Über das Produkt inhomogener Linearformen

Рeter Gruber

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Grundlegende Eigenschaften der polynomischen Operationen. Zweite Mitteilung

S. Mazur, W. Orlicz (1934)

Studia Mathematica

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Laguerresche Differentialgeometrie und Kinematik

Zdeněk Jankovský (1995)

Mathematica Bohemica

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In this paper the plane Laguerre’s geometry in the augmented plane of dual numbers is presented. Basic integral and differential invariants of $ℒ$ -curves in the plane are deduced, i.e. the $ℒ$ -curve arc, $ℒ$ -curvature, $ℒ$ -minimal curves, $ℒ$ -circle. Furthermore the contact of $ℒ$ -curves, $ℒ$ -osculating circle, $ℒ$ -evolute of a curve and some special $ℒ$ -motions are studied from the point of view of $ℒ$ -Differential geometry.