Non-Linear Transformations Visualized | z^2, Swirl, & Exponential Maps #maths #linear #shorts

We explore the visual beauty of Non-Linear Transformations—seeing what happens to a standard grid when we apply mathematical functions that twist, bend, and warp space instead of keeping lines straight. 📽️ Transformation 1: Complex Squaring The grid lines curve into parabolas and hyperbolas. This represents the complex function f(z) = z^2. Transformation 2: The Swirl (Radial Rotation)Space twists around the center. Points further from the origin rotate more, creating a whirlpool effect. Transformation 3: The Exponential Map The rectangular grid is transformed into a polar grid. Vertical lines become circles, and horizontal lines become rays. Trending Topics We Cover: ✅ Math Explanation – Visualizing how functions map inputs to outputs in 2D space. ✅ Linear vs. Non-Linear – Seeing the difference between matrix transformations (straight lines) and curved maps. ✅ Complex Analysis – A visual look at the famous z^2 and e^z functions. ✅ Topology Basics – How space can be stretched and squashed without breaking. ✅ Coordinate Systems – mapping Cartesian coordinates to Polar-like structures. ✅ Visual Math – Satisfying animations of grid warping. 📈 2D Mathematical Graphs 🌀 Topology Animations 📺🔥 Stay Updated with the Best Educational Shorts! 📌 LIKE | COMMENT | SHARE | SUBSCRIBE 🔗 YouTube:    / @therootofinfinity   📸 Instagram:   / the_root_of_infinity   #shorts #youtubeshorts #nonlinear #topology #complexanalysis #maths #geometry #visualmath #mathanimation #education #study #science #mathematics #viralshorts #satisfying #calculus #graphs #mathfacts #stemeducation #therootofinfinity #education #animation #logic #viral #video #viralvideo #viralshorts #viralvideos #viralreels #mathematic #reels #facebook #instagram #integration #graph #2danimation #3dshapes #visulization #trigonometry #explore #explorepage #graphics