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    A New Approach To Homothetic Motions With Tessarines In Semi-Euclidean Space E??
    (Beykent Üniversitesi, 2017) Babadag, Faik
    In this study, by using tessarines in 4-dimension semi-Euclidean space, we describe a variety of algebraic properties and give a matrix that is similar to Hamilton operators and we show that the hypersurfaces are obtained and a new motion is defined in E??. Then, this motion is proven to be homothetic motion. For this one parameter homothetic motion, we defined some theorems about velocities, pole points, and pole curves. Finally, It is found that this motion defined by the regular curve of order r on the hypersurface M??, at every t- instant, has only one acceleration centre of order (R ? 1). Due to the way in which the matter is given with tessarines, the study gives some formulas, facts and properties about homothetic motion and variety of algebraic properties which are not generally known.
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    Tessarines And Homothetic Exponential Motions In 4-Dimensional Euclidean Space
    (Beykent Üniversitesi, 2017) Babadag, Faik
    This paper is a detailed study on homothetic exponential motions by considering tessarines. To do this, we introduce a matrix by using tessarines product and addition rules and give a variety of algebraic properties of this matrix in four dimensional Euclidean space E?. Then, the exponential motion is proven to be homothetic exponential motion. This process allows us to define some theorems about velocities, pole points, and pole curves. Finally, It is found that at every t-instant an exponential motion defined by the regular curve of order n and derivations curves on the hypersurface M has only one acceleration center of order (n ? 1).