Thursday, February 2, 2017

Wheels Within Wheels

Always fun and intriguing to see math equations come to life in this manner! Wheels within wheels and makes me think of the complex systems of epicycles that Ptolemy had to use to make his Earth Centered model of the Solar System jibe with Astronomical observations...



Fourier Series heading towards the square wave

This animation is used to great effect in the Wikipedia article... 
Fourier Series 

The original source seems to be an excellent piece of Java Script created by Pierre Guilleminot...  Fourier Series Visualization


A great video of Ptolemy's System...
   



An interesting sidelight on Ptolemy and his complicated epicycles is that this approach was the first step in the development of Fourier Analysis or the process of decomposing a periodic function into the sum of simple oscillating functions. Today Fourier Analysis has a vast range of engineering and scientific applications...

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The Great Lake Huron Rock Puzzle

  As a boy, I found this chunk of limestone on the shoreline of southern Lake Huron, Canada near the town of Goderich: The rock is 23 cm (9...