Shaping Traffic Jams
Ever wait forever in a traffic jam, only to find that when you finally get clear there was no apparent reason for it? You might have experienced a phantom traffic jam. William Beaty performs some traffic experiments and talks quite eloquently about how to help the situation.
I distinctly recall my father, while on our annual pilgrimage to the east coast, always did what he called "pacing". Being a mathematically (and otherwise) intelligent man I think he came to the same conclusion that others have: a smooth flowing line of traffic will move more cars.
So if you find yourself stuck in a jam, try to leave some extra space in front of you - by doing so you will allow your braking to be less severe and thus cause fewer people behind you to spread the wave of stopped traffic backward.
Imaginary Numbers Explained
I just read a fascinating article about the square root of -1 (or commonly known as i) over at one of the more geeky blogs I read: Good Math, Bad Math. History + Math + Complex Concepts That Make Me Feel Smart = Happy Mike:
It got its name as the imaginary number as a result of a diatribe by Rene Descartes, who believed it was a phony artifact of sloppy algebra. He did not accept that it had any meaning at all: thus it was an "imaginary" number.
...
Once the reality of i as a number was accepted, mathematics was changed irrevocably. Instead of the numbers described by algebraic equations being points on a line, suddenly they become points on a plane.
I'm not sure if I understand i any better, but I certainly enjoyed reading about it.
Happy Pi Day!
3/14 is that one magical day where we can celebrate Pi, 3.1415926535 ... you get the idea. Here are a few tidbits about this "magical" irrational number:
- Ten decimals are sufficient to give the circumference of the earth to a fraction of an inch.
- You can find your hat size by measuring the circumference of your head, divide by Pi, then round off to the nearest 1/8th inch.
- The earliest known record of an individual realizing that the ratio between a circle's circumference and it's diameter is constant comes from an Egyptian scribe named Ahmes in 1650 BCE.
- The Romans often stubbornly used an estimation of 3 and 1/8th for Pi (even though they clearly knew that 3 and 1/7th is a closer estimation). They reasoned that it was eaiser for their legions to determine 1/2 of 1/2 of 1/2 instead of 1/7th.
Most of this information is from The Joy Of Pi by David Blatner. Take a closer look at the Pi image on the right.
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