Is it true that the $\sqrt{3}$ can be written as an infinite fraction? How can we prove that?
I was doing Real Analysis, Algebra and Calculus the other day, and I've read in a book that any irrational number could be written as an infinite fraction, it even showed how tan x could be written as that! ( as part of Lambert's proof that Pi is irrational) then it gave us an infinite fraction that is equal to the square root of 3, so how to prove it? I am not familiar with complicated infinite fractions and I didn't find many answers online, I did try myself but I couldnt't really reach anything, I made a graph and stuffs and it showed that with each new fraction you get closer to the square of 3, I am just starting my Higher Education Journey and improving my Mathemathics would really help, thanks.