something I did not know about pi
 

Under ideal conditions (uniform gentle slope on an homogeneously erodible substrate), the ratio between the actual length of a river and its straight-line from source to mouth length tends to approach π.[85] Albert Einstein was the first to suggest that rivers have a tendency towards an ever more loopy path because the slightest curve will lead to faster currents on the outer side, which in turn will result in more erosion and a sharper bend. The sharper the bend, the faster the currents on the outer edge, the more the erosion, the more the river will twist and so on. However, increasing loopiness will result in rivers doubling back on themselves and effectively short-circuiting, creating an ox-bow lake. The balance between these two opposing factors leads to an average ratio of π between the actual length and the direct distance between source and mouth.[86]

You know, the "pi" character in my browser looks just like "n". Took me a minute to figure out WTF was going on!

PS aren't the "loops" referred to as "meanders" or something like that?

ETA: Just looked around, the technical term is, in fact, meander.

http://cgz.e2bn.net/e2bn/leas/c99/sc....processes.jpg

That's just freakin irrational!

transcends my thoughts, also! :)

We tried to straighten our creek as kids by cutting into the 10ft bank one shovel width wide for 30ft+ over the summer, once we dug the channel, we choked up the creek's regular flow by placing sticks vertically deep into the bed, then horizontal sticks, then raked leaves like crazy. Once we had a cheap temporary dam, we took out the ends of the channel.

The darn thing went straight for a long time, guess what? It uses its old path now....

Chuck Norris counted to infinity.
Twice.

And when meanders get cut off, Oxbow lakes are fun!

http://www.uleth.ca/vft/Oldman_River/oxbow.jpg

I don't think it's anything special that pi fits in the equations. It's involved itself in a lot of physical manifestations.

And don't forget about slope. The higher the slope the less meandering.

It's as if...mathematics can explain the universe around us... go figure!

Today is National pi Day, and also Albert Einstein's birthday. From the Joy of Pi website, I found this:

Pi and the Length of Rivers
From Fermat's Enigma, by Simon Singh

"Professor Hans-Henrik Stolum, an earth scientist at Cambridge University has calculated the ratio between the actual length of rivers from source to mouth and their direct length as the crow flies. Although the ratio varies from river to river, the average value is slightly greater than 3, that is to say that the actual length is roughly three times greater than the direct distance. In fact the ratio is approximately 3.14, which is close to the value of the number pi... The ratio of pi is most commonly found for rivers flowing across very gently sloping planes, such as those found in Brazil or the Siberian tundra."

Every fisherman knows that intuitively.

If at least one of you guys doesn't own a pocket protector I will be highly shocked....

all hail National pi Day!


now, who remembers which southern state it was that legislated the value of pi equal to be exactly 3.0?

IIRC, it was KY or TN - early 20th century

I liked the pi movie:

<object width="480" height="385"><param name="movie" value="http://www.youtube.com/v/oQ1sZSCz47w&hl=en_US&fs=1&"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/oQ1sZSCz47w&hl=en_US&fs=1&" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object>

wow - did he do a film on e?

how about erf() ?

I think a film about e would be too intense for the general public.