Some Notes on Geometry of Bézier Curves in Euclidean 4-Space

On the Quaternionic Curves in the Semi-Euclidean Space E_4_2

In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.

Notes on Euclidean Geometry Contents

Some Characterizations of Special Curves in the Euclidean Space E

In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some new characterizations of involute of a helix are presented.

Some Characterizations of Isotropic Curves In the Euclidean Space

The curves, of which the square of the distance between the two points equal to zero, are called minimal or isotropic curves [4]. In this work, first, necessary and sufficient conditions to be a Pseudo Helix, which is a special case of such curves, are presented. Thereafter, it is proven that an isotropic curve’s position vector and pseudo curvature satisfy a vector differential equation of fou...

Some Characterizations of Inclined Curves in Euclidean E Space

We consider a unit speed curve α in the Euclidean ndimensional space E and denote the Frenet frame of α by {V1, . . . ,Vn}. We say that α is a cylindrical helix if its tangent vector V1 makes a constant angle with a fixed direction U . In this work we give different characterizations of such curves in terms of their curvatures. AMS Mathematics Subject Classification (2000): 53C40, 53C50