Vedere la Quarta Dimensione con la Radice Quadrata | Superfici di Riemann e Numeri Complessi

🏆Discover the ClearMath Academy🏆 ▶ https://clearmath.it/ 📩IF YOU WANT A LESSON WITH ME📩▶ email me at [email protected] 🚀🚀 IF YOU WANT TO SUPPORT THE CHANNEL WITH €1 🚀🚀 ▶ https://www.paypal.com/donate/?hosted... Riemann surfaces are the most beautiful geometric objects in mathematics. We owe their creation to Bernhard Riemann, who figured out how functions of complex variables, which exist in the fourth dimension, could be represented. These Surfaces, besides being aesthetically pleasing, are extremely useful for representing multi-valued functions (i.e., functions that return multiple outputs for a single input) and for enhancing mathematical theorems like the Residue Theorem. Let's explore all the nuances of this latest marvel of Complex Analysis! Many thanks to @mathemaniac and @WelchLabs for enlightening me with their explanations, and of course, as always, thanks to @3blue1brown. Grant, I don't know if you'll ever watch this video, but know that over the past five years, you've always been my greatest professional aspiration. I can't thank you enough for creating this wonderful tool that is Manim, which has allowed me to do my dream job and do it exactly the way I want, replicating 1:1 what I've always had in mind but never been able to express as I wanted. Thanks again. THANK YOU also to all of you for your continued support, thanks to my subscribers, to those who comment, to those who share my videos, to my friends who have been putting up with the test videos I send them while I edit for 5 years: without you, ClearMath would be 1/20 of what it is now. Sorry, I'm very emotional today; towards the end of the video you'll understand why :') Happy studying! -Marco, ClearMath 00:00-01:15 The Square Root Paradox (Polydromy and Monodromy) 01:15-03:00 Riemann Surfaces in the Fourth Dimension 03:00-04:15 4D Rotations 04:15-05:37 Euler's Formula and Riemann Surfaces 05:37-06:50 Brackets and Technique (Branch Points and Cuts) 06:50-07:53 Generalization and Solved Exercise 07:53-08:27 Riemann Surface of the Logarithm Function 08:27-09:46 Review of the Residue Theorem 09:46-12:27 Residue Theorem and Riemann Surfaces (Solved Exercise) 12:27-14:52 Personal Reflections (and Saccharine)