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Euclidean space motions with affinely equivalent trajectories

Adolf Karger (1983)

Aplikace matematiky

The author studies the Euclidean space motions with the property that the trajectory of every point is an affine image of a given space curve. Such motions split into plane motions and translations and their trajectories are cylindrical curves. They are characterized as motions with the following property: Not all trajectories are plane curves and if any trajectory has a planar point, it lies in a plane. Motions with infinitely many straight trajectories form a special subclass of those motions....

Exercices sur le tétraèdre

J. Wolstenholme (1871)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Exkurze do světa vyšší dimenze

Christian Genest, Johanna Genest Nešlehová (2022)

Pokroky matematiky, fyziky a astronomie

Trojrozměrný svět je pro nás tak přirozený, že si lze jen obtížně představit a popsat vesmír ve čtyřech nebo více dimenzích. Pojďme společně poodhalit závoj tohoto tajemství a prozkoumat vlastnosti vícerozměrných analogií krychle a koule.

Extending Nearaffine Planes to Hyperbola Structures

Kinga Cudna-Salmanowicz, Jan Jakóbowski (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

H. A. Wilbrink [Geom. Dedicata 12 (1982)] considered a class of Minkowski planes whose restrictions, called residual planes, are nearaffine planes. Our study goes in the opposite direction: what conditions on a nearaffine plane are necessary and sufficient to get an extension which is a hyperbola structure.

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