Transforming a Rubber Band into a Trefoil Knot

AI Thread Summary
The discussion centers on an article from Scientific American about transforming a rubber band into a trefoil knot, highlighting the contrast between mathematical theory and real-world applications. Participants express admiration for the video demonstrating the transformation but note that using a knife to cut the band diminishes its impressiveness. The conversation emphasizes the innovative thinking involved, likening it to the Mobius strip, while also acknowledging the limitations of mathematical models. One contributor points out that the math does allow for a torus to be made into a trefoil knot, underscoring the importance of model selection. Overall, the thread celebrates the creativity in exploring knot theory through practical demonstrations.
Mathematics news on Phys.org
Very cool video!

However, using a knife to cut the band is a bit cheating, so it becomes a bit less impressive :-p Still cool though.
 
micromass said:
Very cool video!

However, using a knife to cut the band is a bit cheating, so it becomes a bit less impressive :-p Still cool though.

True, I liked the thinking outside the box even though we knew this trick from the mobius strip. I also liked how he compared the real to the math to show how one allows it but the other doesn't.
 
jedishrfu said:
True, I liked the thinking outside the box even though we knew this trick from the mobius strip. I also liked how he compared the real to the math to show how one allows it but the other doesn't.

That's not strictly true. The math allows for a torus to be made into a trefoil knot, which is what he did. It's a lesson in choosing mathematical models carefully. Still, it was a very cool video; I think I'll make one for myself.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top