Francis October 16, at The rules of topology forbid you to make new holes or close up old ones in surfaces.
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DrMRFrancis on Twitter PhysicistLisa on that note, I cannot wait for "Stray" 4 hours ago PhysicistLisa he is a very cute cat 4 hours ago however, I rescued Spider-Man the Cat, which is important 4 hours ago the only problems I have with Spider-Man are my usual problems: that I simply suck at video games 4 hours ago acarriebear it's always like "these things just happen", to avoid assigning any responsibility 6 hours ago.
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The surface is orientable if, when you come back from your walk, you can always read the note. On a nonorientable surface, you may come back from your walk only to find that the words you wrote have apparently turned into their mirror image and can be read only from right to left. On the two-sided loop, the note will always read from left to right, no matter where your journey took you. When the GIF starts, the dots listed off clockwise are black, blue and red.
This transformation is impossible on an orientable surface like the two-sided loop. The concept of orientability has important implications. Take enantiomers. These chemical compounds have the same chemical structures except for one key difference: They are mirror images of one another.
For example, the chemical L-methamphetamine is an ingredient in Vicks Vapor Inhalers. If one of the astronauts had lost their right leg before flight, upon return, the astronaut would be missing their left leg. While hopefully your mind is blown — at least just slightly — we need to take a step back. The strip itself is defined simply as a one-sided nonorientable surface that is created by adding one half-twist to a band.
Ever since its discovery, the one-sided strip has served as a fascination for artists and mathematicians. The strip even infatuated M. Topology is vital to certain areas of mathematics and physics, like differential equations and string theory.
For example, under topographical principles, a mug is actually a doughnut. Mathematician and artist Henry Segerman explains it best in a YouTube video : "If you take a coffee mug, you can sort of un-indent the place where the coffee goes and you can squish out the handle a little bit and eventually you can deform it into [a] symmetrical round doughnut shape. Associate professor NJ Wildberger of the School of Mathematics at the University of New South Wales, Australia, explained during a lecture series that a twist is often added to driving belts in machines, "purposefully to wear the belt out uniformly on both sides.
Edward English Jr. Simply take a piece of paper and cut it into a thin strip, say an inch or 2 wide 2. Once you have that strip cut, simply twist one of the ends degrees, or one-half twist. Then, take some tape and connect that end to the other end, creating a ring with one-half twist inside.
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