Download PDF by Felix Klein, Walter Rosemann: Vorlesungen über nicht-Euklidische Geometrie

By Felix Klein, Walter Rosemann

Als Felix Klein den Plan faBte, die wichtigsten seiner autogra phierten Vorlesungen im Druck erscheinen zu lassen, gedachte er, mit der Nichteuklidischen Geometrie zu beginnen und den alten textual content zu vor mit Hille eines jiingeren Geometers, des Herro Dr. Rosemann, in der Anlage und den Einzelheiten einer griindlichen Neubearbeitung zu unterziehen. Diese Arbeit erwies sich als langwieriger wie urspriing lich geschatzt. Klein selbst konnte ihren AbschluB nicht mehr erleben. Zwar hatte er in taglichen, durch mehr als ein J ahr fortgesetzten Be sprechungen den Stoff bis in die Einzelheiten hinein mit seinem Mit arbeiter durchdacht, gesichtet und geordnet; aber die eigentliche Aus arbeitung des Textes muBte er von vornherein Herro Rosemann uber lassen. Bei Kleins Tode lagen die Fahnenkorrekturen der ersten Ka pitel vor; es bedurfte jedoch noch jahrelanger opferwilliger Arbeit seitens Herro Rosemanns, urn auf Grund des urspriinglichen Programmes das Manuskript fertigzustellen und den Druck durchzufiihren. So ist bei diesem Werke eigener Antell und Verdienst, aber auch eigene Ver antwortung des Bearbeiters viel heher zu bewerten als sonst ublich.

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Extra resources for Vorlesungen über nicht-Euklidische Geometrie

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Applying the trapezoidal rule (using one strip) gives the area as 32. The geometric interpretation of the trapezoidal rule is quite straightforward: the cubic curve is approximated as a straight line and the integral is equal to the area of the trapezium. 3 Analysis of Consolidation using Finite Elements 88 Sec. l) three times and solving the resulting equations. In fact one can write down the quadratic straight away as f(x) ~1 1' ~! I' ,d "1 ~\I~ I~. ). I~ I !! 1 /=/1 (X3 -X)(X2 -x) (X3 (X2 - X) (X I + /3 )!

5. The next section covers the mathematical preliminaries (numerical integration, interpolation polynomials, the approximate solution of differential equations and Green's theorem in the plane). 3 presents the fundamentals of the 'displacement' (or 'stiffness') method of finite element analysis via a simple example using linear elastic springs. 4 covers the virtual work principle. We include this section because we are aware that many engineers find the principle rather obscure . However, it turns out to be a very versatile and powerful tool in formulating finite element methods as well as the theory of structures.

In drained tests, one simply has a total stress path (equivalent to the ESP) inclined a t some other angle in the (p', q) plot, and it is a matter of simple geometry to calculate the intersection of the ESP with the CSL and the current yield locus. In undrained tests, although the total stress path will differ, the effective stress path remains the same . The calcula tion of the pore pressure in a test is again just a geometric exercise . Fig. ess­ strain behaviour of soils was first proposed by Drucker et al.

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Vorlesungen über nicht-Euklidische Geometrie by Felix Klein, Walter Rosemann


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