6-figures and distance in octonion planes

In this thesis; the correspondings of some known results related to 6-figures on the Dezarg planes, Moufang planes and a class of Moufang-Klingenberg plane are examined on the octonion plane class constructed by the special matrices of 3x3, whose entires are from A1 plural algebra of order m and on the octonion plane class constructed by the matrices, whose entries are from A2 (defined in the manner that will be not isomorphic to A1 ). It is showed that a 6-figure can be represented by an inversible element of A1 or A2 with help of the result that group of collineations of both octonion plane classes are transitive on 4-gons. Finally, a non-metric distance definition is given on a projective Klingenberg plane class by using matrix representations of points and lines of the octonion plane class constructed by and with the help of this distance definition, correspondings of the concepts of circle, ellipse and hyperbola, which are well known from the Euclidean plane, are examined in finite projective planes.