It is well known that any planar convex body A permits to inscribe an affine-regular hexagon HA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_A$$\\end{document}. We prove that the centroid of A belongs to the homothetic image of HA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_A$$\\end{document} with ratio 421\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{4}{21}$$\\end{document} and the center in the center of HA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_A$$\\end{document}. This ratio cannot be decreased.

This paper characterizes curves where a regular polygon of either a variable side length or a constant side length is allowed to rotate during k full revolutions while having its vertices on the curve during the motion. A constructive method to generate these curves is given based on the curve described by the polygon centers (centroids) during the motion and some examples are shown. Moreover, if the regular polygon divides the curve perimeter into parts of equal length, it is proved that the curve is either a rotational symmetric curve in the case of a variable side length or a circle otherwise. Finally, in the case of a regular polygon of constant side length rotating along a curve, a simple relation between the algebraic areas of such a curve and the curve of polygon centers is revisited.

Székelyhidi was born on 11 May 1952 in Budapest, Hungary.He completed his primary school studies in the western part of Hungary, in Mosonmagyaróvár and Hegyeshalom.After primary school, he continued his studies at Temesvári Pelbárt Ferences Gimnázium (a Franciscan High School) in Esztergom.The years he spent there-as he would often tell us-had a decisive impact on his life.With some of his classmates, he established a band there playing beat music, which at the time was very popular in Hungary as well.His interest in mathematics also became deeper during his high school years.Based on these experiences, he had two ideas regarding his possible future career.One of them was to do something related to music: he was considering becoming an audio engineer.

Abstract In the present paper we prove a generalized version of the famous decomposition theorem of Ng. We also focus on the problem posed by Zsolt Páles concerning the Wright-convex functions.