What is the graph of x^a when a is not an integer? An unusual look at familiar functions скачать в хорошем качестве

What is the graph of x^a when a is not an integer? An unusual look at familiar functions

This is my entry into the Second Summer of Math Exposition. I used to wonder about these questions ever since my first year in university, so in a sense this is a rather personal subject for me. I hope that this video reaches someone else who is also wondering about these issues. Here's the Desmos document for visualizing the n complex roots of any complex number: https://www.desmos.com/calculator/1v4... Videos mentioned in order of apparition: e to the pi i, a nontraditional take (old version)    • e to the pi i, a nontraditional take (old ...   The 'Everything' Formula - Numberphile    • The 'Everything' Formula - Numberphile   Winding numbers and domain coloring    • Winding numbers and domain coloring   The 5 ways to visualize complex functions | Essence of complex analysis #3    • The 5 ways to visualize complex functions ...   Visualizing Complex-Valued Functions    • Visualizing Complex-Valued Functions   Jeff Tupper's webpage on the graph of x^x http://www.peda.com/grafeq/gallery/ro... A relevant Stack Exchange question and answer that touches on these ideas: https://mathematica.stackexchange.com... Chapters: 00:00 Intro and problem motivation 01:49 The R-to-C graph of x^a 04:37 The R-to-C graph of a^x 06:37 Rotations in complex exponentiation 07:27 The R-to-C graph of x^x 08:17 An alternative version of the graph of x^x 12:37 Recap of the various graphs of x^x 13:49 Homework 14:09 Summary and outro Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a... Stream the music on Spotify: https://open.spotify.com/album/1dVyjw...