A Knotty Problem by David Cole

Author:David Cole
Language: eng
Format: epub
Publisher: Common Deer Press
Published: 2022-09-15T00:00:00+00:00

“This is what a mathematician would call a trivial knot, or sometimes an unknot.”

“I’d call it a dough-knot,” Jordan said.

“Of course you would,” Justin said. “But if that’s an unknot, what would they call a knot?”

“Great question. This is what is known as a trefoil knot.” He drew another picture on the whiteboard.

“I would call it a pretzel knot,” Jordan said.

Mr. Duchesne smiled and shook his head. “You’ll notice that there is no way to untie this knot. That makes it much more interesting to a mathematician,” Mr. Duchesne explained. “With a knot like this, we can start to talk about characteristics such as knot crossings—this one has three crossings, for example—and even things like adding two knots together to make a third knot. Really interesting things.”

“But none of that helps to solve our problem,” Justin said. “I mean, it doesn’t explain why the hose got all knotted up when I tried to water the flowers.”

“No, it doesn’t,” Mr. Duchesne agreed. “And the topic of knots and tangles are definitely of interest. I mean, think of the hours people spend untangling hoses and necklaces and Christmas lights. But it’s much more important than that. One example is in molecular biology.”

“Biology?” Justin asked.

“Exactly. You’ve heard of DNA, right?”

“DNA is what carries all of the genes, isn’t it?” Jordan said.

“Exactly,” Mr. Duchesne said. “DNA is a molecule that has two strings that coil around each other. It controls the development, function, and reproduction of all organisms, including things like cancer.”

“Where do knots fit in?” Justin asked.

“There are enzymes that change the topology of DNA, causing the strings to form knots. If we can create drugs that inhibit this knot tying, it can cause these cells to die. Drugs like this could be used to treat cancer or as antibiotics to fight infections.”

“Maybe my dad should try an antibiotic on his Christmas lights,” Jordan quipped.

Mr. Duchesne laughed. “I wish it were that easy, Jordan. Unfortunately, no one has really done much math around the issue of Christmas light tangling.”

“If math can’t help, I guess we’re out of luck, huh?” Jordan asked.

“Just because most mathematicians aren’t looking at the problem of tangled Christmas lights, it doesn’t mean that it’s being completely ignored,” Mr. Duchesne responded. “I read a study from a couple of physicists who did some experiments with putting ropes into boxes that were tumbled at different speeds. They found that complex knots sometimes formed in just seconds.”

“Did they figure out why?” Catherine asked.

“No, but they did learn some interesting things with their experiment. They learned that the longer the rope was, the more likely it was to get tangled. But they also found that the smaller the box, the less likely the rope would get tangled. So, while it’s not exactly an exact science, it does give us something to work with, right?”

“How does that help my dad with his Christmas lights?” Jordan asked.

“Well, he can start by making the string of lights shorter,” Mr. Duchesne said.

“How does he do that?”

“Simple,” Mr. Duchesne said, “tell him to connect the two ends of the lights together.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.