Thinking visually about higher dimensions
How do you think about a sphere in four dimensions? What about ten dimensions? Podcast! https://www.benbenandblue.com/ Problem-driven learning on at ...
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Math is sometimes a real tease it seduces us with the beauty off reasoning geometrically in two and three dimensions Where there's this really nice back-and-forth between pairs or triplets of numbers and spatial stuff that our visual Cortex is good at processing for example if you think about a circle with radius one centered at the origin You are in effect conceptualizing every possible pair of numbers x and y that satisfy a certain numerical property that x² + y² is 1 and The usefulness here is that a lot of facts that look opaque in a purely analytic context become quite clear geometrically and vice-versa Honestly this channel has been the direct beneficiary of this back and forth Since it offers such a rich library of that special category of cleverness that involves connecting two Seemi...
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Math is sometimes a real tease it seduces us with the beauty off reasoning geometrically in two and three dimensions Where there's this really nice back-and-forth between pairs or triplets of numbers and spatial stuff that our visual Cortex is good at processing for example if you think about a circle with radius one centered at the origin You are in effect conceptualizing every possible pair of numbers x and y that satisfy a certain numerical property that x² + y² is 1 and The usefulness here is that a lot of facts that look opaque in a purely analytic context become quite clear geometrically and vice-versa Honestly this channel has been the direct beneficiary of this back and forth Since it offers such a rich library of that special category of cleverness that involves connecting two Seemi...
