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Go to to get started learning STEM for free. The first 200 people get 20% off an annual premium subscription. One of the most fundamental properties of geometry is connectedness: when a shape is a single continuous entity. But how do you define this idea precisely so that you can apply it even to extremely bizarre shapes in very strange spaces? =Chapters= 0:00 - The Topologist's Sine Curve 1:54 - The goal of this video 3:06 - Path-Connectedness 6:56 - A new definition? 7:37 - Topology basics 10:27 - A snag 12:04 - Connectedness 2.0 and the Topologist's Sine Curve 15:48 - Who's right? 17:38 - The Ordered Square 19:32 - The connection between the definitions 21:18 - The underappreciated art of crafting definitions 22:16 - Brilliant ad =============================== CREDITS The songs used in this video are (in order of first appearance) “Dream Escape“, “Checkmate“, “Rubix Cube“, and “Twinkle in the Night“. The song “Rubix Cube“ comes courtesy of =============================== Want to support future videos? Become a patron at Thank you for your support! =============================== The animations in this video were mostly made with a homemade Python library called “Morpho“. If you want to play with it, you can find it here:
