大学卓越班英语几何问题演示文档

.,Geometry,.,Contents,1,2,3,4,The history of geometry,Important concepts in geometry,An example of geometric problem,Applications of geometry,.,Part One,The history of geometry,.,The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia(美索不达米亚) and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes(体积), which were developed to meet some practical need in surveying, construction, astronomy, and various crafts.,.,In the 7th century BC, the Greek mathematician Thales (泰勒斯) used geometry to solve problems such as calculating the height of pyramids(金字塔) and the distance of ships from the shore.,.,Pythagoras(毕达哥拉斯) established the Pythagorean School, which is credited with the first proof of the Pythagorean theorem(勾股定理), the statement of the theorem has a long history.,.,Archimedes(阿基米德) (c. 287212 BC) used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave remarkably accurate approximations of .,.,In the early 17th century, there were two important developments in geometry. The first was the creation of analytic geometry(解析几何) or geometry with coordinates and equations by Ren Descartes(笛卡尔) and Pierre de Fermat(费马).,.,Part,Two,Important concepts in geometry,.,Points,Lines,Planes,Curves,Cambers,.,Topologies and metrics(拓扑和度量)A topology is a mathematical structure on a set that tells how elements of the set relate spatially to each other and measuring distances between points.,Mbius strip 莫比乌斯带,.,Compass and straightedge constructions(尺规作图)Classical geometers paid special attention to constructing geometric objects. Classically, the only instruments allowed in geometric constructions are the compass and straightedge.,.,Dimension(维度)Where the traditional geometry allowed dimensions 1 (a line), 2 (a plane) and 3 (our ambient world conceived of as three-dimensional space),.,Symmetry(对称)The theme of symmetry in geometry is nearly as old as the science of geometry itself. Symmetric shapes such as the circle, regular polygons.,.,Part Three,An example of geometric problem,.,Princess Dido story,.,The relationship of different shapes with the same perimeter to their areas,S=26=12,S=35=15,S=44=16,The square with its four equilateral sides has the biggest area of all possible rectangles of a given perimeter.,Perimter=16,.,All the triangles and rectangles, if all the angles and sides are the same, have the biggest area for a given perimeter. This is true for any possible shape of equilateral polygons(等边多边形).,S=18.5,S=19.9,S=20.4,.,Part Four,Applications of geometry,.,ArtMathematics and art are related in a variety of ways. For instance, the theory of perspective showed that there is more to geometry than just the metric properties of figures: perspective is the origin of projective geometry.,.,ArchitectureMathematics and architecture are related, since, as with other arts, architects use mathematics for several reasons. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building.,.,AstronomyThe field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, have served as an important source of geometric problems throughout history.,.,Reference,Elissar, Dido, the Queen of Carthage