A note on ovals and their evolutoides
type: Item
instance of: scholarly article
title: A note on ovals and their evolutoides
zbMATH Open document ID: 1188.53003
author: Marco Hamann
published in: Beiträge zur Algebra und Geometrie
publication date: 2009-09-02T00:00:00Z
full work available at URL: https://eudml.org/doc/226766
full work available at URL: 11.html
review text: The author considers special curves related to ovals. These curves can uniformely be generated by families of secants with respect to an arbitrary given oval. These secants envelop a curve and this curve gives informations about the oval. If the secants connect the points of contact of parallel tangents of the given oval the envelope is called midenvelope. Using such lines of a one-parameter set of oriented lines which intersect the oval isogonally with the constant angle \(\alpha\) the corresponding envelope \(e_{\alpha}\) is called evolutoide. With the help of these envelopes several properties are discussed. In particular the author demonstrates that to any evolutoide of the given oval a global property can be shown which is invariant under regular affine transformations. This is a generalization of a corresponding result about the evolute of a oval given by \textit{O. Giering} [Sitzungsber., Abt. II, Österr. Akad. Wiss., Math.-Naturwiss. Kl. 198, No.~1--3, 45--66 (1989; Zbl 0661.52002)].
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 51M04
Mathematics Subject Classification ID: 51N20
zbMATH DE Number: 5601577
zbMATH Keywords: evolute
zbMATH Keywords: evolutoide
zbMATH Keywords: kinematics
zbMATH Keywords: minimal curve
zbMATH Keywords: oval
zbMATH Keywords: certain secants
reviewed by: Johannes Böhm
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5601577