Museletter the Seventy-ninth

When you hear the phrase "a good mystery," do you think of Agatha Christie and Sherlock Holmes? After all, for most of the past two hundred years, the word mystery was used to indicate a situation in which, if you just searched for all the clues, you could find a solution.

And isn't that supposed to be the promise of science and math, of industry, of modern thought: that there are answers… if you just work hard enough. But it's not true, and the best and simplest example of this is the circle.

You probably remember from school that if you measure the distance around a circle, it's always just a little more than 3 times the distance across the circle. And if you measure really, really carefully, you'll find that it's just about 3.14 times, a number that has long been known by the Greek letter π (pi).

But the real distance around the circle is a tiny bit more: it's 3.1415926… and those three dots mean "and so on," because there is no end to the number. There are mathematical proofs that show π is infinitely long, which means that if you know the diameter of a circle, you literally cannot know its circumference, and vice versa.

To me, this is the ultimate mystery — one with plenty of clues, but no solution. In fact, the more we search, the more questions and mysteries we find about pi.

The past hundred years has uncovered many more wonderful, truly unknowable mysteries, including quantum physics and chaos theory. But next time you want to curl up in front of a fire with a good mystery, you need look no farther than the simple circle.

Pi Day

Quick reminder that the USA is one of the only countries on Earth that writes dates with the month first. This is most obvious when "pi day" comes around — March 14, which is written 3/14 in the US (just as π = 3.14…)

The rest of the world wonders what the big deal is about 14/3… and they have to wait until 22/7 (July 22) for "π approximation" day!?

(Alternatively, we could all celebrate at about 6:30 am on April 26, which is about 1/π-th of the way through the year)

Smells like Pi Spirit

Here are few more awesome pi factoids:

• Measure a long river, from source to mouth, as it twists and turns along a gently sloping plane… and measure the distance "as the crow flies." Divide one by the other and you get: 3.14.
• OK, now let's say you have thousands of little needles, all the same length. And you have a piece of lined paper, where the distance from one line to the next is exactly twice the length of the needles. Throw the needles randomly on the paper, and count how many needles land crossing a line. If you divide the number of needles by the number that cross the line you get: 3.14
• The true math nerds in the audience will appreciate that 1.23456789 to the power 5.4321 = 3.141 (thank you Peter Mansell for sharing that obscurity)
• In the 1996 film Mission Impossible, the secret code that Tom Cruise used to signal the conspirators was "Job 3:14". The name of the East German secret spy organization in Alfred Hitchcock’s Torn Curtain (staring Paul Newman and Julie Andrews)? π, of course.
• One year contains just over π x 10 million seconds.
• What's interesting about the next sentence? (Hint: count the letters) —?"For a time, I stood pondering on circle sizes. The large computer mainframe quietly processed all of its assembly code."

Looks True!

Pi day is a good time to remember that just because something appears to be obviously true, doesn't mean it is.?

Pi is all about curves, like circles, and one of the most common ways to estimate a curved line is by making smaller and smaller straight lines. But while this can work beautifully in some cases, this can also lead to amusingly erroneous results.

For example, look at the image above, which implies that pi must equal 4.

It does appear that the increasingly tiny line segments are approximating the curve as they going up, down, and sideways. But notice that they don't angle diagonally. It's only when you start using triangles that you start to approach 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679…

Thank You!

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