Early Historical Research On Platonic Solids

The rational discussion of the problem of ultimate reality began in ancient Greece around the 6th century BC.The early Ionian philosophers reduced the problem to earth,water,air and fire,and later the Pythagorean school classified it into the problem of Numbers(or mathematics).Plato,who was deeply influenced by Pythagoras,further geometrized the four elements and held that they corresponded to the first four of the only five regular polyhedra--regular hexahedron,regular icosahedron,regular octahedron and regular tetrahedron.The fifth kind of regular polyhedron,the regular dodecahedron,corresponds to what makes up the "lunar world",which Aristotle named the "ether".These five regular polyhedra are called "The Platonic Solids",and their ideas have had a profound impact on many fields such as western science and philosophy.Based on Plato's five regular polyhedron as the main research object,through careful study of the specific content of Platonic solid,and the time background,and academic background of mathematics,geometry,and aims to clarify the early Platonic solid historical development vein,analyzes the role of Platonic solid in the cosmological thought and its implicit in the political thought,and in the case of Aristotle and Euclid,further illustrates these thoughts give after Plato the impact of Greek mathematics and science.This paper mainly discusses the specific content of Plato's five regular solids Works of Plato,and studies from the following three aspects and draws the conclusion:First,a review of the development of the early "Platonic solids",and focused on the discussion and interpretation of the current controversy over the origin of the "Platonic solids".Understand the social background of the time and the influence of mathematics before Plato on him.Second,the in-depth study of the specific content of the "Platonic solids",including: a brief analysis of the mathematical ideas behind the formation of the "Platonic solids",and the concept of Plato before and the composition of the "Platonic solids" The key idea-physical geometry thoughts are compared,and the ideological foundation of the formation of "Platonic solids" is deeply understood,paving the way for further exploration.Emphasis is placed on the in-depth analysis of Plato's original work in Plato's original work,revealing its important position in Plato's thought.Onthe basis of this analysis,the real purpose and use of the "Platonic solids" is introduced,which is explained in two aspects: cosmic order and political order.Third,Plato's three-dimensional study was further placed in the social environment at that time.Because there were many characters involved at that time and the time span was large,Aristotle and Euclid,two typical examples,were selected in this paper to reveal some influences brought to them by Plato's three-dimensional proposal.Finally,out of consideration of the completeness of this thesis and the expansion of future research space,it further explains the influence of Plato's stereoscopic thinking on the development of western mathematics and modern science in the long history.