文件名称：Perspectives on Projective Geometry
文件大小：5.83MB
文件格式：PDF
更新时间：2016-01-03 17:30:12
math 3d graphics Geometry mathematics
Geometry is the mathematical discipline that deals with the interrelations of objects in the plane, in space, or even in higher dimensions. Practicing geometry comes in very different flavors. More than any other mathematical discipline, the field of geometry ranges from the very concrete and visual to the very abstract and fundamental. In the one extreme, geometry deals with very concrete objects such as points, lines, circles, and planes and studies the interrelations between them. On the other side, geometry is a benchmark for logical rigor, the elegance of axiom systems, and logical chains of proof. There is a third way of thinking about geometry that stands alongside the visual and the logic-based approaches: the algebraic treatment. Here algebraic structures such as vectors, matrices, and equations are used to form a kind of parallel world, in which each geometric object and relation has an algebraic manifestation. In this parallel world, too, the considerations may be very concrete and algorithmic or very abstract and functorial.