Open AccessGeneralized Conchoids
Author(s) -
Boris Odehnal
Publication year - 2017
Publication title -
kog/kog
Language(s) - English
Resource type - Journals
eISSN - 1846-4068
pISSN - 1331-1611
DOI - 10.31896/k.21.3
Subject(s) - transformation (genetics) , euclidean geometry , mathematics , linear map , plane (geometry) , geometry , line (geometry) , algebra over a field , pure mathematics , biochemistry , chemistry , gene
We adapt the classical definition of conchoids as known from the Euclidean plane to geometries that can be modeled within quadrics. Based on a construction by means of cross ratios, a generalized conchoid transformation is obtained. Basic properties of the generalized conchoid transformation are worked out. At hand of some prominent examples - line geometry and sphere geometry - the actions of these conchoid transformations are studied. Linear and also non-linear transformations are presented and relations to well-known transformations are disclosed.