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Quaternions and the Hopf Fibration
Below are some links about William Rowan Hamilton's
quaternion algebra
and about the
Hopf fibration
of the 3-sphere by linked circles.
Some of the
history
of the quaternions, including a picture of
Broom Bridge
in Dublin.
Hamilton's original paper
on the quaternions.
A wonderful paper
by
David W. Lyons
using quaternions to give an undergraduate-accessible exposition of the Hopf bundle.
There are several fun ways to explore the Hopf fibration (and other beautiful mathematics) on the
University of Tokyo Mathematics Department
page of
foliations
animations.
Some
images
from the
American Mathematical Society
.
Some
screenshots
from Maximilian Albert's
C++ program
to explore the 3-sphere.
Robert G. Scharein's
Knotplot
site is well worth spending time on; it has a cool
animation
of the Hopf bundle
here
.
Last updated December 5, 2009