Results 261 to 270 of about 283,852 (314)

Geometry Without Points

The American Mathematical Monthly, 1985
(1985). Geometry Without Points. The American Mathematical Monthly: Vol. 92, No. 10, pp. 707-711.
G. Gerla, R. Volpe
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Point-Reflection Geometries, Geometric K-Loops and Unitary Geometries

Results in Mathematics, 1997
The authors use unitary geometries to show the existence of reflection geometries to which correspond \(K\)-loops with an incidence fibration \(F\) [\textit{E. Zizioli}, J. Geom. 30, 144-156 (1987; Zbl 0632.51019)] where \(F\) consists of proper subloops (other than groups).
Gabrieli, Elisabetta, Karzel, Helmut
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Point-regular geometries

Journal of Geometry, 1997
The author continues his investigation in Geom. Dedicata 46, No. 1, 47-60 (1993; Zbl 0783.51002) of how geometries can be reconstructed from their automorphism groups. In the paper under review he considers incidence structures \((P,{\mathcal L})\) that admit sharply point transitive groups \(G\) of automorphisms. In this case, \(P\) is identified with
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25-Point Geometry

The Mathematical Gazette, 1952
Finite Galois arithmetics are well-known; finite geometries however, though more interesting to the amateur, have not really acquired professional status and do not appear to any great extent in standard works. The following example arose from a chance remark in Mathematics for T. C.
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31-Point Geometry

The Mathematical Gazette, 1955
The following paragraphs have been assembled in consequence of my reading Dr. Cundy’s note on 25-point geometry. Towards the end of it, apparently mindful of the adjunction of a “ line at infinity ” to the Euclidean plane, he adjoins a line to the 25-point plane and so obtains a geometry of 31 points. Here I reverse this procedure :
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Axiomatizability of Geometry without Points

Synthese, 1960
The aim of this paper is to make more precise the well-known conviction that geometry may be built without speaking about points. In the first section we prepare some general syntactical theorems which are needed. In the second section we apply these theorems to a certain theory of topology without points.
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Some Finite Point Geometries

Mathematics Magazine, 1977
Finite sets with distinguished subsets called lines give examples of the theory of balanced incomplete block designs.
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