)

    So here's the distinction between range and codomain. I can't even begin to talk about a function without knowing its codomain. But I can waffle on for hours without caring about its range. 14/n
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    1 reply 1 korisnik označava da mu se sviđa
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  15. proslijedio/la je Tweet
    29. sij

    Here's a graph of Coxeter's loxodromic sequence of tangent circles using this () color scheme.

    1 reply 20 proslijeđenih tweetova 80 korisnika označava da im se sviđa
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  16. proslijedio/la je Tweet
    28. sij

    (Not just any subset, but that's not the important bit here.) Crucial to this is that before I can start talking about the function itself, I *have* to know what A and B are. In other words, a function begins with its domain and codomain and proceeds from there. 13/n

    1 reply 1 proslijeđeni tweet 2 korisnika označavaju da im se sviđa
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  17. proslijedio/la je Tweet
    28. sij

    As you keep zooming in, you think: it's a point! No, it's a line! No, it's a rectangle! No, it's a bunch of points! No... It's a subset of the plane invented by Simon Willerton, which shows that your estimate of the dimension can keep changing as you zoom in more and more.

    13 replies 53 proslijeđena tweeta 257 korisnika označava da im se sviđa
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  18. proslijedio/la je Tweet
    28. sij

    Before you welcome analytic philosophy into your life think back to that drummer friend in high school who wouldn't stop bippity-bapping on everything and ask yourself if you want that but with first-order logic

    9 replies 53 proslijeđena tweeta 292 korisnika označavaju da im se sviđa
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  19. proslijedio/la je Tweet
    27. sij
    Odgovor korisniku/ci

    2 proslijeđena tweeta 32 korisnika označavaju da im se sviđa
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  20. proslijedio/la je Tweet
    26. sij

    323 years ago , Johann Bernoulli challenged Isaac Newton with a six month deadline to solve the problem of the brachistochrone: Newton got the message on January 29 at 4 pm and solved it going to bed that same night [more: ]

    14 replies 254 proslijeđena tweeta 931 korisnik označava da mu se sviđa
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  21. proslijedio/la je Tweet
    26. sij

    This is a recently discovered illusion, and it’s really quite striking. The strange effect is called the ‘curvature blindness’ illusion

    9 replies 371 proslijeđeni tweet 1.223 korisnika označavaju da im se sviđa
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