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Molson_Hart's profile
Molson Hart
Molson Hart
Molson Hart
@Molson_Hart

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Molson Hart

@Molson_Hart

CEO at http://amazon.com/viahart . CEO at http://edisonlf.com . I tweet about business, e-commerce, supply chain, health, law, & infrastructure

Austin, TX
Joined July 2015

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    1. Alexander Bogomolny‏ @CutTheKnotMath 7 Mar 2018
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      A problem from an old @CruxMathematicorum https://www.cut-the-knot.org/m/Geometry/DiagonalsInPolygon.shtml … #FigureThat #math #geometrypic.twitter.com/HkQ3Mhl2Jc

      2 replies 4 retweets 10 likes
    2. Molson Hart‏ @Molson_Hart 8 Mar 2018
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      • Report NetzDG Violation
      Replying to @CutTheKnotMath

      Assume every diagonal is parallel to a side. Number of unique diagonals for a 2n gon is (2n-3)*n. Sides will have an average of (2n-3)*n/(2n) parallel to it. You can simplify and then round this up to say that some side has n-1 diagonals parallel to it. Including the side, ...

      1 reply 0 retweets 0 likes
    3. Molson Hart‏ @Molson_Hart 8 Mar 2018
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      Replying to @Molson_Hart @CutTheKnotMath

      ...we have n-1+1 parallel line segments, each with a pair of unique vertices (2n total) that are shared with the 2n gon. Let's now attempt to draw the shape, starting with the parallel side, connecting it to the diagonals. 1 side, connect to the first diagonal (+2 sides), second

      2 replies 0 retweets 0 likes
    4. Molson Hart‏ @Molson_Hart 8 Mar 2018
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      Replying to @Molson_Hart @CutTheKnotMath

      Diagonal (+2 sides)... And so on. When you reach the final diagonal you have accumulated 3+(n-1)*2 sides = 2n -1 sides. You have one side left to connect the two vertices but there is no way to do that without overlapping the diagonal completely making it not a diagonal...

      1 reply 0 retweets 0 likes
      Molson Hart‏ @Molson_Hart 8 Mar 2018
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      Replying to @Molson_Hart @CutTheKnotMath

      By contradiction, not all diagonal lines in a 2n gon have a side to which they are parallel.

      6:54 AM - 8 Mar 2018
      1 reply 0 retweets 0 likes
        1. Molson Hart‏ @Molson_Hart 8 Mar 2018
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          Replying to @Molson_Hart @CutTheKnotMath

          My third tweet should say 1+2*(n-1) not 3+2*(n-1) sorry.

          0 replies 0 retweets 0 likes
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