Permalink Submitted by Chris Budd on November 19, 2020

Yes you can, and in fact these are the best rational approximations to the golden ratio. However, they are still poor approximations and even if you take numbers in the higher range the approximation is not good, and only slowly converges to the correct value. This is in contrast to a transcendental number such as pi which you can approximate much better by using a fraction. For example the approximation of pi given by 355/113 is very good indeed, and much much better than you would get for phi for the ratio of two succesive numbers in the Fibonacci sequence such as 233/144.

## Approximation of phi

Yes you can, and in fact these are the best rational approximations to the golden ratio. However, they are still poor approximations and even if you take numbers in the higher range the approximation is not good, and only slowly converges to the correct value. This is in contrast to a transcendental number such as pi which you can approximate much better by using a fraction. For example the approximation of pi given by 355/113 is very good indeed, and much much better than you would get for phi for the ratio of two succesive numbers in the Fibonacci sequence such as 233/144.