Domain Coloring the Real Number Line // #SoME2 [ALGEBRA] [ANALYSIS]

I wanted to do something special for Grant Sanderson's (of  @3Blue1Brown  fame) Summer of Math Exposition 2, so I decided to work out an idea I've had for a while: what if we visualized a real-valued function along the number line using a domain coloring, similarly to how we can visualize a complex-valued function in the complex plane? Subscribe: https://bit.ly/polymathematic | Enable ALL push notifications 🔔 Right away, the one-dimensional representation reveals some of the limitations of domain colorings. Although direction is represented well-enough, magnitude is quite difficult to distinguish. But something's better than nothing, and so it's worth putting in the effort to develop intuitions about the "shape" of a complex mapping from its coloring. If you'd like to explore more about domain colorings, particularly how they translate the magnitude and direction of a complex output into an HSV format, check out the Wikipedia page here: https://en.wikipedia.org/wiki/Domain_.... If you'd like to play with some of the  @Desmos  graphs I put together, you can find them here: Image of the Complex Disc: https://www.desmos.com/calculator/dw3... Transforming Two Number Lines into the Coordinate Plane: https://www.desmos.com/calculator/mkl... Number Line Coloring: https://www.desmos.com/calculator/ttp... Domain Coloring: https://www.desmos.com/calculator/xyx... This video is my entry into SoME2. I think there will be a playlist of other entries at some point, and when I get my hands on it, it'll go here. #some2 #realanalysis #algebra Follow Tim Ricchuiti: TikTok:   / polymathematic   Twitter:   / poly_mathematic   Instagram:   / polymathematicnet   Reddit:   / polymath-matic   Facebook:   / polymathematic   Watch more Math Videos: Math Minis:    • Math Mini   Math Minutes:    • Math Minutes   Number Sense:    • Number Sense (UIL / PSIA)   MATHCOUNTS:    • MATHCOUNTS   real analysis