Geometric topology | Manifolds | Topological spaces | Surfaces
In topology, a branch of mathematics, the Klein bottle (/ˈklaɪn/) is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined. Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. Other related non-orientable objects include the Möbius strip and the real projective plane. While a Möbius strip is a surface with boundary, a Klein bottle has no boundary. For comparison, a sphere is an orientable surface with no boundary. The concept of a Klein bottle was first described in 1882 by the German mathematician Felix Klein. (Wikipedia).
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/3kIo
From playlist 3D printing
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/2p3Z
From playlist 3D printing
A mirror paradox, Klein bottles and Rubik's cubes
The Mathologer puts the latest $2000 addition to his Klein bottle collection to work. A couple of first-ever fun mathematical stunts in this video. This video finishes with a puzzle for you to think about. We posted a video with the solution on 1 August 2015: https://youtu.be/ZMC61C5tigA
From playlist Recent videos
How to make a Klein Bottle (in three dimensions) - Numberphile
Cliff Stoll on how he makes Klein Bottles from glass. More links & stuff in full description below ↓↓↓ More videos on Klein Bottles: http://bit.ly/KleinBottles ACME Klein Bottles: http://bit.ly/ACME_Klein Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: htt
From playlist Klein Bottles on Numberphile
The Coca-Cola Klein Bottle - Numberphile
Cliff Stoll - the King of Klein Bottles - shows us more designs, including the Coke Klein Bottle... Full Klein Bottle Playlist: http://bit.ly/KleinBottles More links & stuff in full description below ↓↓↓ More videos with Cliff Stoll: http://bit.ly/Cliff_Videos Cliff's Klein Bottle shop:
From playlist Klein Bottles on Numberphile
Your Klein Bottle is in the Post - Numberphile
Klein bottle enthusiast Cliff Stoll shows us his unique system for sending bottles to customers. More links & stuff in full description below ↓↓↓ Cliff's online store: https://www.kleinbottle.com More videos on our Klein Bottle playlist: http://bit.ly/KleinBottles Cliff Stoll playlist:
From playlist Klein Bottles on Numberphile
Cliff Stoll is passionate about Klein Bottles. More links & stuff in full description below ↓↓↓ Don't miss the video about how he uses a robot to store 1,000 bottles UNDER his house... https://youtu.be/-k3mVnRlQLU More videos on Klein Bottles: http://bit.ly/KleinBottles ACME Klein Bottl
From playlist Klein Bottles on Numberphile
The 17-Klein Bottle - Numberphile
17 Klein Bottles become 1 - featuring Cliff Stoll and the glasswork of Lucas Clarke. More links & stuff in full description below ↓↓↓ More Cliff videos: http://bit.ly/Cliff_Videos More Klein Bottle videos: http://bit.ly/KleinBottles Buy glassware from Cliff (if you dare): https://www.kl
From playlist Klein Bottles on Numberphile
Hunt for the Elusive 4th Klein Bottle - Numberphile
Carlo Séquin on his search for the elusive "fourth type of Klein bottle". More videos on Klein Bottles: http://bit.ly/KleinBottles More links & stuff in full description below ↓↓↓ Carlo's paper: http://bit.ly/Carlo_Klein Also featuring Carlo: Mobius House https://youtu.be/iwo7JReFTeg Tor
From playlist Carlo Séquin on Numberphile
Cutting a Klein Bottle in Half - Numberphile
Klein Bottle enthusiast Cliff Stoll uses a diamond saw on a glass Klein Bottle. More links & stuff in full description below ↓↓↓ More videos about his bottles: http://bit.ly/KleinBottles Cliff's site (selling bottles): http://bit.ly/ACME_Klein Support us on Patreon: http://www.patreon.c
From playlist Klein Bottles on Numberphile
Klein Bottles with Cliff (extra footage)
Some extras with Cliff Stoll including his unique sales pitch - find the main videos at: http://bit.ly/KleinBottles Bottles under the house: https://youtu.be/-k3mVnRlQLU NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberph
From playlist Klein Bottles on Numberphile
Professor Carlo Séquin explains super bottles - and a super duper bottle. More Klein Bottle videos: http://bit.ly/KleinBottles More Carlo videos: http://bit.ly/carlo_videos More links & stuff in full description below ↓↓↓ Carlo Séquin is based at the University of California, Berkeley. S
From playlist Carlo Séquin on Numberphile
Can you solve THE Klein Bottle Rubik's cube?
In this video I tell you about Klein bottle Rubik’s cubes, Torus Rubik's Cubes and Klein Quadric Rubik's cubes as an introduction to a whole new universe of twisty puzzles. Get your own Klein bottle Rubik’s cube, as well as more than 800 other topological twisty puzzles by downloading th
From playlist Recent videos
Applied topology 4: An introduction to the torus and Klein bottle
Applied topology 4: An introduction to the torus and Klein bottle Abstract: We explain how the torus (the surface of the donut) is a 2-dimensional manifold that fits in 3D, whereas the Klein bottle is a 2-dimensional manifold that doesn't fit in 3D but does fit in 4D. This video accompan
From playlist Applied Topology - Henry Adams - 2021
How to make a Klein Bottle from an old pair of jeans - Numberphile
More Klein bottle videos: http://bit.ly/KleinBottles More links & stuff in full description below ↓↓↓ Visit Cliff Stoll's online store: http://www.kleinbottle.com/ More Cliff videos: http://bit.ly/Cliff_Videos Numberphile is supported by the Mathematical Sciences Research Institute (MSR
From playlist Klein Bottles on Numberphile