Project Description: |
During the Hope College REU in the summer of 2004, two
undergraduates worked on the following problem: Given 3 distinct
points in the plane P0, P1, P2,
a parameter t in (0,1), and
the rule Pk+3 = t Pk + (1-t) Pk+1,
determine the length of the
resulting spiral. In 2006, a second group of REU
students at Hope worked on a generalization of the problem that
begins with m points in the plane and classifies which starting
configurations lead to spirals in which the lengths of the
segments form a geometric series. Their work appears in the
current Pi Mu Epsilon Journal. In particular, the students
began to use some of the techniques of experimental mathematics as
described by Borwein, Bailey, et al. For the current project,
we'll generalize the problem to points in R3 and
explore the length of the spiral and the location of its limit
point. We may also consider some additional questions about the
spiral in the plane. (Background Needed: a semester of linear algebra,
experience with infinite series and complex numbers, some familiarity with programming
or computer algebra systems.) |
