Contemporary Geometry

94 Pages Indexed. Geometry is certainly the branch of mathematics which most attracts the layman. Nowhere with so much power as in geometry do truth and beauty appear so intimately connected. Was it not Fenelon who said: Defy the bewitchments and devilish charms of geometry attracted first of all by the supreme harmony of forms, the mind soon lets itself be captivated by the wonderful chain of ratiocination to which they have given rise. It wishes to pursue more profoundly its excavations in this monument of pure classic beauty: mathematics. Ancient Greece, until Euclid, regarded mathematics as an art more than a science, but although there often are fascinating aesthetic satisfactions which stimulate contemporary mathematicians to cultivate their beloved science, the modern Occident has not sanctioned this point of view. It is to the cultured man of the twentieth century who has known how to appreciate this beauty but whose business has kept him away from the Temple of Mathematics that we wish to dedicate this work. After making a hasty survey to recall the condition of geometry in the last century, we shall endeavor to show the influence of the notion of group in geometry and we shall seek to guide the reader, in the simplest possible manner, from the concrete notions of elementary geometry to the modern conceptions of" abstract spaces.…