Babadag, Faik2018-01-072018-01-072017Sayı 10(1) 2017, 1 – 131307-3818This 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).enTessarinesHomothetic exponential motionHypersurfaceRegular curveTessarines And Homothetic Exponential Motions In 4-Dimensional Euclidean SpaceArticle