Pumped up over triangles

I meant to mention this earlier since it happened a little while ago. There is this "mini-conference" with three schools: Southeastern Louisiana University, Southern Mississippi University, and the University of South Alabama. The purpose is to give students (and some faculty) a chance to present their work at a smaller conference. I really enjoy this, mostly because it is small and I get to see lots of undergrad talks. There are two talks that stuck in my head.

Dr. Jiu Ding "Dynamical Geometry: From Order to Chaos and Sierpinski Pedal Triangles"

Jiu Ding is a mathematics professor at Southern Mississippi. The talk was basically about inscribing triangles inside triangles using different "rules." The question was: what (if anything) do these triangles converge to as you keep on inscribing them. Here is an example for the paper: "Sierpinski Pedal Triangles", Jiu Ding, L. Richard Hitt, and Xin-Min Zhang.

I don't want to talk about triangles. I want to talk about how pumped up Jui Ding was about triangles. I mean PUMPED UP excited. I love that. You may ask: who cares about triangles? What's the big deal? The answer is: that doesn't matter. Are there any applications for triangles in triangles? Yes. But that is not what excites Jiu. He just likes seeing what will happen if you change the inscribing rules.

"What Goes Up Must Go Round: Final Analysis of the Autorotation of a Falling Maple
Seed"
by Ty McCleery and Dr. Lawrence Mead - USM Physics

Here is the abstract for this talk.

Seeds of maple trees increase their dispersion range by extending their fall time
through autorotation. By rotating, the seed remains airborne for a time longer than
without rotation, which increases its chances of being blown laterally by the wind and
therefore increases its dissemination. The seed's descent has been studied to determine
trends between flight characteristics and seed parameter's.

Theoretical and experimental analysis was used to determine what parameters control
the motion of the seed. These parameters were assumed to consist of the following: a
characteristic length of the seed (m), the seed's weight (N), the kinematic viscosity of air
(s/m), or the density of air (kg/m²).

Next, through dimensional analysis, these parameters were used to derive equations
for the dependent variables: terminal velocity, rotational speed, and coning angle. The
parameters and dependent variables were measured using experimental techniques such as
watching the falling seed's motion progressively with a still camera and a strobe light.

The measured dependent variables were then multiplied by powers of the parameters
in such a way that a dimensionless number was formed according to the Buckingham Pi
Theorem. The dimensionless numbers corresponding to each dependent variable (coning
angle, rotational speed, and terminal velocity) was plotted versus the others. Analysis of
these plots have yielded a relation between the parameters and the dependent variables.
The trends between the parameters and the dependent variables were also analyzed and
compared to previous research.

Again - here is an example of a cool project. I like this because:

• It seems simple, but there are many layers to this question. Sort of a like an onion has layers. (not because it makes me cry)
• There is not a lot of equipment or background work that needs to be done first. Really, anyone interested could just jump in and start working on this kind of thing.
• There is not a clear motivation for the work other than "how does that work". That is not to say this won't lead to something useful, but that doesn't seem like the point.

The other undergraduate talks were also quite interesting, but I just wanted to give that as an example.