| Title | An analysis of the dual-complex unit circle with applications to line geometry |
| Publication Type | Journal Article |
| Year of Publication | 2019 |
| Authors | Bongardt B |
| Date Published | 11/2019 |
| Type of Article | Preprint |
| Keywords | adjoint trigonometric representation of displacements, Computational kinematics, generalized complex numbers, Lie theory, Paden–Kahan problems, principle of transference |
| Abstract | This article contributes to the conception of oriented dual angles by introducing two geometric representations of the dual-complex unit circle in context of Cayley-Klein geometries. By means of these representations and the principle of transference, line-geometric trigonometric constraint equations are stated and solved analytically. The trigonometric constraints and their solutions build the foundation to obtain closed-form solutions to generalized, line-geometric variants of Paden-Kahan problems. |
