Mastering Math Puzzles: Higher Dimensions & Geometric Challenges
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Today, the lads at 3Blue1Brown have cooked up a series of mind-bending puzzles that'll have your brain doing more laps than a Formula 1 race. First up, they're diving headfirst into the world of higher dimensions, starting with a hexagon tiling extravaganza. Imagine rotating hexagons like a Rubik's cube on steroids to create new patterns - it's like a geometric dance that'll leave you dizzy with excitement. But hold onto your helmets because the real challenge lies in figuring out the maximum number of moves needed to shift from one mind-bending pattern to another. It's a puzzle so complex, it'll make your head spin faster than a Bugatti Veyron.
Next on the agenda is the Tarski-Planck problem - a mathematical conundrum that'll have you scratching your head like a confused chimpanzee. Picture covering a circle with strips like a giant mathematical pie, and the question is, can you do it in a way that minimizes the sum of widths? It's a race against the clock to crack the code and find the most efficient strip strategy. And just when you thought things couldn't get any wilder, the lads throw in a curveball with the intersection of external tangents to three circles. Strap in, because this puzzle will have you navigating through a mathematical maze that's trickier than a rally stage in the Amazon rainforest.
But fear not, because the lads at 3Blue1Brown have a trick up their sleeve - a leap into the third dimension. By projecting circles onto spheres and visualizing external tangents as cones, they unveil a whole new perspective that'll have you seeing math in a way you never thought possible. It's like taking a rollercoaster ride through a mathematical wonderland, where every twist and turn reveals a new layer of complexity. So buckle up, because this mathematical journey is about to take you on a ride of a lifetime, where the only limit is your imagination.
Image copyright Youtube
Image copyright Youtube
Image copyright Youtube
Image copyright Youtube
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Mention of using Monge's Theorem in practical applications like building laser pointing systems
Comments on the uniqueness and difficulty of comprehending 4D structures
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