#### Presentation Title

P-42 A Curve Satisfying τ/κ=1/s With Constant κ > 0

#### Presenter Status

Student, Department of Mathematics

#### Second Presenter Status

Associate Professor, Department of Mathematics

#### Preferred Session

Poster Session

#### Start Date

26-10-2018 2:00 PM

#### End Date

26-10-2018 3:00 PM

#### Presentation Abstract

According to the Fundamental Theorem of Curves, any regular curve with a smooth positive curvature and smooth torsion can be completely determined up to its position. Helices have the property that the ratio of torsion to curvature is a constant. For rectifying curves, the ratio of torsion to curvature is a linear function. In this paper, we study a space curve whose ratio of torsion to curvature is given by 1/*s*, where *s* is an arc length. For this problem, we consider the curvature is constant. After reparametrization, we use a series solution to solve a third-order differential equation and obtain the general equation of the curve.

P-42 A Curve Satisfying τ/κ=1/s With Constant κ > 0

According to the Fundamental Theorem of Curves, any regular curve with a smooth positive curvature and smooth torsion can be completely determined up to its position. Helices have the property that the ratio of torsion to curvature is a constant. For rectifying curves, the ratio of torsion to curvature is a linear function. In this paper, we study a space curve whose ratio of torsion to curvature is given by 1/*s*, where *s* is an arc length. For this problem, we consider the curvature is constant. After reparametrization, we use a series solution to solve a third-order differential equation and obtain the general equation of the curve.