An example of a Möbius strip can be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a loop. However, the Möbius strip is not a surface of only one exact size and shape, such as the half-twisted paper strip depicted in the illustration. Rather, mathematicians refer to the closed Möbius band as any surface that is homeomorphic to this strip. Its boundary is a simple closed curve, i.e., homeomorphic to a circle. This allows for a very wide variety of geometric versions of the Möbius band as surfaces each having a definite size and shape. For example, any rectangle can be glued to itself (by identifying one edge with the opposite edge after a reversal of orientation) to make a Möbius band. Some of these can be smoothly modeled in Euclidean space, and others cannot.
Mobius Band was an electronic rock trio from Brooklyn, New York consisting of Noam Schatz (drums), Peter Sax (bass/vocals/keyboards), and Ben Sterling (guitar/vocals/keyboards).
History
The band began when members Schatz, Sterling and Sax met as students at Wesleyan University. After graduation, they moved to Shutesbury, Massachusetts to hone their sound. Following the self-produced, self-released (on their own Prescription Rails label) and mostly instrumental EPs One, Two, and Three, Mobius Band were signed to Ann Arbor, Michigan’s Ghostly International in 2004, becoming the electronic label’s first rock-based act.
Their first Ghostly release was the City Vs. Country EP in March 2005, which earned critical acclaim for its fusion of pop songs with electronic flourishes, paralleling the work of contemporaries like The Notwist and The Postal Service. The first Mobius Band full-length album is August 2005’s The Loving Sounds of Static, which took the ideas of City Vs. Country further, adding a lyrical focus on coming of age and disillusionment with modern America.
Cutting a Möbius strip in half (and more) | Animated Topology |
________________________________________________________________
About the video:
Exploring the properties and other unexpected shapes that we get by cutting up some Mobius strips.
This video is a lot more text heavy compared to most of my previous ones, however it's quite difficult to explain something in more depth without using a lot of words.
Thanks for watching:)
_________________________________________________________________
Support my animations on:
https://www.patreon.com/Think_twice
_________________________________________________________________
Any further questions or ideas:
Email - [email protected]
Twitter - https://twitter.com/thinktwice2580
_________________________________________________________________
More in depth info:
Tadashi Tokieda lecture:
...
published: 11 Sep 2017
Neil deGrasse Tyson Explains the Möbius Strip
What is a Möbius strip? If you’ve never heard of it, that’s alright. Neil deGrasse Tyson and comic co-host Chuck Nice are here to explain what exactly is going on with a Möbius strip.
Neil gets crafty to show us how a Möbius strip only has one side. What would a Möbius strip look like in higher dimensions? You’ll learn about a Klein bottle. All that, plus, Neil tells us about tesseracts and why he’ll stick to calling them 4D cubes.
Support us on Patreon: https://www.patreon.com/startalkradio
About the prints that flank Neil in this video:
"Black Swan” & "White Swan" limited edition serigraph prints by Coast Salish artist Jane Kwatleematt Marston. For more information about this artist and her work, visit Inuit Gallery of Vancouver https://inuit.com/.
FOLLOW or SUBSCRIBE to StarTalk:
...
published: 22 Dec 2020
Paradox of the Möbius Strip and Klein Bottle - A 4D Visualization
Embark on a mind-bending journey into the 4th dimension as we explore the fascinating geometry of the Möbius Strip and Klein Bottle. This video will take you on a whirlwind tour of time travel, geometric paradoxes, 4D visualization, and sentient primitive shapes.
CHAPTERS:
00:00 - A Hexagon Illusion
00:50 - Defining Topology, Manifold, and Boundary
02:11 - An Open 2D Manifold
02:25 - Riddle #1
02:39 - Cutting the Möbius Strip in half
04:05 - Cutting the Möbius Strip in thirds
04:34 - The Grandfather Paradox
05:13 - Grandfather Paradox Solution Using a Möbius Strip
07:11 - A Closed 2D Manifold
07:46 - Riddle #2
08:03 - Visualizing the Klein Bottle with an Ant
09:12 - Spatial and Temporal Dimensions
09:24 - Linus - Two Dimensions for a 1D Creature
10:26 - Squirrel - Three Dimensions for a ...
published: 31 Mar 2022
Mobius Strip Video
Have your students try making a Mobius Strip to explore! Even you might be surprised at what happens if you try the second cut!
published: 05 Apr 2016
Why cutting a Möbius strip is so weird
An explanation for why cutting a Möbius strip down the middle keeps it connected.
Resources to learn more and other interesting notes:
https://en.wikipedia.org/wiki/M%C3%B6bius_strip
The boundary of a Möbius strip is a circle. If you make 3 half-twists, you still get a Möbius strip, but the boundary is knotted into what's called a "trefoil knot." We call a surface that bounds a knot a Seifert surface.
More about Seifert surfaces:
https://en.wikipedia.org/wiki/Seifert_surface
Corrections:
published: 27 Feb 2023
Superconducting Quantum Levitation on a 3π Möbius Strip
From the Low Temperature Physics Lab:
Quantum levitation on a 3π Möbius strip track! Watch the superconductor levitate above the track and suspend below the track, without having to go across the edge.
Our track is not an "ordinary" Möbius strip with just one twist, but rather a Möbius strip with three twists -- 540 degrees, or 3π radians, thus, a 3π Möbius strip track.
You can also check out the video we made that documents the building of the track, if you want to make your own: https://www.youtube.com/watch?v=OQkzXW7arqg
If you have more questions about the physics or how we made the track, see our other videos:
https://www.youtube.com/watch?v=uKnUCz8pads
https://www.youtube.com/watch?v=6lmtbLu5nxw
Chapters:
0:00 What is a Mobius Strip?
0:56 The 3-pi Mobius Strip
1:35 Cooling the ...
________________________________________________________________
About the video:
Exploring the properties and other unexpected shapes that we get by cutting ...
________________________________________________________________
About the video:
Exploring the properties and other unexpected shapes that we get by cutting up some Mobius strips.
This video is a lot more text heavy compared to most of my previous ones, however it's quite difficult to explain something in more depth without using a lot of words.
Thanks for watching:)
_________________________________________________________________
Support my animations on:
https://www.patreon.com/Think_twice
_________________________________________________________________
Any further questions or ideas:
Email - [email protected]
Twitter - https://twitter.com/thinktwice2580
_________________________________________________________________
More in depth info:
Tadashi Tokieda lecture:
https://www.youtube.com/watch?v=SXHHvoaSctc
https://en.wikipedia.org/wiki/M%C3%B6bius_strip
_________________________________________________________________
Programs used:
- Cinema 4D
_________________________________________________________________
Music:
Tom Day - Foreword:
https://www.youtube.com/watch?v=p13ihTQpKwE
Sound Cloud:
https://soundcloud.com/tomday
________________________________________________________________
________________________________________________________________
About the video:
Exploring the properties and other unexpected shapes that we get by cutting up some Mobius strips.
This video is a lot more text heavy compared to most of my previous ones, however it's quite difficult to explain something in more depth without using a lot of words.
Thanks for watching:)
_________________________________________________________________
Support my animations on:
https://www.patreon.com/Think_twice
_________________________________________________________________
Any further questions or ideas:
Email - [email protected]
Twitter - https://twitter.com/thinktwice2580
_________________________________________________________________
More in depth info:
Tadashi Tokieda lecture:
https://www.youtube.com/watch?v=SXHHvoaSctc
https://en.wikipedia.org/wiki/M%C3%B6bius_strip
_________________________________________________________________
Programs used:
- Cinema 4D
_________________________________________________________________
Music:
Tom Day - Foreword:
https://www.youtube.com/watch?v=p13ihTQpKwE
Sound Cloud:
https://soundcloud.com/tomday
________________________________________________________________
What is a Möbius strip? If you’ve never heard of it, that’s alright. Neil deGrasse Tyson and comic co-host Chuck Nice are here to explain what exactly is going ...
What is a Möbius strip? If you’ve never heard of it, that’s alright. Neil deGrasse Tyson and comic co-host Chuck Nice are here to explain what exactly is going on with a Möbius strip.
Neil gets crafty to show us how a Möbius strip only has one side. What would a Möbius strip look like in higher dimensions? You’ll learn about a Klein bottle. All that, plus, Neil tells us about tesseracts and why he’ll stick to calling them 4D cubes.
Support us on Patreon: https://www.patreon.com/startalkradio
About the prints that flank Neil in this video:
"Black Swan” & "White Swan" limited edition serigraph prints by Coast Salish artist Jane Kwatleematt Marston. For more information about this artist and her work, visit Inuit Gallery of Vancouver https://inuit.com/.
FOLLOW or SUBSCRIBE to StarTalk:
YouTube: https://www.youtube.com/user/startalkradio?sub_confirmation=1
Twitter: http://twitter.com/startalkradio
Facebook: https://www.facebook.com/StarTalk
Instagram: https://www.instagram.com/startalkradio/
About StarTalk:
Science meets pop culture on StarTalk! Astrophysicist & Hayden Planetarium director Neil deGrasse Tyson, his comic co-hosts, guest celebrities & scientists discuss astronomy, physics, and everything else about life in the universe. Keep Looking Up!
#StarTalk #NeildeGrasseTyson
What is a Möbius strip? If you’ve never heard of it, that’s alright. Neil deGrasse Tyson and comic co-host Chuck Nice are here to explain what exactly is going on with a Möbius strip.
Neil gets crafty to show us how a Möbius strip only has one side. What would a Möbius strip look like in higher dimensions? You’ll learn about a Klein bottle. All that, plus, Neil tells us about tesseracts and why he’ll stick to calling them 4D cubes.
Support us on Patreon: https://www.patreon.com/startalkradio
About the prints that flank Neil in this video:
"Black Swan” & "White Swan" limited edition serigraph prints by Coast Salish artist Jane Kwatleematt Marston. For more information about this artist and her work, visit Inuit Gallery of Vancouver https://inuit.com/.
FOLLOW or SUBSCRIBE to StarTalk:
YouTube: https://www.youtube.com/user/startalkradio?sub_confirmation=1
Twitter: http://twitter.com/startalkradio
Facebook: https://www.facebook.com/StarTalk
Instagram: https://www.instagram.com/startalkradio/
About StarTalk:
Science meets pop culture on StarTalk! Astrophysicist & Hayden Planetarium director Neil deGrasse Tyson, his comic co-hosts, guest celebrities & scientists discuss astronomy, physics, and everything else about life in the universe. Keep Looking Up!
#StarTalk #NeildeGrasseTyson
Embark on a mind-bending journey into the 4th dimension as we explore the fascinating geometry of the Möbius Strip and Klein Bottle. This video will take you on...
Embark on a mind-bending journey into the 4th dimension as we explore the fascinating geometry of the Möbius Strip and Klein Bottle. This video will take you on a whirlwind tour of time travel, geometric paradoxes, 4D visualization, and sentient primitive shapes.
CHAPTERS:
00:00 - A Hexagon Illusion
00:50 - Defining Topology, Manifold, and Boundary
02:11 - An Open 2D Manifold
02:25 - Riddle #1
02:39 - Cutting the Möbius Strip in half
04:05 - Cutting the Möbius Strip in thirds
04:34 - The Grandfather Paradox
05:13 - Grandfather Paradox Solution Using a Möbius Strip
07:11 - A Closed 2D Manifold
07:46 - Riddle #2
08:03 - Visualizing the Klein Bottle with an Ant
09:12 - Spatial and Temporal Dimensions
09:24 - Linus - Two Dimensions for a 1D Creature
10:26 - Squirrel - Three Dimensions for a 2D Creature
11:19 - Time Evolution of a Flattened Möbius Strip's Boundary
12:07 - Klein Bottle
12:36 - Visualizing the Klein Bottle in 4 Dimensions
SUPPORT
Patreon: https://patreon.com/andrewscampfire
GCash: https://imgur.com/a/3UOUHG6
Embark on a mind-bending journey into the 4th dimension as we explore the fascinating geometry of the Möbius Strip and Klein Bottle. This video will take you on a whirlwind tour of time travel, geometric paradoxes, 4D visualization, and sentient primitive shapes.
CHAPTERS:
00:00 - A Hexagon Illusion
00:50 - Defining Topology, Manifold, and Boundary
02:11 - An Open 2D Manifold
02:25 - Riddle #1
02:39 - Cutting the Möbius Strip in half
04:05 - Cutting the Möbius Strip in thirds
04:34 - The Grandfather Paradox
05:13 - Grandfather Paradox Solution Using a Möbius Strip
07:11 - A Closed 2D Manifold
07:46 - Riddle #2
08:03 - Visualizing the Klein Bottle with an Ant
09:12 - Spatial and Temporal Dimensions
09:24 - Linus - Two Dimensions for a 1D Creature
10:26 - Squirrel - Three Dimensions for a 2D Creature
11:19 - Time Evolution of a Flattened Möbius Strip's Boundary
12:07 - Klein Bottle
12:36 - Visualizing the Klein Bottle in 4 Dimensions
SUPPORT
Patreon: https://patreon.com/andrewscampfire
GCash: https://imgur.com/a/3UOUHG6
An explanation for why cutting a Möbius strip down the middle keeps it connected.
Resources to learn more and other interesting notes:
https://en.wikipedia.or...
An explanation for why cutting a Möbius strip down the middle keeps it connected.
Resources to learn more and other interesting notes:
https://en.wikipedia.org/wiki/M%C3%B6bius_strip
The boundary of a Möbius strip is a circle. If you make 3 half-twists, you still get a Möbius strip, but the boundary is knotted into what's called a "trefoil knot." We call a surface that bounds a knot a Seifert surface.
More about Seifert surfaces:
https://en.wikipedia.org/wiki/Seifert_surface
Corrections:
An explanation for why cutting a Möbius strip down the middle keeps it connected.
Resources to learn more and other interesting notes:
https://en.wikipedia.org/wiki/M%C3%B6bius_strip
The boundary of a Möbius strip is a circle. If you make 3 half-twists, you still get a Möbius strip, but the boundary is knotted into what's called a "trefoil knot." We call a surface that bounds a knot a Seifert surface.
More about Seifert surfaces:
https://en.wikipedia.org/wiki/Seifert_surface
Corrections:
From the Low Temperature Physics Lab:
Quantum levitation on a 3π Möbius strip track! Watch the superconductor levitate above the track and suspend below the tr...
From the Low Temperature Physics Lab:
Quantum levitation on a 3π Möbius strip track! Watch the superconductor levitate above the track and suspend below the track, without having to go across the edge.
Our track is not an "ordinary" Möbius strip with just one twist, but rather a Möbius strip with three twists -- 540 degrees, or 3π radians, thus, a 3π Möbius strip track.
You can also check out the video we made that documents the building of the track, if you want to make your own: https://www.youtube.com/watch?v=OQkzXW7arqg
If you have more questions about the physics or how we made the track, see our other videos:
https://www.youtube.com/watch?v=uKnUCz8pads
https://www.youtube.com/watch?v=6lmtbLu5nxw
Chapters:
0:00 What is a Mobius Strip?
0:56 The 3-pi Mobius Strip
1:35 Cooling the superconductor
2:01 Around the Mobius Strip!
2:37 Credits
From the Low Temperature Physics Lab:
Quantum levitation on a 3π Möbius strip track! Watch the superconductor levitate above the track and suspend below the track, without having to go across the edge.
Our track is not an "ordinary" Möbius strip with just one twist, but rather a Möbius strip with three twists -- 540 degrees, or 3π radians, thus, a 3π Möbius strip track.
You can also check out the video we made that documents the building of the track, if you want to make your own: https://www.youtube.com/watch?v=OQkzXW7arqg
If you have more questions about the physics or how we made the track, see our other videos:
https://www.youtube.com/watch?v=uKnUCz8pads
https://www.youtube.com/watch?v=6lmtbLu5nxw
Chapters:
0:00 What is a Mobius Strip?
0:56 The 3-pi Mobius Strip
1:35 Cooling the superconductor
2:01 Around the Mobius Strip!
2:37 Credits
________________________________________________________________
About the video:
Exploring the properties and other unexpected shapes that we get by cutting up some Mobius strips.
This video is a lot more text heavy compared to most of my previous ones, however it's quite difficult to explain something in more depth without using a lot of words.
Thanks for watching:)
_________________________________________________________________
Support my animations on:
https://www.patreon.com/Think_twice
_________________________________________________________________
Any further questions or ideas:
Email - [email protected]
Twitter - https://twitter.com/thinktwice2580
_________________________________________________________________
More in depth info:
Tadashi Tokieda lecture:
https://www.youtube.com/watch?v=SXHHvoaSctc
https://en.wikipedia.org/wiki/M%C3%B6bius_strip
_________________________________________________________________
Programs used:
- Cinema 4D
_________________________________________________________________
Music:
Tom Day - Foreword:
https://www.youtube.com/watch?v=p13ihTQpKwE
Sound Cloud:
https://soundcloud.com/tomday
________________________________________________________________
What is a Möbius strip? If you’ve never heard of it, that’s alright. Neil deGrasse Tyson and comic co-host Chuck Nice are here to explain what exactly is going on with a Möbius strip.
Neil gets crafty to show us how a Möbius strip only has one side. What would a Möbius strip look like in higher dimensions? You’ll learn about a Klein bottle. All that, plus, Neil tells us about tesseracts and why he’ll stick to calling them 4D cubes.
Support us on Patreon: https://www.patreon.com/startalkradio
About the prints that flank Neil in this video:
"Black Swan” & "White Swan" limited edition serigraph prints by Coast Salish artist Jane Kwatleematt Marston. For more information about this artist and her work, visit Inuit Gallery of Vancouver https://inuit.com/.
FOLLOW or SUBSCRIBE to StarTalk:
YouTube: https://www.youtube.com/user/startalkradio?sub_confirmation=1
Twitter: http://twitter.com/startalkradio
Facebook: https://www.facebook.com/StarTalk
Instagram: https://www.instagram.com/startalkradio/
About StarTalk:
Science meets pop culture on StarTalk! Astrophysicist & Hayden Planetarium director Neil deGrasse Tyson, his comic co-hosts, guest celebrities & scientists discuss astronomy, physics, and everything else about life in the universe. Keep Looking Up!
#StarTalk #NeildeGrasseTyson
Embark on a mind-bending journey into the 4th dimension as we explore the fascinating geometry of the Möbius Strip and Klein Bottle. This video will take you on a whirlwind tour of time travel, geometric paradoxes, 4D visualization, and sentient primitive shapes.
CHAPTERS:
00:00 - A Hexagon Illusion
00:50 - Defining Topology, Manifold, and Boundary
02:11 - An Open 2D Manifold
02:25 - Riddle #1
02:39 - Cutting the Möbius Strip in half
04:05 - Cutting the Möbius Strip in thirds
04:34 - The Grandfather Paradox
05:13 - Grandfather Paradox Solution Using a Möbius Strip
07:11 - A Closed 2D Manifold
07:46 - Riddle #2
08:03 - Visualizing the Klein Bottle with an Ant
09:12 - Spatial and Temporal Dimensions
09:24 - Linus - Two Dimensions for a 1D Creature
10:26 - Squirrel - Three Dimensions for a 2D Creature
11:19 - Time Evolution of a Flattened Möbius Strip's Boundary
12:07 - Klein Bottle
12:36 - Visualizing the Klein Bottle in 4 Dimensions
SUPPORT
Patreon: https://patreon.com/andrewscampfire
GCash: https://imgur.com/a/3UOUHG6
An explanation for why cutting a Möbius strip down the middle keeps it connected.
Resources to learn more and other interesting notes:
https://en.wikipedia.org/wiki/M%C3%B6bius_strip
The boundary of a Möbius strip is a circle. If you make 3 half-twists, you still get a Möbius strip, but the boundary is knotted into what's called a "trefoil knot." We call a surface that bounds a knot a Seifert surface.
More about Seifert surfaces:
https://en.wikipedia.org/wiki/Seifert_surface
Corrections:
From the Low Temperature Physics Lab:
Quantum levitation on a 3π Möbius strip track! Watch the superconductor levitate above the track and suspend below the track, without having to go across the edge.
Our track is not an "ordinary" Möbius strip with just one twist, but rather a Möbius strip with three twists -- 540 degrees, or 3π radians, thus, a 3π Möbius strip track.
You can also check out the video we made that documents the building of the track, if you want to make your own: https://www.youtube.com/watch?v=OQkzXW7arqg
If you have more questions about the physics or how we made the track, see our other videos:
https://www.youtube.com/watch?v=uKnUCz8pads
https://www.youtube.com/watch?v=6lmtbLu5nxw
Chapters:
0:00 What is a Mobius Strip?
0:56 The 3-pi Mobius Strip
1:35 Cooling the superconductor
2:01 Around the Mobius Strip!
2:37 Credits
An example of a Möbius strip can be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a loop. However, the Möbius strip is not a surface of only one exact size and shape, such as the half-twisted paper strip depicted in the illustration. Rather, mathematicians refer to the closed Möbius band as any surface that is homeomorphic to this strip. Its boundary is a simple closed curve, i.e., homeomorphic to a circle. This allows for a very wide variety of geometric versions of the Möbius band as surfaces each having a definite size and shape. For example, any rectangle can be glued to itself (by identifying one edge with the opposite edge after a reversal of orientation) to make a Möbius band. Some of these can be smoothly modeled in Euclidean space, and others cannot.
this world's not right it's a losing fight and this music's not what you want it's a business now there's ins and outs and the life you had you'll lose somehow you know you head wont suggest anything that hasn't passed the test by 1996 yeah that's not part of it you keep it to yourself and no one knows the deal but you're not alone that's just a show and gold in a cross some spoken thoughts they rust a lot the life we had that's over now yeah that's not part of it you know your head wont suggest anything that hasn't passed the test by 1996