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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 24 Aug 2019
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    Viviani's Theorem: in an equilateral △, the sum of the distances from any interior point to the 3 sides is equal to the height of the △pic.twitter.com/ZM5Cb0GBpf

    5:20 AM - 24 Aug 2019
    • 2,598 Retweets
    • 12,314 Likes
    • Sofiane Where Is My Mind... ^Tetra Cube^ Ujjwal Panda 🐼 Gabre Turing Hawking . Infotek3000 Сергій
    55 replies 2,598 retweets 12,314 likes
      1. New conversation
      2. Maths Ed‏ @MathsEdIdeas 24 Aug 2019
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        Replying to @fermatslibrary

        Maths Ed Retweeted Maths Ed

        https://twitter.com/mathsedideas/status/979349140273532929?s=21 …

        Maths Ed added,

        Maths Ed @MathsEdIdeas
        If you break a stick at 2 random points, the #probability that the 3 smaller sticks you now have can form a triangle is 1/4 (a,b and c are perpendiculars to the 3 sides) — The beautiful 'Broken Stick' problem, a 19th century problem from @Cambridge_Uni, first HT Martin Gardner. pic.twitter.com/p253FvQil6
        1 reply 11 retweets 72 likes
      3. ......‏ @rgbxthpkhjm 24 Aug 2019
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        Replying to @MathsEdIdeas @fermatslibrary

        how do you difine at random ? do you break the first one uniformly? and choose one of the sticks and break itat some uniformely random point? or the both points are coosen uniformely and indepedantly in the stick ?

        0 replies 0 retweets 1 like
      4. End of conversation
      1. New conversation
      2. Vincent Pantal 🍩ni‏ @panlepan 24 Aug 2019
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        Replying to @fermatslibrary @GHSMaths

        Alternative proof using the area A of the triangle with the three different orange heights h1, h2, h3. A=blue+pink+yellow A=1/2.side(h1+h2+h3) So: (h1+h2+h3)=2A This generalizes to any convex polygon with equal side lengths or in 3D to any polyhedron with faces of equal area.pic.twitter.com/vyNPGo6W3x

        4 replies 4 retweets 58 likes
      3. Karim TIT‏ @orochigan 24 Aug 2019
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        Replying to @panlepan @fermatslibrary @GHSMaths

        I think you forget to divide by 'side', so that, h1+h2+h3 = (2A)/side = h where h denotes the hight of the equilateral triangle. It's a nice proof 😀, but is more analytical than geometrical 📐.

        1 reply 0 retweets 13 likes
      4. 1 more reply
      1. Gerardo‏ @gerardolaflame 24 Aug 2019
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        Replying to @fermatslibrary

        that’s crazy

        0 replies 0 retweets 7 likes
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      1. Walter Tross  🇪🇺@ 🏠2 ✋ 👑 🦠‏ @waltertross 24 Aug 2019
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        Replying to @fermatslibrary

        which makes for a nice way of visualizing 3 quantities whose sum is fixed

        0 replies 0 retweets 10 likes
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      1. Uvula King‏ @tonyver45 24 Aug 2019
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        Replying to @fermatslibrary

        Now this strikes me as a profound insight. Gotta do some reading!

        0 replies 0 retweets 3 likes
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      1. ......‏ @rgbxthpkhjm 24 Aug 2019
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        Replying to @fermatslibrary

        There is an other way to prove that: the area of the equilateral sums up to the area o the 3 triangles that decomposse the equilateral: each one is defined with a side of the equilateral and the inside point: sum the 3 areas factorize by the equilateral side , and you get it

        0 replies 0 retweets 3 likes
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      1. New conversation
      2. Tebo Guerrero‏ @Tebo_GS 24 Aug 2019
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        Replying to @fermatslibrary

        Only if perpendicular to the sides

        2 replies 0 retweets 3 likes
      3. Tokoonz‏ @Tokoonz 28 Aug 2019
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        Replying to @Tebo_GS @fermatslibrary

        That's what means distance.

        0 replies 0 retweets 0 likes
      4. End of conversation

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