This formula is attributed to Binet (1843).<p>See <a href="https:&#x2F;&#x2F;math.temple.edu&#x2F;~reich&#x2F;Fib&#x2F;fibo.html" rel="nofollow">https:&#x2F;&#x2F;math.temple.edu&#x2F;~reich&#x2F;Fib&#x2F;fibo.html</a> for more on the Fibonacci sequence and the golden mean.