Strange Spheres in Higher Dimensions - Numberphile
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I'm gonna try and capture, contain and investigate a higher dimensional sphere. Starting with a circle. So, if we begin in 2D, you've come across circles before. They look, you know, roughly like that. We're gonna try and contain a circle so we can look at how big it can be. So, what I'm gonna do is start with a box, four by four, for reasons I'll explain in a moment. So that's four units that way, it's four units that way. And now I'm going to put some safety padding spheres in there. So if you kind of measure, if I was to actually split this into quarters, I'm gonna put safety spheres, well, they're, they're circles. I'm gonna call them spheres no matter what dimension they're in, right? So when I say sphere,...
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I'm gonna try and capture, contain and investigate a higher dimensional sphere. Starting with a circle. So, if we begin in 2D, you've come across circles before. They look, you know, roughly like that. We're gonna try and contain a circle so we can look at how big it can be. So, what I'm gonna do is start with a box, four by four, for reasons I'll explain in a moment. So that's four units that way, it's four units that way. And now I'm going to put some safety padding spheres in there. So if you kind of measure, if I was to actually split this into quarters, I'm gonna put safety spheres, well, they're, they're circles. I'm gonna call them spheres no matter what dimension they're in, right? So when I say sphere,...
