Modern Geometry And Competitive Mathematics

Modern Geometry originated in the second half of the 19th century, from then it was very prosperous till the beginning of the 20th century. Now, some of its research results often are simplified in the form of Mathematics Olympiad, making more secondary school teachers and students sharing the interest of Euclidean geometry. In this paper, we will review the history of modern geometry and the development of competitive mathematics firstly. Then basing on the book "Modern Geometry" and the latest mathematics proposition on the tournament question of plane geometry, explores the contact of Competitive Mathematics and Modern Geometry.The main content are as follows:(1) This author focused on the research purpose and meaning. (2) By comparing the history of mathematical competition with its present situation, we can get a more comprehensive understanding on competitive mathematics, especially the research on plane geometry in China. (3) According to a book "Modern Geometry". the writer introduced the latest research developments of modern geometry. (4) By combining with the contents and research methods in modern geometry and the latest mathematics proposition on the tournament question of plane geometry, The author researched on the inspiration of modern geometry for the development of competitive mathematics. (5) Thinking and outlook.In this paper, we will build the bridge between the research of modern geometry, competitive mathematics and the geometric teaching in secondary school, by discussing " Modern Geometry and Mathematics Competition problem on geometry" and " Modern Geometry and Mathematics Competition proposition on geometry"The main innovation are:(1) Publish part of reserch on the proof of theorem in Modern Geometry for the first time, which was not given in that book. (2) Revise more than 30 scientific or typesetting errors in Modern Geometry. (3) Publish some simpler geometric solution independently.