Results 261 to 270 of about 30,282 (293)

Translation Planes

, 1995
The book discusses various construction principles for translation planes and spreads from a general and unifying point of view and relates them to the theory of kinematic spaces. The book is intended for people working in the field of incidence geometry
Knarr, Norbert
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Ovoidal translation planes

Archiv Der Mathematik, 1972
J A Thas, Thas J A
exaly   +2 more sources

A family of translation planes [PDF]

Australas. J Comb., 2010
Summary: An infinite family of non-Desarguesian translation planes of order \(q^4\) with kernel \(\text{GF}(q^2)\) is constructed, for any odd prime power \(q\). The collineation group of each plane has orbits of lengths 1, \(q^2\), and \(q^4- q^2\) on the translation line.
Andrew Hudson, Tim Penttila
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Translating polygons in the plane

2005
Let P = (p1,...,pn) and Q = (q1,...,qm) be two simple polygons with non-intersecting interiors in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. It has been shown that this problem can be solved in time proportional to
Jörg-Rüdiger Sack, Godfried T. Toussaint   +1 more
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SOME CLASSES OF TRANSLATION PLANES

The Quarterly Journal of Mathematics, 1984
This article considers the following. Let \(\pi\) be a finite translation plane of order \(p^ r\) with an autotopism group G which has an orbit of length \(p^ r\)-p on \(\ell_{\infty}\), the line at infinity. The authors make the following additional assumptions: (a) p is an odd prime and \(r=2\); (b) G acts faithfully on \(\ell_{\infty}\).
Cohen, Stephen D., Ganley, Michael J.
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Pencils of translation ovals in translation planes

Geometriae Dedicata, 1994
Let \({\mathcal T}\) be a translation plane of even order \(q\) with translation line \(I_ \infty\). An oval \({\mathcal O}\) in \({\mathcal T}\) is called a translation oval if \(I_ \infty\) is a tangent at a point \(a\) and if the stabilizer of \({\mathcal O}\) in the translation group acts transitively on \({\mathcal O}\setminus\{a\}\).
Glynn, D. G., Steinke, G. F.
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On Translations in General Plane Geometries

American Journal of Mathematics, 1938
In a well-known paper, Hilbelt 1 has characterized the Euclidean and hyperbolic plane geometries by mere group and continuity axioms. He gets all the motions at once by requiring the existence of sufficiently many rotations. The present paper tries to point out how the existence of more and more translations gradually specializes the rather general ...
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Quasigroups and translation planes

Journal of Geometry, 1992
A quasigroup \((Q,\cdot)\) is said to be medial if \((x\cdot y)\cdot(z\cdot t)=(x\cdot z)\cdot(y\cdot t)\) for all \(x,y,z,t\in Q\), and is called idempotent if \(x\cdot x=x\) for all \(x\in Q\). If \((R,+,\cdot)\) is the coordinatizating ring of a translation plane and the kernel of \(R\) contains at least one element \(k\) distinct from 0 and 1, then
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Homologies in Translation Planes

Proceedings of the London Mathematical Society, 1973
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Foundations of Translation Planes

2001
BILIOTTI, Mauro, JHA V., JOHNSON N. L.
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