We discuss the well-known importance of the golden ratio in Science and Art with few examples: its theoretical value is often taken as a good model in many applications. How good is this model in practice? We agree with many authors that more precision is needed giving, when possible, a measure of the best possible approximation. We deal with several definitions and representations, also comparing this irrational number and its rational approximations to other similar constants.
Falcolini, C. (2020). How gold is the golden ratio?. In 19th Conference on Applied Mathematics, APLIMAT 2020 Proceedings (pp.402-407). Bratislava : Slovak University of Technology in Bratislava.