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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. Dave Richeson‏ @divbyzero 28 Sep 2018
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      Really enjoyed working with @TedG to find this "proof without words" of Gregory's theorem on the areas of inscribed and circumscribed regular polygons. See my blog post for details! https://divisbyzero.com/2018/09/28/proof-without-word-gregorys-theorem/ …pic.twitter.com/f0hZ1m8jR6

      1 reply 26 retweets 53 likes
    2. Laurens Gunnarsen‏ @MathPrinceps 3 Oct 2018
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      Replying to @divbyzero @TedG

      It has long been my impression that this theorem you ascribe to Gregory is due originally to Archimedes, and that it was he who first put it to the use you suggest, namely, to approximate pi. Am I the dupe of a folk story?

      1 reply 0 retweets 0 likes
    3. Tom Edgar‏ @TedG 3 Oct 2018
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      Replying to @MathPrinceps @divbyzero

      In the blog post Dave explains that Archimedes used perimeters to approximate the circumference of a circle in order to approximate pi. Gregory used areas and found these formulas relating areas of the associated inscribed and circumscribed polygons. You can use those to get pi.

      1 reply 0 retweets 1 like
    4. Laurens Gunnarsen‏ @MathPrinceps 3 Oct 2018
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      Replying to @TedG @divbyzero

      Thank you for this helpful remark; I'm embarrassed not to have noticed the shift from perimeters to areas here. But my impression is that Archimedes found (and exploited) exactly the same recurrence for the perimeters of inscribed and circumscribed regular polygons. Am I wrong?

      1 reply 0 retweets 0 likes
    5. Tom Edgar‏ @TedG 3 Oct 2018
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      Replying to @MathPrinceps @divbyzero

      Yes. The recurrence for perimeters is the same. It’s not obvious how to show this “without words” though it might be possible. Interested in showing that via a related diagram?

      1 reply 0 retweets 1 like
      Laurens Gunnarsen‏ @MathPrinceps 4 Oct 2018
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      Replying to @TedG @divbyzero

      Very much so! I am aware of a pretty nearly wordless proof for the recursion in the case of the perimeters. I also have some history of success in devising such proofs. Any ideas, right off the top of your head?

      12:17 AM - 4 Oct 2018
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