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MathPrinceps's profile
Laurens Gunnarsen
Laurens Gunnarsen
Laurens Gunnarsen
@MathPrinceps

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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.

Joined June 2012

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    1. James Propp‏ @JimPropp 19 May 2019
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      • Report NetzDG Violation

      1/2 Given a unit square, equilateral triangles of side-length 1 are placed so that each corner of the square coincides with the midpoint of a side of one of the triangles, and the altitude of the triangle passing through that point is aligned with a side of the square, as shown.pic.twitter.com/TatlC9HKRy

      2 replies 5 retweets 19 likes
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    2. James Propp‏ @JimPropp 19 May 2019
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      • Report NetzDG Violation

      2/2 What fraction of the square is not covered by the triangles? I know an algebraic proof that involves some lucky cancellations at the end; I suspect there's a simpler way.

      5 replies 1 retweet 4 likes
      Show this thread
    3. Ian Agol‏ @agolian 19 May 2019
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      Replying to @JimPropp

      This 30-60-90 triangle shows that the square scales by 1/2, the ratio of the two edges.pic.twitter.com/R1ipTg7InF

      4 replies 0 retweets 10 likes
    4. Laurens Gunnarsen‏ @MathPrinceps 25 May 2019
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      Replying to @agolian @JimPropp

      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.pic.twitter.com/BGUt2LKOe2

      1 reply 0 retweets 1 like
    5. James Propp‏ @JimPropp 25 May 2019
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      Replying to @MathPrinceps @agolian

      Laurens, can you say more? It’s a pretty picture but I don’t understand how you shift the pink triangles or how you arrive at the answer 1/4.

      1 reply 0 retweets 1 like
      Laurens Gunnarsen‏ @MathPrinceps 25 May 2019
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      Replying to @JimPropp @agolian

      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.)pic.twitter.com/uvX9T3JmHq

      9:02 AM - 25 May 2019
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      • Alex Kontorovich Ian Agol
      1 reply 0 retweets 2 likes
        1. New conversation
        2. Ian Agol‏ @agolian 25 May 2019
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          Replying to @MathPrinceps @JimPropp

          I get it, nice!

          2 replies 0 retweets 1 like
        3. James Propp‏ @JimPropp 25 May 2019
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          Replying to @agolian @MathPrinceps

          I’m afraid I still don’t get it.

          1 reply 0 retweets 1 like
        4. 1 more reply

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