Bayram, BengüÖztürk, Günay2024-11-222024-11-222016-12-011406-2283https://doi.org/10.12697/ACUTM.2016.20.11https://hdl.handle.net/11452/48377We consider translation surfaces in Euclidean spaces. Firstly, we give some results of translation surfaces in the 3-dimensional Euclidean space E-3. Further, we consider translation surfaces in the 4-dimensional Euclidean space E-4. We prove that a translation surface is flat in E-4 if and only if it is either a hyperplane or a hypercylinder. Finally we give necessary and sufficient condition for a quadratic triangular Bezier surface in E-4 to become a translation surface.eninfo:eu-repo/semantics/closedAccessFormTranslation surfaceMean curvatureGaussian curvatureSecond fundamental mapScience & technologyPhysical sciencesMathematicsArticle00040923080000312313320210.12697/ACUTM.2016.20.11