Wednesday, November 12, 2014 5:30 pm
-
5:30 pm
EST (GMT -05:00)
Sylvester's 4-point problem and straight line drawings of the complete graph K_n
Speaker: | Bruce Richter |
---|---|
Affiliation: | University of Waterloo |
Room: | Mathematics and Computer Building (MC) 4042 |
Abstract:
In
the
1880's,
Sylvester
raised
the
following
question:
if
we
pick
4
points
at
random
from
the
Euclidean
plane,
what
is
the
probability
that
they
make
a
convex
quadrilateral?
Equivalently,
what
is
the
probability
that
one
point
is
inside
the
triangle
formed
by
the
other
three?
We
will
make
this
question
more
precise
in
the
talk.
A
problem
in
graph
theory
is
to
determine,
over
all
sets
of
n
points
in
the
plane,
no
three
collinear,
the
smallest
number
f(n)
of
crossings
of
the
n
choose
2
straight
line
segments
joining
all
pairs
of
these
n
points.
It
is
easy
to
see
that
no
crossings
are
required
for
n
<=
4,
f(5)=1,
f(6)=3,
f(7)=9.