Euclid of Alexandria provided the first comprehensive definition and appearance of what we now know as the Golden Ratio (approximately 1.618) around 300 B.C.
While the Golden Ratio may have been observed in art and architecture before Euclid, he was the first to formalize its mathematical properties within geometry. He did this by defining what he called the "extreme and mean ratio," which is essentially the Golden Ratio. Euclid described it in Elements as dividing a line segment into two parts such that the ratio of the whole segment to the longer part is the same as the ratio of the longer part to the shorter part.
Therefore, while not necessarily discovering it in the sense of being the first to observe it in nature or art, Euclid is credited with its initial, comprehensive mathematical definition and formalization.
