Mark Logan shows off two of his recent origami efforts

This origami design represents a DNA string

A most elegant bat

The 10-point dragon

A woven design using folded paper strips

Mark Logan:

Math Man With Folding Finesse

Mark Logan joined the UMM Math faculty in the fall of 2002.   Since that time, he's been busy teaching everything from Survey of Mathematics to Abstract Algebra.   Any student who enters his office with a question about homework soon realizes that Logan's enjoyment of mathematics takes on a physical form in his leisure time.

Origami is his hobby's name and folding paper is the game.   Origami may be thousands of years old, but the last several decades have seen great advancements in complexity of design.   No wonder it drew the attention of a budding mathematician.

"I was six or seven years old when I found a library book about origami and started making animals and figures," Logan recalls.   "I made grocery bags full of them.   But my favorites were a deep sea diver and an octopus with four legs."

While these early models didn't engage Logan's talents with geometry, they did provide a challenge and he liked the attention to detail required to achieve good results.   Not bad skills to hone for later explorations in math.

Logan now uses origami to demonstrate some lessons about mathematics in the classroom.   "For example, a lot of research has been done looking at ancient Greek constructions," he explains.   "It was found impossible to trisect an arbitrary angle with a compass and straight edge, but it can be done with origami.   I like to demonstrate this in class."

In the last ten years, Logan has seen origami designers use the tools of mathematics to create new, more complicated shapes.   The technical challenge lies in how many points the design has and the size of paper required to create it.

"I'm interested in simple figures that do what they need to do elegantly, with an efficiency of design," says Logan.   Take a look at the photo of an origami bat that Logan recently folded.   He finds this to be an elegant design because the stretched wing tips approximate the full length of the paper size used to create it.   There is no wasted bulk of folds on the inside of the bat's body (which is hollow).

The next photo shows another of Logan's origami models--a three-headed dragon folded from a piece of map paper.   This design has ten points and looks fairly complicated to the uninitiated eye.   Yet he contends that the new origami books are full of designs that have 20 to 50 points on them!   One he says he plans to try in the near future is a fish, complete with scales.

"The key to origami is precision of folding.   You need to go to the edge and corner precisely," Logan says.   "I prefer using a type of paper called elephant hide.   It has a leathery texture and is harder to work with than typical origami paper but it gives a very nice effect."

  Some math students have recently caught the origami fever. "There's talk of creating a student group on origami," Logan says.   "I'd be glad to be their faculty advisor if they decide to go for it."

A rose by any other name would still be: origami!