Sunday, February 14, 2016

Most Beautiful Mathematical Equations

http://www.bbc.com/earth/story/20160120-you-decide-what-is-the-most-beautiful-equation-ever-written

One of  the equations is Euler's: e^(i*pi)+1=0. Looks nice.The explanation / proof is here. Another is here.

Another interesting equation is the logistics equation: x[n+1]=r.x[n](1-x[n]) where x[n] should be read as x with subscript n.


A quote from the BBC article: 
"How the population behaves turns out to be enormously sensitive to the value of r, in counterintuitive ways. If r is between 0 and 1 the population will always die, but if it is between 1 and 3 the population will approach a fixed value – and if it is above 3.56995 the population becomes wildly unpredictable." 
I guess it  doesn't matter what the initial value of x is.

Additional reading:

http://vbala99.blogspot.com/2010/12/maths-puzzle-5.html

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