
Understanding Quaternions (2012) - yati
http://3dgep.com/?p=1815
======
thearn4
Where the author talks about imaginary numbers being completely "made up" and
suggests you shouldn't bother with trying to understand them, I think that's
selling them short.

Imagine, if you will, trying to explain to the ancient Greeks the idea of a
number that can't be written as a division of integers (the irrational
numbers). That would have seemed completely "made up" to them, but we don't
really see them that way, they just "are". That concept is has since become
normalized, in terms of everyday concepts (like the area of a unit circle).
Similar situations arise with fractions or negative numbers to some indigenous
tribes, etc.

I guess what I'm saying is that complex numbers only as fictitious or
imaginary as any other set of numbers that we otherwise feel like we have a
good handle on.

~~~
andrewflnr
I like this explanation. A friend said it helped him.
[http://betterexplained.com/articles/a-visual-intuitive-
guide...](http://betterexplained.com/articles/a-visual-intuitive-guide-to-
imaginary-numbers/)

Basically, multiplying by i "rotates a number" 90 degrees.

~~~
thearn4
And with a little bit of trigonometry intuition on top of this, powers of i
and Euler's formula become much easier to understand as well. Great ways to
think about it!

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juretriglav
Not bad, but I find this to be a state of the art explanation of quaternions:
[http://acko.net/blog/animate-your-way-to-glory-
pt2/#quaterni...](http://acko.net/blog/animate-your-way-to-glory-
pt2/#quaternions)

~~~
batguano
O. M. G.

That is so awesome.... (Yes, so this probably counts as the kind of "+1" post
that should be downvoted. But check out the link and if you don't think it's
the most amazing quaternion explanation, then I will humbly accept your
downvote.)

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gfodor
Another good reference:

[http://www.songho.ca/math/quaternion/quaternion.html](http://www.songho.ca/math/quaternion/quaternion.html)

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NAFV_P
There's also octonions and sedenions. I prefer the blanket term onion-
algebras.

~~~
spiritplumber
Thanks, my head was already hurting :P

~~~
leoc
Now your eyes can hurt as well.

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wtracy
Has anyone here ever seen a good explanation of _why_ quaternion
multiplication maps to rotation concatenation?

~~~
ajkjk
I think of it as the opposite: there exists a Lie group of spatial rotations,
so we want to use it, and we found a relatively convenient notation.

There are many other kinds of 'complex' numbers
([http://en.wikipedia.org/wiki/Hypercomplex_number](http://en.wikipedia.org/wiki/Hypercomplex_number))
- but you probably won't hear about them outside of mathematics and physics
because they're less useful.

The same applies to 2d - the SO(2) group exists; we map it to the complex
numbers because it's convenient to do math with.

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davidgerard
I love that plaque, and that Ireland is the sort of place that that would rate
a plaque.

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ergoproxy
This recently posted YouTube video by UNSW Professor Norman J. Wildberger
discusses the discovery of the quaternions by Hamilton and the subsequent
discovery of the octonians. It's 59 minutes, 30 seconds long, and it was
published on March 5, 2014:

MathHistory18: Hypercomplex numbers
[https://www.youtube.com/watch?v=uw6bpPldp2A](https://www.youtube.com/watch?v=uw6bpPldp2A)
[video]

