You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more
Suppose you're a little creature living on a Möbius strip.
Then after "walking in a circle" (i.e. 2π radians), you will actually be upside-down.
In order to get back to where you started, you have to go around twice!
Check out my neat gif! 
pic.twitter.com/1MMvp83IWG
The 𝐏𝐚𝐮𝐥𝐢 𝐈𝐝𝐞𝐧𝐭𝐢𝐭𝐲 tells us how to rotate a 2 component 𝒗𝒆𝒄𝒕𝒐𝒓 of complex numbers, called a "spinor", around an axis θ̂.
for spinors, a rotation by 2π yields -1
only a rotation by 4π yields identity
..sound familiar?pic.twitter.com/ECGtLshlH2
An object that existed in a Möbius-strip-shaped universe would be indistinguishable from its own mirror image
This crab's larger claw switches between left to right with every circulation
(GIF not mine)pic.twitter.com/n3JHJdy0jJ
The Möbius strip therefore doesn't have a well defined "inward" or "outward" pointing direction.
Such surfaces are called 𝙣𝙤𝙣-𝙤𝙧𝙞𝙚𝙣𝙩𝙖𝙗𝙡𝙚
I can’t find anyone pointing out that this is the way electrons have 1/2 spin. Its the main real world example I give my students when teaching Möbius Strips. Would love to see the cutting in half animated.
Incalculable, = the no# of hours spent spagetifying Mobius strips, for the purpose of understanding them better. Amazing still to me handedness arises, apparently spontaneously.
I like to live on the edge!
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.
