By Marcel Berger

Both classical geometry and smooth differential geometry were energetic matters of analysis through 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 contemporary geometric tradition via an entire sequence of visually attractive unsolved (or lately solved) difficulties that require the production of ideas and instruments of various abstraction. beginning with such normal, classical items as strains, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex units, etc., the most important rules and especially summary suggestions wanted for reaching the implications are elucidated. those are conceptual notions, each one equipped "above" the previous and allowing a rise in abstraction, represented metaphorically through Jacob's ladder with its rungs: the 'ladder' within the previous testomony, that angels ascended and descended...

In all this, the purpose of the booklet 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 center 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 areas and locate a lot excitement all through in accordance their very own intuitions and inclinations.

Marcel Berger is t

he writer of various profitable books on geometry, this e-book once more is addressed to all scholars and academics of arithmetic with an affinity for geometry.

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