Classification of complete (k,2)-arcs in NFPG(2,9) using veronesean

Abstract

In this paper, we investigate the Veronesean arc, the non-Veronesean arc by converting a point expressed in Cartesian coordinates to homogeneous coordinates in left nearfield plane of order 9 where a k − arc in a finite projective or affine plane is a set of k points no three of which are collinear. And also, we examine that whether founded complete (7, 2)-Non-Veronesean arc satisfy Pascal’s Theorem in the left nearfield projective plane of order 9. Six of (7, 2)-Non-Veronesean arc’s all points which are {1, 4, 11, 21, 35, 38} points line on same conic. But it is determined that (7, 2)-Non-Veronesean arc does not satisfy Pascal’s Theorem.