Newton's method, from 1670, is a crazy fast way of generating square roots. The number of accurate digits in the square root doubles every single step.
It is derived by taking the Newton Raphson equation
https://en.wikipedia.org/wiki/Newton%...
and plugging in the equation for a square as the function x^2 = a
Images I used
newton https://pixabay.com/vectors/isaacnew...
telescope https://en.wikipedia.org/wiki/File:Ne...
prism https://en.wikipedia.org/wiki/File:Di...
Mercury https://commons.wikimedia.org/wiki/Fi...
calculus https://commons.wikimedia.org/wiki/Fi...
Newton Apple https://commons.wikimedia.org/wiki/Fi...
laws of motion https://commons.wikimedia.org/wiki/Fi...
quarter https://pixabay.com/photos/coinquart...
chemistry https://pixabay.com/photos/testtube...
binomial https://pixabay.com/vectors/bayesian...