#nonoriental

[mathhombre]

Möbius Strip -> Cube

Ned Beebe posted this to the FB Bridges group. Want to understand and try it.

[dailypolyhedra]

Polyhedron of the Day #11: Small icosihemidodecahedron

The small icosihemidodecahedron is a uniform star polyhedron. It has 26 faces, 60 edges, and 30 vertices. Its vertex figure is a bowtie, or more formally, a crossed rectangle. Its dual is the small icosihemidodecacron. It is nonorientable and nonconvex, and as some of its faces pass through its centre, it is a hemipolyhedron.

Small icosihemidodecahedron GIF created by Dzmitry Lysiankou, obtained from https://grabcad.com/library/small-icosihemidodecahedron-1. Small icosihemidodecahedron image created using Robert Webb's Stella software (http://www.software3d.com/Stella.php).

[lotus-tower]

my brain is too small to understand how to put nonorientable surfaces into my gintama hwbm fic but I want to

[yesterdays-xkcd]

To really expand your mind try some noncartesian porn. Edwin Abbot Abbott has nothing on "Girls on Girls in Tightly Closed Nonorientable Spaces"

Right-Hand Rule [Explained]

Transcript Under the Cut

[Picture of a right hand with fingers curved, thumb pointed away, with axes drawn to demonstrate the right-hand rule of physics.] Alternatives to the Right-Hand Rule in vector multiplication:

[A slightly-open book with labeled axes drawn on.] Book Rule: Open the front cover along the first vector and the back cover along the second. The result vector is along the spine, out the top.

[A handgun with axes.] Handgun Rule: Point the grip along the first vector and rotate it so that the second vector is on the safety latch side. Fire. The result vector is toward the bullet holes.

[A person with right arm extended.] Body Rule (males only): Point your right arm along the first vector and your legs along the second, then watch some porn.

[six-of-cringe]

A nonorientable shape is a shape that can be illustrated but cannot actually be created in real life. I have discovered a new nonorientable shape I call it "two people living in the same house and working to love each other unconditionally without it eventually falling apart"

[beyond-mogai-pride-flags]

Orientationless Pride Flag

Orientationlessness: a term that refers to the state of not having an orientation, either sexual, nor romantic, nor any other.

Source. -AP

[mysticstronomy]

WHAT IS A MOBIUS STRIP??

Blog#112

Saturday, August 7th ,2021

Welcome back,

The mathematics of otherwise simple-looking objects can be surprisingly perplexing. There's likely no greater example of this than the Möbius strip.

It's a one-sided object that can be made by simply twisting a piece of paper and connecting the ends with some tape. If you were to follow the loop around with your finger, you'd eventually end up right back where you started, having touched the entire surface of the loop along the journey. This simple creation, the Möbius strip, is fundamental to the entire field of topology and serves as a quintessential example of various mathematical principles.

One of these principles is non orientability, which is the inability for mathematicians to assign coordinates to an object, say up or down, or side to side. This principle has some interesting outcomes, as scientists aren't entirely sure whether the universe is orientable.

This poses a perplexing scenario: If a rocket with astronauts flew into space for long enough and then returned, assuming the universe was non orientability, it's possible that all the astronauts onboard would come back in reverse.

In other words, the astronauts would come back as mirror images of their former selves, completely flipped. Their hearts would be on the right rather than the left and they may be left-handed rather than right-handed. If one of the astronauts had lost their right leg before flight, upon return, the astronaut would be missing their left leg. This is what happens as you traverse a nonorientable surface like a Möbius strip.

While hopefully your mind is blown – at least just slightly – we need to take a step back. What's a Möbius strip and how can an object with such complex math be made by simply twisting a piece of paper?

The Möbius strip (sometimes written as "Mobius strip") was first discovered in 1858 by a German mathematician named August Möbius while he was researching geometric theories. While Möbius is largely credited with the discovery (hence, the name of the strip), it was nearly simultaneously discovered by a mathematician named Johann Listing. However, he held off on publishing his work, and was beaten to the punch by August Möbius.

The strip itself is defined simply as a one-sided nonorientable surface that is created by adding one half-twist to a band. Möbius strips can be any band that has an odd number of half-twists, which ultimately cause the strip to only have one side, and consequently, one edge.

Ever since its discovery, the one-sided strip has served as a fascination for artists and mathematicians. The strip even infatuated M.C. Escher, leading to his famous works, "Möbius Strip I& II".

The discovery of the Möbius strip was also fundamental to the formation of the field of mathematical topology, the study of geometric properties that remain unchanged as an object is deformed or stretched. Topology is vital to certain areas of mathematics and physics, like differential equations and string theory.

The Möbius strip is more than just great mathematical theory: It has some cool practical applications, whether as a teaching aid for more complex objects or in machinery.

For instance, since the Möbius strip is physically one-sided, using Möbius strips in conveyor belts and other applications ensures that the belt itself doesn't get uneven wear throughout its life. 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." The Möbius strip also may be seen in architecture, for example, the Wuchazi Bridge in China.

Dr. Edward English Jr., middle school math teacher and former optical engineer, says that as when he first learned about the Möbius strip in grade school, his teacher had him create one with paper, cutting the Möbius strip along its length which created a longer strip with two full twists.

"Being intrigued by and exposed to this concept of two 'states' helped me, I think, when I encountered up/down spin of electrons," he says, referring to his Ph.D. studies. "Various quantum mechanics ideas weren't such strange concepts for me to accept and understand because the Möbius strip introduced me to such possibilities." For many, the Möbius strip serves as the first introduction to complex geometry and mathematics.

Creating a Möbius strip is incredibly easy. Simply take a piece of paper and cut it into a thin strip, say an inch or 2 wide (2.5-5 centimeters). Once you have that strip cut, simply twist one of the ends 180 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. You're now left with a Möbius strip!

You can best observe the principles of this shape by taking your finger and following along the sides of the strip. You'll eventually make it all the way around the shape and find your finger back where it started.

If you cut a Möbius strip down the center, along its full length, you're left with one larger loop with four half-twists. This leaves you with a twisted circular shape, but one that still has two sides. It's this duality that Dr. English mentioned helped him understand more complex principles.

SOURCE: science.howstuffworks.com

COMING UP!!

(Wednesday, August 11th, 2021)

“ASTRONOMERS SPOT LIGHT FROM BEHIND A BLACK HOLE FOR THE FIRST TIME??”

[xbuster]

So Klein’s introduction interested me because the name “Klein” immediately makes me think of one thing. The Klein bottle. The “3-dimensional Möbius strip.” A nonorientable surface, one without a definitive “inside” and “outside.” This, of course, got me thinking about lord Moebius. Eas pronounces his name like “Mebiusu,” so I had been wondering this entire time if “Moebius” was a bad translation or if I was missing something. I decided to translate Möbius to Japanese and got「メビウス」(mebiusu), so Möbius, or Moebius, is pronounced that was in Japanese.

Well, it all makes sense now because Moebius is looking for “Infinity.” The Möbius strip is the symbol for “infinity” because you can trace its surface forever and touch both “sides” of it without lifting your finger.” Likewise, you can trace the surface of a Klein bottle and touch both the “inside” and “outside” of it without lifting your finger. So they’re both named after representations of infinity. Nonorientable surfaces. The lesser antagonists, Eas, Westar, and Soular, are named after East, West, and South. Orientations.

[thearistocratsblog]

The Möbius band, closed two-dimensional surfaces, and metazoan body plans. s, sphere; t, torus; t , toroid; shaded areas, 'interior'. (a) Nonorientable surfaces, the nonclosed Möbius band (up) and the closed 'Klein bottle' (section, down). (b), (c) Twodimensional orientable surfaces; (b), spheres of different shapes (sphere proper, dumb-bell, 'inverted dumb-bell'), sections; (c) torus ('tire'), as seen from 'outside'. (d)-(h) Metazoan development and body plans (sections). Bold lines represent epithelia, 'stitches' indicate fusion of epithelia. m, mouth; a, anus. (d) Single coelenterates, polyp or medusa, are topological spheres; colonial and budding stages are (multiple) toroids, due to secondary mouth openings. (e)-(i) Bilaterian development and body plans: except for flatworms [(g); ex, excretion organ], there is a transition from sphere to torus during the formation of the second opening of the primitive gut (anus in protostomia, definitive mouth in deuterostomia). (f) Alternative formation of second gut opening in certain protostomians (see text for explanation). Torus-like body plans of (h) a round worm (nematode) and (i) a vertebrate (bull, ital., span. toro). In (h), epidermal invaginations schematically indicate lacrimal (head), sweat and sebaceous glands (in a female, mammary glands would have to be added). Evaginations of the gut represent epithelial linings of lungs, pancreas and liver. 

[theunlitpath]

We present an outline of the forthcoming proof of the embedding theorem, to orient the reader before we begin. The nonorientable reader is requested to pass to their orientation double cover before continuing.

— Arunima Ray, The Disc Embedding Theorem, chapter 2

[kammerelektronik]

🤚🏻✂️
#plastercast #musicalinstrument
#kammerelektronik 9 #möbiusband
#konzertperformance


[mathhombre]

Nonorientable Humor

via Effie Seiberg on Bluesky.

[reblogs-the-art]

Terry Berlier. Nonorientable (Kokedera), 2019.

[nyktomorphia]

Klein Oroboros screams nonorientably

[spacydenden]

Stacinator Adventures, continues...

Stacinator Adventures, continues…

Stacinator

When already wandering on an one-sided, nonorientable surface, where does one begin? Some call the route, ‘the twisted cylinder ‘, whilst, others insist on calling the same, a mobius strip. It’s best to acknowledge the irrelevance of where the beginning ends or where the ending begins…

This way…

The setting, ‘Sun’

For now, the ending begins with the shrill announcement and…

[ainsleighdouglas]

MOBIUS

The piece is a redesigned Möbius Strip, a structure that is recognized for its famous features of being a one sided nonorientable surface with only one single edge. The strips unique structure defines this piece due its infinite one sided perspective. The shape is a manipulated from its original form, essentially twisted to have one side. This piece is in reference to both self oriented and societal conflicts that are left unresolved as a result of an infinite loop of problem solving and mistake making. We are essentially trapped in race against ourselves.