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Studies of curves in 3D-space have been developed by many geometers and it is known that any regular curve in 3D space is completely determined by its curvature and torsion, up to position. Many results have been found to characterize various types of space curves in terms of conditions on the ratio of torsion to curvature. Under an extra condition on the constant curvature, Y. L. Seo and Y. M. Oh found the series solution when the ratio of torsion to curvature is a linear function. Furthermore, this solution is known to be a rectifying curve by B. Y. Chen’s work. This project, uses a different approach to characterize these rectifying curves. This paper investigates two problems. The first problem relates to figuring out what we can say about a unit speed curve with nonzero curvature if every rectifying plane of the curve passes through a fixed point in ℝ3. Secondly, some formulas of curvature and torsion for sphere curves are identified. KEYWORDS: Space Curve; Rectifying Curve; Curvature; Torsion; Rectifying Plane; Tangent Vector; Normal Vector; Binormal Vector

In the present paper, we investigate a space curve in which the curvature is constant and the torsion is a linear function. The aim of this paper is to find an explicit formula for this space curve when the ratioof the torsion to the curvature is a linear function when the curvature is constant. KEYWORDS: Space Curve, Curvature, Torsion, General Helix, Frenet Frame, Series Solution, Rectifying Curve