In mathematics, a solid Klein bottle is a three-dimensional topological space (a 3-manifold) whose boundary is the Klein bottle. It is homeomorphic to the quotient space obtained by gluing the top disk of a cylinder to the bottom disk by a reflection across a diameter of the disk. Alternatively, one can visualize the solid Klein bottle as the trivial product , of the möbius strip and an interval . In this model one can see that the core central curve at 1/2 has a regular neighborhood which is again a trivial cartesian product: and whose boundary is a Klein bottle. (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
Can you REALLY put a Rubik's cube in a Klein bottle?
The Mathologer goes to extremes to get some Rubik's cubes into weird shaped bottles. Again a fairly long video, so if you are in a rush try watching it at 2x its original speed through the YouTube preferences. If you interested in more details about various possible methods for advanced/cr
From playlist Recent videos
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
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
How to Fill a Klein Bottle - Numberphile
In a 3D world, it's possible to fill 4D Klein Bottles - featuring Cliff Stoll. More Cliff videos: http://bit.ly/Cliff_Videos More links & stuff in full description below ↓↓↓ More Klein Bottle videos: http://bit.ly/KleinBottles You can buy a bottle from Cliff: https://www.kleinbottle.com
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
Hypertwist: 2-sided Möbius strips and mirror universes
In this video the Mathologer sets out to track down the fabled 2-sided Möbius strips and Klein bottles inside some very exotic 3D universes. Also featuring 1-sided circles and cylinders and other strange mathematical creatures. Check out Jeffrey Weeks's amazing free "Torus Games" (play c
From playlist Recent videos
Quantifying nonorientability and filling multiples of embedded curves - Robert Young
Analysis Seminar Topic: Quantifying nonorientability and filling multiples of embedded curves Speaker: Robert Young Affiliation: New York University; von Neumann Fellow, School of Mathematics Date: October 5, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
This week’s video is about the beautiful mathematics you encounter when you try to turn ghostlike closed surfaces inside out. Learn about the mighty double Klein bottle trick, be one of the first to find out about a fantastic new way to turn a sphere inside out and have another go at earni
From playlist Recent videos
Robert YOUNG - Quantifying nonorientability and filling multiples of embedded curves
Abstract: https://indico.math.cnrs.fr/event/2432/material/17/0.pdf
From playlist Riemannian Geometry Past, Present and Future: an homage to Marcel Berger
AlgTop7: The Klein bottle and projective plane
The Klein bottle and the projective plane are the basic non-orientable surfaces. The Klein bottle, obtained by gluing together two Mobius bands, is similar in some ways to the torus, and is something of a curiosity. The projective plane, obtained by gluing a disk to a Mobius band, is one o
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Shapes and geometry of surfaces by Mahan Mj
WHEN: 4pm to 6pm Sunday, 26 November 2017 WHERE: J. N.Planetarium, Sri T. Chowdaiah Road, High Grounds, Bangalore Almost all shapes that we see around in space are examples of surfaces. We shall describe a method dating back to the 19th century of understanding these. Time-permitting, we
From playlist Kaapi With Kuriosity (A Monthly Public Lecture Series)
What is the 4th Dimension REALLY? - 4D Golf Devlog #2
A more practical explanation for those interested in exploring 4D spaces. For those not already familiar with basic 4D concepts, here's some videos I can recommend: "Visualizing 4D Geometry" https://www.youtube.com/watch?v=4URVJ3D8e8k "The things you'll find in higher dimensions" https:/
From playlist 4D Golf
Henry Adams (6/4/20): Descriptors of Energy Landscapes using Topological Analysis (DELTA)
Title: Descriptors of Energy Landscapes using Topological Analysis (DELTA) Abstract: Many of the properties of a chemical system are described by its energy landscape, a real-valued function defined on a high-dimensional domain. I will explain how topology, and in particular persistent ho
From playlist DELTA (Descriptors of Energy Landscape by Topological Analysis), Webinar 2020
Susan Goldstine - Maps of Strange Worlds: Beyond the Four-Color Theorem - CoM Jan 2021
In 1852, a math student posed a deceptively simple-sounding question: if you want to color a map so that bordering regions always have different colors, how many colors do you need? This opened a rabbit hole that has kept mathematicians, computer scientists, and philosophers occupied for
From playlist Celebration of Mind 2021
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
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