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Archive for March 14th, 2014

Another snagged feather

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Small White Feather Caught on Dry Grass Stalk 1348A

While I wandered along Brushy Creek near Parmer Ln. on February 21st in the town of Cedar Park, I noticed—not for the first time and not for the last—a small feather that had gotten caught on something, in this case a dry grass stalk. I think the photograph’s overall blue cast is due to the fact that the scene was largely in the shade of the trees that you can make out indistinctly in the background.

I’d originally planned to show this picture in a conventional rectangular cropping, but March 14th, 3/14, happens to be π Day. You’ll recall that π, whose value is about 3.14, is the ratio of the circumference of a circle to its diameter. In other words, if you take a diameter of a circle, bend it to match the curvature of the circle, and lay that curved diameter successively around the circumference, it will fit approximately 3.14 times.

It may surprise you to learn that π turns up in many places that seemingly have nothing to do with circles. How, you wonder, is that possible? Now that I have your rapt attention, let me give you an example. Suppose you have a hardwood floor in one of your rooms, and let’s say that the long planks of wood are 4 inches wide. Imagine you take a 4-inch-long needle and repeatedly toss it onto the wooden floor. More often than not the needle will come to rest touching one of the parallel cracks between the rows of boards. Sometimes, though, the needle will end up in such a way that it’s entirely on a board and doesn’t touch the crack on either side. What are the chances that a tossed needle will touch one of the cracks? It turns out that the chances are 2/π. If you divide 2 by π, you’ll see that that amounts to about 0.637; in other words, if you repeatedly toss a needle that’s as long as the boards are wide, then in the long run the needle will end up touching a crack between the rows of parallel boards about 63.7% of the time.

If you’d like to learn more about this question, which has been called the Buffon needle problem, you can read various articles about it. And while we’re being brainy today, you might also be interested to know that 3/14 was the birth date of Albert Einstein (in 1879).

© 2014 Steven Schwartzman

Written by Steve Schwartzman

March 14, 2014 at 6:00 AM

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