On rosettes and almost rosettes

✍ Scribed by Waldemar Cieślak; Witold Mozgawa

• Book ID: 104643596
• Publisher: Springer
• Year: 1987
• Tongue: English
• Weight: 215 KB
• Volume: 24
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00150937

✦ Synopsis

ON ROSETTES AND ALMOST ROSETTES

ABS fRAC]'. ]'he closed plane curves of class C 2 which have curvature k(s) > 0 or k(s) >I 0 with a finite number of zeros are studied. The results concern the existence of normal lines which divide the perimeter into equal parts and the existence of some special kinds of pairs of points on these curves as orthodiameter pairs, antipodal pairs, etc. The paper also contains some generalizations of the theorems of Blaschke-Siiss and Barbier.

1. PRFI. IMINARIES

In this paper we shall consider the class of all positively oriented rosettes and almost rosettes. We recall that C 2, a plane closed curve of positive curvature, is called a rosette (see ). Ovals (see ) are a special class of rosettes. By s, L and k we shall denote, respectively, the arc length, the perimeter and the curvature of a fixed rosette.