Pendulum Waves

This week’s entry in the “Wow, the Internet is Awesome!” file:

These pendula of staggered lengths are set swinging, and the result is fascinating.  At first, the weights seem to trace out sine waves, but they quickly start to cycle through a wide range of behaviors.

At times the pendula appear highly organized, and at times almost chaotic, as they cycle through various patterns.  Amazingly, the weights eventually return to their initial state!

A really beautiful mathematical demonstration.

Applications of Mathematics

This is an amazing resource from the British Columbia Institute of Technology:  a cross-referenced list of how various mathematical ideas are used in various technology fields.

Interested in how Linear Algebra can be applied to Nuclear Medicine?  Or how Logs and Exponentials can be applied to Forestry and Wildlife?  Or how Differential Equations can be applied to Mechanical Engineering?

Well, look no further!

Mobius Transformation Video

Not only is this visualization of generalized Mobius transformations mesmerizing and beautiful, it is the clearest demonstration of inversion that I have ever seen:

This short movie visually explains all the basic transformations of the plane:  translation, rotation, dilation, and inversion.  Then it demonstrates how all of these transformations of the plane can really be thought of as simple translations and rotations of the sphere!

If I had seen this video a few decades ago, I might not have given up on topology as quickly as I did.


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