A surface is non-orientable if there is no consistent notion of right handed versus left handed on it. The simplest example is the Mobius band, a twisted strip with one side, and one edge. An important deformation gives what we call a crosscap. This is the sixth lecture in this beginner's course on Algebraic Topology, given by Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW. ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com/. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated. *********************** Here are all the Insights into Mathematics Playlists: Elementary Mathematics (K-6) Explained: null list=PL8403C2F0C89B1333 Year 9 Maths:    • Year9Maths   Ancient Mathematics:    • Ancient Mathematics   Wild West Banking:    • Wild West Banking   Sociology and Pure Mathematics:    • Sociology and Pure Mathematics   Old Babylonian Mathematics (with Daniel Mansfield): null list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov Math History:    • MathHistory: A course in the History ...   Wild Trig: Intro to Rational Trigonometry:    • WildTrig: Intro to Rational Trigonometry   MathFoundations:    • Math Foundations   Wild Linear Algebra:    • Wild Linear Algebra   Famous Math Problems:    • Famous Math Problems   Probability and Statistics: An Introduction:    • Probability and Statistics: an introd...   Boole's Logic and Circuit Analysis:    • Boole's Logic and Circuit Analysis   Universal Hyperbolic Geometry:    • Universal Hyperbolic Geometry   Differential Geometry:    • Differential Geometry   Algebraic Topology:    • Algebraic Topology   Math Seminars:    • MathSeminars   ************************ And here are the Wild Egg Maths Playlists: Triangle Centres: https://www.youtube.com/watch?v=iLBGXDSUohM Six: An elementary course in pure mathematics:    • Six: An elementary course in Pure Mat...   Algebraic Calculus One:    • Algebraic Calculus One   Algebraic Calculus Two:    • Algebraic Calculus Two   м