The beauty of number π (PI)

&#960 (PI) approximation day


The following Wednesday 22 July the &#960 (PI) celebration day will be celebrated worldwide. The date was selected because 22 July also written as 22/7 is equivalent to 3.14285714286 which is very closest to the value of &#960 (3.14159265359); a difference of only 0.00126448926 or 0.04 % of the true &#960 value.
It is well known that &#960 is an irrational number (It can't be written exactly as a fraction or decimal number) that represents the ratio of a circle's circumference to its diameter. &#960 has several applications in our life. Some field where &#960 is commonly applied are:
  • Geometry: The simplest place &#960 is used is in finding the circumference or area of a circle. Of course, finding circumferences and areas can be useful in the real world. For instance, if you know the radius of a wheel and count the number of times the wheel turned, then it is possible to estimate the traveled distance and the speed (if you measure the time).
  • Signals: Sine waves have a fundamental period of 2*&#960, so &#960 becomes vital in signal processing, spectrum analysis. 
  • Probability: Everyone's favorite distribution (normal or Gaussian) has &#960 in the formula, and it is used in all areas of engineering to simulate unknown factors and loading conditions
  • Navigation: When planes fly great distances they are actually flying on a arc of a circle. The path must be calculated as such in order to accurately gauge fuel use, etc. Additionally, when locating yourself on a globe, &#960 comes into the calculation in most methods.
The beauty of PI as art
However, most of us did not realize that &#960 can be viasualized and it really is a very beautiful number.
Scientist Martin Krzywinski and artist Cristian Ilies Vasile published some visualizations of &#960. First, each digit of pi is represented by a dot of a different color and then these colored dots into a spiral. Then, series of circular representations of pi where the numbers are connected across the circle with a chord were created. New visualizations of &#960 were recently developed considering treemaps and paths.

The following images show some of the visualizations showing the beauty of &#960. The video has a more detailed explanation about the visualization process.

Image 1. Some &#960 visualizations made by Krzywinski and Vasile


In this video you can see an explanation of this visualization.

References & further reading
Visualizing PI
10 stunning images show the bauty hidden in pi
PI is beautiful

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