A Truly Crazy "Right" Triangle

Check out the main channel @polymathematic ! In today's video, I'm tackling the fascinating equation "π^4 + π^5 ≈ e^6" and bringing it to life through geometry. I'll show you how I turn this abstract mathematical statement into a tangible geometric figure - almost a right triangle with sides of π^2, π^(2.5), and a hypotenuse eerily close to e^3. Using Pythagoras' theorem as my guide, I dive into the relationship between π and e, dissecting how these transcendental numbers interact in a geometric setting. We'll walk through the algebra needed to morph our initial equation into this geometric wonder, all the while understanding the precision and boundaries of such an approximation. It's a journey from the realm of algebra into the visual world of geometry, shedding light on the intriguing dance between π and e. With great thanks to John Cook who first introduced me to this approximation. You can find more of his work here: https://www.johndcook.com/blog/. #PiAndEUnveiled #GeometricMath #AlgebraMeetsGeometry Follow Tim Ricchuiti: TikTok: https://www.tiktok.com/@polymathematic Mathstodon: https://mathstodon.xyz/@polymathematic Instagram: https://www.instagram.com/polymathematicnet Reddit: https://www.reddit.com/user/polymath-matic Facebook: https://www.facebook.com/polymathematic Watch more Math Videos: Math Minis: https://www.youtube.com/playlist?list=PLrc8spN1b3jkQynJ5heNvSs72gCPj_hwj Math Minutes: https://www.youtube.com/playlist?list=PLrc8spN1b3jmVFYwHiuMzCYJ0y_yiwUge Number Sense: https://www.youtube.com/playlist?list=PLrc8spN1b3jksKkY_oarNFEFAHjrIV97U MATHCOUNTS: https://www.youtube.com/playlist?list=PLrc8spN1b3jlqDkZXtby9lnEaOBy7-ZY0