| Abstract:
In 1843, William Rowan Hamilton invented the algebra of quaternions,
a four dimensional associative algebra over the reals. But his main
intention was to find a three-dimensional analog of the planar
algebra of complex numbers, but as was later proved, no such division
algebra exists. Many proofs of this non-existence result, both
conceptual and computational, are known but they are not that
accessible to, say the advanced undergraduates. Here we present two
proofs: one computational but not difficult and other a "one-line"
proof accessible even to high school students.
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