59: A Good Source of Fibers (Fiber Bundles)
Breaking Math Podcast
English - March 21, 2021 21:43 - 42 minutes - 57.7 MB - ★★★★ - 316 ratingsMathematics Science math mathematics computer science a.i. machine learning physics science nerdy linguistics Homepage Download Apple Podcasts Google Podcasts Overcast Castro Pocket Casts RSS feed
Previous Episode: 58: Bringing Curvy Back (Gaussian Curvature)
Next Episode: 60: HAMILTON! [But Not the Musical] (Quaternions)
Mathematics is full of all sorts of objects that can be difficult to comprehend. For example, if we take a slip of paper and glue it to itself, we can get a ring. If we turn it a half turn before gluing it to itself, we get what's called a Möbius strip, which has only one side twice the length of the paper. If we glue the edges of the Möbius strip to each other, and make a tube, you'll run into trouble in three dimensions, because the object that this would make is called a Klein flask, and can only exist in four dimensions. So what is a fiber? What can fiber bundles teach us about higher dimensional objects?
All of this, and more, on this episode of Breaking Math.
[Featuring: Sofía Baca, Meryl Flaherty]