The Study Of Golden Section

The golden section is one of the most elegant and beautiful rations in the universe.Defined as a line segment divided into two unequal parts,such that the ratio of the shorter portion to the longer portion is the same as the longer portion to the whole.The study of golden section can be traced back to the ancient Greek,the Pythagoreans had discovered and very likely mastered it.A deep research into it by Eudoxus later,Euclid gave an integral geometry solution to it and proved it in his famous monograph Elements.After the Revival of Leaming,golden section was used more and more extensively in production and living.It has been focused on not only by mathematicians,but also painters,musicians and architects.Through researching on the beginning and early development of golden section,the paper draws a conclusion that the conception of golden section was brought forward for the construction of regular pentagon and perhapas the incommensurable quantity was first discovered via golden section.The paper also summarizes the names and signs which standed for golden section before and discusses the properties and applications of golden section.Analyzing the reason why golden section couldn't be discovered by Chinese mathematicians and the research of Qian—Qing mathematicians on it, the paper tries to probe into the educational significance of golden section at last.