Is this one connected curve, or two? Bet you can’t explain why...
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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
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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
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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:
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