Colloquium
2:00 p.m., Wednesday (December 14, 2005)
WMAX 110 (PIMS Seminar Room)
Alexander Jones
University of Toronto
Locus theorems in ancient Greek geometry
During the third century B.C. Greek mathematicians (including Euclid and Apollonius) took
a particular interest in locus theorems and their applications in problem solving. A Greek
locus theorem demonstrated that a geometrical object (typically a point) having a defined
relation to given objects lies on a geometrical object (typically a line or surface) that
can be constructed from the givens. A classification was devised of locus theorems, and
construction problems in general, according to whether they could be solved using only the
postulates in Euclid's Elements, i.e. straight lines and circles, or required conic sections
or special curves. An interesting question is whether anyone in antiquity broke from this
rigid conception of loci by defining a curve or surface as a locus.
Refreshments will be served at 1:45 p.m. (PIMS Lounge).
