For example; the Fibonacci sequence is a string of numbers, F = 1.
You can see quickly that the string of numbers is 0, 1, 1, 2, 3, 5, 8, 13, 21, …
His pupils handed these on, formed them partly into Hieroi Logoi (“Sacred Discourses”), of which different versions were current from the 4th century on, and interpreted them according to their convictions.
The golden ratio is defined in many (equivalent) ways but the best known is: if A and B are two numbers such that the ratio of A B to A is equal to the ratio of A to B, then g=A/B.
Text is available under the CC BY-SA 4.0 license; additional terms may apply.By laying stress on certain inner experiences and intuitive truths revealed only to the initiated, Pythagoreanism seems to have represented a soul-directed subjectivism alien to the mainstream of pre-Socratic Greek thought centring on the , which often claimed to achieve through intoxication a spiritual insight into the divine origin and nature of the soul.Yet there are also aspects of it that appear to have owed much to the more sober, “, as did their naturalistic predecessors, though they claimed to find its key in mathematical form rather than in any substance.Expressed algebraically: The golden ratio is often denoted by the Greek letter Adolf Zeising, whose main interests were mathematics and philosophy, found the golden ratio expressed in the arrangement of branches along the stems of plants and of veins in leaves.He extended his research to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, even to the use of proportion in artistic endeavors.A rectangle, where the ratio of the long side to the short side is g, is called the “golden rectangle”.