Winter 2012 - Austin College Magazine

A C E N T U R Y
eye on the future
Jack Mealy:
Pushing the Boundaries of Geometry
The geometry taught in high school seems rational,
straightforward, and natural. But in non-Euclidean
geometries, when it comes to something you think you
know, as the old song goes, “it ain’t necessarily so.”
For example, in contrast to the oft-repeated line, “The
angles of a triangle add up to 180 degrees,” that generally
isn’t the case in non-Euclidean geometries. “In these
systems there are numerous things that might seem
obvious, but are untrue—but a different set of things that
seem absurd are now true!” said Jack Mealy, associate
professor of mathematics. These systems are among the
many “Wonderlands” in the mathematics field, he said.
Along with a number of student researchers over the
past few years, Mealy is investigating a subset of non-
Euclidean geometry that has received very little attention
from mathematicians. He has used both computer
modeling and theoretical arguments to demonstrate the
existence of, and investigate the properties of, a number
of strange objects, such as ‘discs’ with a radius of one
inch and an infinite circumference.
“It’s Forrest-Gump-like; there’s this infinite box of
chocolates out there, and you never fully know what you’re
going to get,” Mealy said. “But there’s a good chance it’ll
be interesting, even surprising.”
Because it’s theoretical, there currently aren’t any
practical uses for this research, but historically, “what has
started out as evidently ‘only’ theoretical, at times
ultimately has turned out to be useful,” Mealy said. “One
occasionally hopes for that sort of thing; but regardless,
we’ll have learned new and fascinating things in the
process.”
Alumnus
Integral
To The
Manhattan
Project
The 1919 chromascope
included a “prophecy” for each
graduating senior.
Among them was the prediction that
Percival Cleveland Keith, Jr.,
would become a prize fighter and
“his fame was to spread across
the waters.”
H
24 | Austin College Magazine Winter 2012