QUATERNIONS ASSOCIATED TO CURVES AND SURFACES

Document Type

Article

Publication Date

1-1-2024

Abstract

This paper investigates the use of quaternions in studying space curves and surfaces in affine 3-space. First, we generate a large variety of rational space curves and rational surfaces via quaternion multiplication by taking advantage the fact that quaternions represent space rotations. Then, we prove that the curvature and the torsion of a space curve can be computed by a quaternion function that is associated to this space curve. Finally, we show that the Gaussian and the mean curvature of a surface can also be computed by a quaternion function that is associated to this surface.

Publication Source (Journal or Book title)

Palestine Journal of Mathematics

First Page

43

Last Page

54

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