L. Boi, D. Flament, Jean-Michel Salanskis's 1830-1930: A Century of Geometry PDF

By L. Boi, D. Flament, Jean-Michel Salanskis

ISBN-10: 0387554084

ISBN-13: 9780387554082

ISBN-10: 3540554084

ISBN-13: 9783540554080

Within the first 1/2 the nineteenth century geometry replaced appreciably, and withina century it helped to revolutionize either arithmetic and physics. It additionally placed the epistemology and the philosophy of technological know-how on a brand new footing. In this quantity a legitimate evaluate of this improvement is given via best mathematicians, physicists, philosophers, and historians of technology. This interdisciplinary strategy supplies this assortment a different personality. it may be utilized by scientists and scholars, however it additionally addresses a basic readership.

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The map P-^ip describes the "afline" geometry of ty in terms of the affine linear geometry of W. The next three lemmas make precise this statement, and they constitute the heart of the proof of the main theorem of this section. 12. Let P e $ , P^O. Then a point Qofty lies on the line OwP if and only if for some M e D one has tQ = M-tP. Proof. Let K = Kp £= J be the smallest finite set <= J such that P

If P

Y2n). 2. The definitions in Section 5 are classical. For any line t in a Desarguesian plane n let G be the set of all projectivities of t with itself which are compositions of two perspectivities: from t to a second line s followed by a perspectivity from s to t. The line s, as well as the centers of perspectivity, are arbitrary. Assume that s^t and that the two centers, X, Y are distinct. Then the projectivity has one or two fixed points according as the line Xv Y passes through sAt or not. In the former case the projectivity is called special and the point W, which is on s, t and XV Y, is the unique fixed point and is called its canonical fixed point.

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1830-1930: A Century of Geometry by L. Boi, D. Flament, Jean-Michel Salanskis


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