The first discovery of the Golden Ratio is heavily theorized but actually unknown. Some believe that it was discovered by the Pythagoreans (a group that studied mathematics, music and astronomy under Pythagoras of Samos (c. 570 - c. 495 B.C.)) but some believe that the great pyramids of Egypt were designed and built using the golden ratio prior to Pythagoras. The same can be said for Greek architecture and works of art. Some analyze the works and claim to find the Golden Ratio present. Others critique this idea and believe that the lines and geometries they use are ambiguous and seek too hard to assign the ratio to them when they are not clearly there. The only ones we can be sure about are those where documentation has survived that states the artist or architect's intentions with regards to the Golden Ratio (Livio, 2003).
One thing is for certain and that is that the Golden Ratio has been around for a very long time. Whether the Egyptians and Babylonians knew about the ratio and used it in their designs is unclear. Pythagoras himself probably studied mathematics in Egypt and Babylon and therefore may have learned what he knew of the Golden Ratio instead of discovering it (Livio, 2003). If indeed the Pythagoreans did discover the Golden Ratio, it probably came out of their study of the regular pentagon (a regular polygon with 5 sides) and the pentagram (a regular 5-sided star that can be inscribed in a pentagon).
The pentagram inscribed in a regular pentagon was the symbol used by the Pythagoreans for their organization. The Pythagoreans believed that all geometric shapes could be described using integers. Hippasus of Metapontum (ca. 450 BCE) discovered that the ratio of the side of a regular pentagram to the side length of the pentagon was not expressible in terms of integers and this would have been upsetting to the Pythagoreans. If they did indeed make this discovery then the concept of irrational numbers may have come out of working with the Golden Ratio and/or the Pythagorean Theorem. It just so happens that the irrational number Hippasus found would have been the Golden Ratio (Posamentier, 2007).
The first comprehensive definition and appearance of the Golden Ratio was given about 300 B.C. by Euclid of Alexandria. Euclid is considered the founder of formalized geometry. (Livio, 2003) It has fascinated those who have known about it ever since. The Renaissance was a time in which the Golden Ratio left a strictly mathematical realm, and became a way to explain things in the natural world and to enhance the arts.