Möbius Transformations Visually Explained

I know that most of you out there couldn’t care less about the math stuff I am about to put up, but I thought some of you might like it more than you’d think. The video I came across (ready to be shown below courtesy of YouTube) does a great job of visually demonstrating how in mathematics one can examine what seems to be an odd collection of unrelated phenomena or behaviors (in this case, Möbius transformations) and by looking a dimension or two higher suddenly see them as not only related but as much simpler phenomenon than they first appeared to be.

(Spiritually, I suspect there will be a lot of realizations like this about our own lives that will occur after the first resurrection (Revelation 20:5) when we will be able to see all things from a perspective that now escapes us in this life. As Paul says in 1 Corinthians 13:12, “For now we see in a mirror, dimly, but then face to face. Now I know in part, but then I shall know just as I also am known.”)

Here it is:

Pretty sweet! Many thanks and kudos to Douglas N. Arnold and Jonathan Rogness who apparently put the video together.

3 thoughts on “Möbius Transformations Visually Explained

  1. Banjoben

    Pretty cool. It’s actually a bit ironic that you mention this now because it just came up last week in a paper I’m reading about symplectic sums.

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