The origin of quaternions

From: Glen Able (Glen.Able_at_gmail.com)
Date: 11/29/04 

Date: Mon, 29 Nov 2004 15:35:21 -0000

I've read about how quaternions were invented by Hamilton. What did he find
unsatisfactory about 3 dimensional numbers?
Was it specifically that they can't be used for representing rotations in 3d
space (I'm not clear as to whether Hamilton had this purpose in mind at the
time?) Or is there some more fundamental flaw making it impossible to
sensibly define +, * operators?

thanks,
G.A.

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