Approximate Square Roots with Calculus! @MathVisualProofs

Uploaded December 2024 | Updated September 2026, 2 weeks ago

This is a visual technique that uses linear approximation to find the square root of a whole number by finding the equation of the tangent line to points on the square root curve.

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$Golden Dragon Fractal: Order from Chaos (iterated function system) In this video, we show how to use a random process of iteratively applying two affine transformations in the real plane to generate a fractal known as the Golden Dragon. What happens if you do something similar with different affine transformations? If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! Check out these videos for related constructions: https://youtu.be/fFIyqMiycs4 https://youtu.be/rLxx6b-oJGo https://youtu.be/NBI_5GdvqUo This animation was inspired by Larry Riddles awesome website: https://larryriddle.agnesscott.org/ifs/heighway/goldenDragon.htm #chaos #chaosgame #goldendragon #dragon #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractals #fractal To learn more about animating with manim, check out: https://manim.community Music in this video: idling around by Diamond Ace | https://soundcloud.com/diamond-ace-music Music promoted by https://www.free-stock-music.com Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en_US$

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