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Hamilton's discovery of quaternion is inscribed on
Broom bridge in Dublin.
It is a place of pilgrimage for mathematicians.
One usually also credits Olinde Rodriguez for a codiscovery of quaternions.
However, Rodrigues mostly deals with the rotation group SO(3) and not the
quaternion algebra. You can look at the paper
In this PDF from 1840. There is no surprise for a connection because the unit sphere
in the quaternions is the universal cover of the rotation group. The point of
quaternions however is that they form an algebra, a division algebra.
Rodriques found a neat
Formula
for rotations but I personally believe that there is a big gap from that formula
to the actual quaternion algebra. Historians like to exaggerate sometimes, like that
the Babylonians already discovered trigonometry or that Archimedes already found the
Riemann integral. Or that on Clay tablets, one can see the Pythagorean theorem.
Also, one of the major formulas for quaternions |q p| = |q| |p| was already known to
Euler but it would be false to credit Euler for the quaternion discovery.
You have to judge yourself, look at the Rodrigues paper and see whether you can see
explicitly the quaternion algebra.
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