Newton's Square Roots

This method was used by Newton to find square roots.

sqrt_newton <- function(value, init, epsilon = 0.01){
  while(abs(init**2 - value) > epsilon){
    init <- 1/2 *(init + value/init)
    print(init)
  }
  return(init)
}

sqrt_newton(24, 3)

[1] 5.5
[1] 4.931818
[1] 4.899089
[1] 4.899089