By Marcel Berger
Both classical geometry and sleek differential geometry were lively matters of study in the course of the twentieth century and lie on the middle of many fresh advances in arithmetic and physics. The underlying motivating notion for the current e-book is that it bargains readers the weather of a latest geometric tradition by way of an entire sequence of visually beautiful unsolved (or lately solved) difficulties that require the production of recommendations and instruments of various abstraction. beginning with such typical, classical items as strains, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex units, etc., the most important principles and mainly summary techniques wanted for reaching the implications are elucidated. those are conceptual notions, every one outfitted "above" the previous and allowing a rise in abstraction, represented metaphorically via Jacob's ladder with its rungs: the 'ladder' within the outdated testomony, that angels ascended and descended...
In all this, the purpose of the ebook is to illustrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is especially a lot alive and on the very middle of the paintings of diverse modern mathematicians. it's also proven that there are innumerable paths but to be explored and ideas to be created. The e-book is visually wealthy and welcoming, in order that readers may perhaps open it at random locations and locate a lot excitement all through in accordance their very own intuitions and inclinations.
Marcel Berger is t
he writer of diverse winning books on geometry, this e-book once more is addressed to all scholars and academics of arithmetic with an affinity for geometry.