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Pi Clacks

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In 2003 mathematician Gregory Galperin of Eastern Illinois University offered a remarkable way to calculate π: Launch two masses toward an elastic wall, count the resulting collisions, and you can generate π to any precision, at least in principle.

“On the one hand, our method is purely mathematical and, most likely, will never be used as a practical way for finding approximations of π. On the other hand, this method is the simplest one among all the known methods (beginning from the ancient Greeks!).”

The video above, by 3Blue1Brown, gives the setup; the continuation is below. Via MetaFilter.

(Gregory Galperin, “Playing Pool With π (The Number π From a Billiard Point of View),” Regular and Chaotic Dynamics 8:4 [2003], 375-394.)

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frutiger
266 days ago
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As a card-carrying nerd, this is fascinating.
Chapel Hill, NC
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Area Matters

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area matters 1

If you know the vertices of a polygon, here’s an interesting way to find its area:

  1. Arrange the vertices in a vertical list, repeating the first vertex at the end (see below).
  2. Multiply diagonally downward both ways as shown.
  3. Add the products on each side.
  4. Find the difference of these sums.
  5. Halve that difference to get the area.

area matters 2

This works for any polygon, no matter the number of points, so long as it doesn’t intersect itself. It’s a slight restatement of the shoelace formula.

(Thanks, Derek, Dan, and Kyle.)

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frutiger
292 days ago
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This is witchcraft
Chapel Hill, NC
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The Newtek 'Video Toaster' was pretty exciting

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Remember the days before beautiful CGI was everywhere? Newtek's Video Toaster was revolutionary, now largely forgotten.

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frutiger
341 days ago
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Can confirm. This thing was amazing for the early 90's.
Chapel Hill, NC
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Guess what? Bent Objects is back among the living.

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I changed my mind.
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frutiger
600 days ago
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Huzzah!
Chapel Hill, NC
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All Hockey Hair Team

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It's that time of year again folks, time for the 2018 Minnesota State High School All Hockey Hair Team.
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frutiger
603 days ago
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An annual classic
Chapel Hill, NC
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Sheet pan recipes make weird but efficient party food

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Maximize flavor, minimize cleaning.

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frutiger
620 days ago
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Kind of genius, no?
Chapel Hill, NC
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