I wish math art was a big part of my math education when I was a kid. Being able to physically make some math would have rendered it far more interesting, though, and perhaps math would have lingered as something I wanted to pursue instead of leave behind as a series of boring tests. Have you ever made a Mobius strip? Fasten the ends together, but give the paper a little twist first. Take your finger or use a pen , and run it along one side of the strip. That one little twist turns the strip into what is called a nonorientable surface.
THE MOBIUS STRIP & TIME TRAVEL
Yale physicists have created something similar to a Moebius strip of moving energy between two vibrating objects, opening the door to novel forms of control over waves in acoustics, laser optics, and quantum mechanics. The discovery also demonstrates that a century-old physics theorem offers much greater freedom than had long been believed. The findings are published online July 25 in the journal Nature. Yale's experiment is deceptively simple in concept. The researchers set up a pair of connected, vibrating springs and studied the acoustic waves that traveled between them as they manipulated the shape of the springs. Vibrations -- as well as other types of energy waves -- are able to move, or oscillate, at different frequencies. In this instance, the springs vibrate at frequencies that merge, similar to a Moebius strip that folds in on itself.
What Is Topology?
It can be realized as a ruled surface. For example, any rectangle can be glued left-edge to right-edge with a reversal of orientation. Some, but not all, of these can be smoothly modeled as surfaces in Euclidean space. Such paper models are developable surfaces having zero Gaussian curvature , and can be described by differential-algebraic equations. A line drawn along the edge travels in a full circle to a point opposite the starting point.
To make it more simple, think of a strip of paper. Or you can twist the paper and then connect the two ends. Though it may not seems like much, but by connecting the two ends of the strip of paper with a single twist in it, you have created a single-sided paper.