Tag Archives: complex numbers

Sideband #62: Quaternions

Folded into the mixed baklava of my 2018, was a special mathematical bit of honey. With the help of some excellent YouTube videos, the light bulb finally went on for me, and I could see quaternions. Judging by online comments I’ve read, I wasn’t alone in the dark.

There does seem a conceptual stumbling block (I tripped, anyway), but once that’s cleared up, quaternions turn out to be pretty easy to use. Which is cool, because they are very useful if you want to rotate some points in 3D space (a need I’m sure many of have experienced over the years).

The stumbling block has to do with quaternions having not one, not two, but three distinct “imaginary” numbers.

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Beautiful Math

Take a moment to gaze at Euler’s Identity:

Eulers Identity

It has been called “exquisite” and likened to a “Shakespearean sonnet.” It has earned the titles “the most famous” and “the most beautiful” formula in all of mathematics, and, in a mere seven symbols, symbolizes much of its foundation.

Today we’re going to graze on it!

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