caa a22 4500 605508208 CHVBK 20210128100635.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00010-015-0352-4 doi (NATIONALLICENCE)springer-10.1007/s00010-015-0352-4 On evolutoids of planar convex curves II [Elektronische Daten] [V. Aguilar-Arteaga, R. Ayala-Figueroa, I. González-García, J. Jerónimo-Castro] In this paper we continue the study of evolutoids of convex curves. We proved that if a curve is homothetic to one of its evolutoids then it is a circle. This result is analogous, for the case of evolutoids, to the planar case of the famous homothetic floating body problem which states that if a floating body is homothetic to the body itself then it is an ellipsoid. Among other things, we proved that a curve and any of its evolutoids have the same Steiner point. Moreover, some relations between evolutoids and constant angle caustics are also given, for instance, that if for a given angle the left and right evolutoids describe the same curve then the curve possesses a constant angle caustic. Springer Basel, 2015 Convex evolutoid nationallicence Convex floating body nationallicence Illumination body nationallicence Constant angle caustic nationallicence Aguilar-Arteaga V. Universidad Autónoma de Querétaro, Querétaro, Querétaro, Mexico aut Ayala-Figueroa R. Universidad Autónoma de Querétaro, Querétaro, Querétaro, Mexico aut González-García I. Universidad Autónoma de Querétaro, Querétaro, Querétaro, Mexico aut Jerónimo-Castro J. Universidad Autónoma de Querétaro, Querétaro, Querétaro, Mexico aut Aequationes mathematicae Springer International Publishing 89/6(2015-12-01), 1433-1447 0001-9054 89:6<1433 2015 89 10 https://doi.org/10.1007/s00010-015-0352-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-015-0352-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Aguilar-Arteaga V. Universidad Autónoma de Querétaro, Querétaro, Querétaro, Mexico aut NATIONALLICENCE 700 1- Ayala-Figueroa R. Universidad Autónoma de Querétaro, Querétaro, Querétaro, Mexico aut NATIONALLICENCE 700 1- González-García I. Universidad Autónoma de Querétaro, Querétaro, Querétaro, Mexico aut NATIONALLICENCE 700 1- Jerónimo-Castro J. Universidad Autónoma de Querétaro, Querétaro, Querétaro, Mexico aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer International Publishing 89/6(2015-12-01), 1433-1447 0001-9054 89:6<1433 2015 89 10