On Leonardo Da Vinci's Geometrical Thought And Its Application In Painting

Leonardo di ser Piero da Vinci(1452.4.23(July 15th)– 1519.5.2)with clever brains,keen observation and tireless diligence became "The most perfect representative of the Renaissance",he is not only a brilliant painter,but also a skilled inventor,architect,and a mathematic thinker.Da Vinci's mathematical thoughts are mainly embodied in geometry,especially in his paintings.This paper attempts to use the golden section as the main line to explain Da Vinci's geometric thoughts and explore its perspective painting.The article involves two important works related to Da Vinci,one is Luca Paccioli's "Divina proportione",in which nearly 90% of the 60 illustrations are drawn by Leonardo based on five variants of regular polyhedrons,and the other is the "Painting Theory" compiled by the descendants of Da Vinci's numerous manuscript notes.The book records geometric problems such as perspective and proportion.This article discusses Da Vinci's geometry through the interpretation and research of his two works and the early works "Angel's Annunciation","The goddess of the Rocks" and the mid-term work "The Last Supper" and the late work "Mona Lisa".This article is divided into five chapters.The first chapter is the introduction,expounds the reason and significance of the topic selection;summarizes the research status of the Renaissance culture and Da Vinci in the academic circles at home and abroad;introduces the research ideas,research methods and research value and so on.The second chapter introduces the background and life of Da Vinci's time,clarifies the influence of ancient Greek Archimedes' geometric thought on Da Vinci's geometric thoughts,and focuses on Da Vinci's childhood and apprenticeship and career.The third chapter discusses Da Vinci's geometric thoughts,mainly discussing Da Vinci's research on the geometric problems of the regular polyhedron,the golden section and the rounded square.In the appendix of Luca Paccioli's "Divina proportione",there are five models of regular polyhedrons in the illustrations by Da Vinci.The geometry of polyhedrons has been extensively studied in ancient Greece,Da Vinci's research on the polyhedron and the golden section is presented in the form of an illustration set.The research on the problem of turning the circle into a square is in his complicated manuscript notes.Da Vinci's sketch "Vitruvian" and the circular "flower knot" in the three-dimensional space he designed is the expression of "rounding into a square".The fourth chapter discusses the application of Da Vinci's geometric thoughts in painting.One of the manifestations is the application of perspective.Da Vinci's "Theory of Painting" records his mathematical problems related to perspective,proportion,etc,and focuses on his early works "Angel's Annunciation","The goddess of the Rocks" and the mid-term work "The Last Supper" and in the late work "Mona Lisa".The fifth part is the summary part of this article.This chapter explains Da Vinci's geometric thoughts and the conceptual basis of his application from the perspective of epistemology-the religious and natural views,and further comments on Da Vinci's geometric ideas and perspective painting.