I have always had a strange fascination with Pi - π. (The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi".)
I guess it all started with Carl Sagan's book "Contact" where scientists found a strange message hidden very, very, very deep inside this infinite number that turned out to be a message from God! (This was not addressed in the movie with Jody Foster, but it was basically a code, that when opened formed a perfect circle, thereby confirming that Someone, or Something, had woven this equation into the very fabric of the Universe!)
Since then I have looked into this strange number several times:
AND FINALLY:By James Grime:
Of the many weird and wonderful facts about pi, one of my favourites is a surprising connection between the number 3.14 and the world around us. It’s about rivers. Or more precisely, the bendiness of rivers.
As you will know, some rivers are relatively straight while other rivers twist and turn across the landscape like the scribble of someone checking if their pen is dry.
You can measure how “bendy” a river is by measuring its total length and dividing by straight route from its source to mouth, this measure is called “sinuosity”. So a totally straight river would have a sinuosity of 1, while very bendy rivers can have very high sinuosity, with no limit to how high it can go.
Yet, it is claimed the average sinuosity of rivers around the world is pi.
This is an incredible fact, and if true means that rivers are typically a little over three times longer than the direct route from source to mouth. Of course some rivers are straighter, and some rivers are longer, but the average sinuosity is around 3.14.
The result was first published in Science, dated 22 March 1996 (eight days after that year’s Pi Day – gutted). In a paper titled River Meandering as a Self-Organization Process, Hans-Henrik Stølum, used empirical data and simulation to study the chaotic behaviour of a river’s form over time, noting that the value of sinuosity tended to oscillate between a low-value of 2.7 and a high-value of 3.5, but with an average sinuosity of 3.14.
Stølum justified this result using fractal geometry. This is the idea that if the bends of a river can be approximated by arcs of circles, and the little wiggles of a river by arcs of smaller circles, then the sinuosity of the river can be calculated to be pi.
I was fascinated by this paper and last year presented a Numberphile video about it:
Want some more?