Jack TenneyExtra Point

by Jack Tenney, Publisher

January 2012

Having a leap year start on a Sunday is unusual enough to consider numerical permutations. Unless, of course, you wanted to talk about politics.

Here’s the deal on leap years. Most years — three out of four — end on the same day of the week they start on. Leaps, however, being a day longer, end on the day after the day they start on. To have a leap start on a Sunday requires the previous year to start and end on a Saturday.

Because days run in a series of seven, while leaps occur every fourth year, the last time a leap year began on Sunday was 1984 and the next time will be 2040. Multiplying the two series’ intervals yields the answer to how often it happens: every 28 years.

Moving right along to pi (π). I once struggled with the problem of reducing scrap when punching round shapes out of linear strips. No matter how I tried to vary the width of the strip and the spacing of the shapes I couldn’t get the scrap factor to be less than around 25 percent.

Remembering geometry vaguely, the formula for the area of a circle came back to me: pi times the radius squared. Assuming a two-inch-wide strip and wishing to punch out circles with a 1-inch radius (1 being a number I am good at squaring), I saw the problem. The absolute lowest scrap factor I could achieve was, like, 22 percent. Pi, by the way, is the relationship of the circumference of a circle to its diameter, which is why the formula for the circumference is πd.

Which brings me to phi and Mr. Fibonacci. Mr. F’s famous sequence begins 0,1,1,2,3,5,8,13, .... Phi is the so-called Golden Ratio, or something like 1.6180339, which is very much like 1 plus the square root of 5, divided in half. Each permutation of the Fibonacci sequence gets closer to phi (13/8 = 1.625; 21/13 = 1.61538 ...)

Phi is used to explain tons of stuff, like the relationship of your mouth to the distance between your nostrils and their relationship to the length of your face and the change over time of LIBOR (London Interbank offered rate) to the price of West Texas crude.

It’s all a bit spooky, no? But not political. Happy leap year!