scholarly journals Non-circular algebraic curves of constant width: an answer to Rabinowitz

2021 ◽  
pp. 1-7
Author(s):  
Yves Martinez-Maure
Keyword(s):  
Algebraic Curves ◽  
Constant Width ◽  
Curves Of Constant Width

Real algebraic curves of constant width

2016 ◽  
Vol 74 (2) ◽  
pp. 235-244
Author(s):  
Chatchawan Panraksa ◽  
Lawrence C. Washington
Keyword(s):  
Algebraic Curves ◽  
Constant Width ◽  
Real Algebraic Curves ◽  
Curves Of Constant Width

scholarly journals Morgan-Voyce Polynomial Approach for Quaternionic Space Curves of Constant Width

2021 ◽  
Vol 46 (1) ◽  
pp. 71-83
Author(s):  
Tuba Ağirman Aydin ◽  
Rabil Ayazoğlu ◽  
Hüseyin Kocayiğit
Keyword(s):  
Differential Equations ◽  
Constant Width ◽  
Approximate Solutions ◽  
Geometric Properties ◽  
Space Curves ◽  
Curve Type ◽  
Curves Of Constant Width ◽  
Quaternionic Space

Abstract The curves of constant width are special curves used in engineering, architecture and technology. In the literature, these curves are considered according to different roofs in different spaces and some integral characterizations of these curves are obtained. However, in order to examine the geometric properties of curves of constant width, more than characterization is required. In this study, firstly differential equations characterizing quaternionic space curves of constant width are obtained. Then, the approximate solutions of the differential equations obtained are calculated by the Morgan-Voyce polynomial approach.The geometric properties of this curve type are examined with the help of these solutions.

scholarly journals THE ROSENTHAL–SZASZ INEQUALITY FOR NORMED PLANES

2018 ◽  
Vol 99 (1) ◽  
pp. 130-136
Author(s):  
VITOR BALESTRO ◽  
HORST MARTINI
Keyword(s):  
Differential Geometry ◽  
Upper Bound ◽  
Constant Width ◽  
Convex Bodies ◽  
Euclidean Case ◽  
Planar Convex ◽  
Arbitrary Norms ◽  
Bodies Of Constant Width ◽  
Curves Of Constant Width ◽  
Normed Planes

We study the classical Rosenthal–Szasz inequality for a plane whose geometry is determined by a norm. This inequality states that the bodies of constant width have the largest perimeter among all planar convex bodies of given diameter. In the case where the unit circle of the norm is given by a Radon curve, we obtain an inequality which is completely analogous to the Euclidean case. For arbitrary norms we obtain an upper bound for the perimeter calculated in the anti-norm, yielding an analogous characterisation of all curves of constant width. To derive these results, we use methods from the differential geometry of curves in normed planes.

Sign in / Sign up

Export Citation Format

Share Document