March 14, 2015

It's March 14, 2015, & it's π day!

March 14, 2015, is the last day the U.S. date will align with the first five digits of pi (3,1415) until 2115.
photos by Styrous®

 The circumference of a circle is slightly more than three times as long as its diameter.
The exact ratio is called π.

π can be computed from the Mandelbrot set, by counting the
number of iterations required before point (−0.75, ε) diverges.


mathematical constant π

Because π is a transcendental number, squaring the circle is not possible in a finite number of steps using the classical tools of compass and straightedge.


π can be estimated by computing the perimeters of circumscribed and inscribed polygons. Check out the humorous article, Prehistoric Calculus: Discovering Pi, by Kalid Azad who makes use of these polygons to demonstrate π (link below).  


Sine and cosine functions repeat with period 2π

A graph of the Gaussian function
ƒ(x) = ex2. The colored region between the function and the x-axis has area  \sqrt{\pi} .

Random dots are placed on the quadrant of a square with a circle inscribed in it.

Links to info about :                             
Why Pi Matters - The New Yorker     
NBC News     

Styrous® ~ Saturday, March 14, 2015

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