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fermatslibrary's profile
Fermat's Library
Fermat's Library
Fermat's Library
@fermatslibrary

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Fermat's Library

@fermatslibrary

A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv: https://fermatslibrary.com/librarian 

fermatslibrary.com
Joined September 2015

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    Fermat's Library‏ @fermatslibrary 25 Jun 2018
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    Here's a curious mathematical constant: the Universal Parabolic Constant - the ratio, for any parabola, of the arc length of the parabolic segment formed by the latus rectum to the focal parameterpic.twitter.com/VymK9DyUcA

    5:58 AM - 25 Jun 2018
    • 412 Retweets
    • 1,693 Likes
    • Brandon Yowakim 名 SilentDead Luanna Ochoa big fax 📠🇨🇴 Josue Parra Benjamin Lamont Amer Yaghi jacob
    17 replies 412 retweets 1,693 likes
      1. Tamás Görbe‏ @TamasGorbe 25 Jun 2018
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        Replying to @fermatslibrary

        It should read L₂/L₁. For y=x² the focal length is 1/4 so L₁=1/2 and the arc length from x=-1/2 to x=1/2 is L₂=(ln(1+√2)+√2)/2. Its universal, because all parabolas can be obtained from y=x² by shifting or scaling as explained by @standupmaths here: https://youtu.be/hoh4TmPzu1w .

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      1. DℝOℕ∈‏ @d_r_o_n_e 25 Jun 2018
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        Replying to @fermatslibrary

        Expected distance from a randomly selected point in the unit square to its center (square point picking) is P/6 (where P is Universal Parabolic Constant = √2 + ln (1 + √2) Lindemann-Weierstrass Theorem shows that Universal Parabolic Constant is Transcendental Number.

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      1. Adam Wagner‏ @Adam__Wagner 25 Jun 2018
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        Replying to @fermatslibrary

        pic.twitter.com/O9K7m7U7OZ

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      1. David Gunter‏ @dogunter 25 Jun 2018
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        Replying to @fermatslibrary

        l1 is twice the focal length, say 2P. The latus rectum is always 4P (the blue line). l2 is to be longer than the blue line, thus larger than l1. Your fraction has to be less than 1 or you have it the other way around.

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      1. Taylor Hodge‏ @jtaylorhodge 25 Jun 2018
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        Replying to @fermatslibrary

        Seems like the ratio is backwards in the image; l_1 and l_2 should be inverted, no?🤔

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      1. New conversation
      2. hassan‏ @hbou 25 Jun 2018
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        Replying to @fermatslibrary

        Do you think this is a sign?

        1 reply 0 retweets 0 likes
      3. JC Rock‏ @thefuzak 25 Jun 2018
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        Replying to @hbou @fermatslibrary

        pic.twitter.com/yEX1lLKimZ

        1 reply 0 retweets 0 likes
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      1. Shiban Lal Pandita‏ @lal_shiban 25 Jun 2018
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        Replying to @fermatslibrary

        The problem however is: How to find d multiple of 2.2955....

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      1. Stealth.py‏ @NeemeshYadav 25 Jun 2018
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        Replying to @fermatslibrary

        Oh wow that is just so unknown

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      1. Cynthia Garde‏ @cygarde 26 Jun 2018
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        Replying to @fermatslibrary

        Great pic illustrating ratio variables clearly (Parabolic chord : 2a). My quick look up: http://mathworld.wolfram.com/LatusRectum.html …

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