Fibonacci sequence is a very interesting sequence. In this paper, first the casual characteristics of the involute curve, and Mannheim partner of a non-null curve are examined. We find that the number of different forms of the casual characteristics of nth order involute and Mannheim mate of a spacelike curve can be given using Fibonacci sequence with in a table. Also the kind of the casual characteristics of the nth order Bertrand mate are examined. It is found that timelike Bertrand curve has 2n different forms, and the nth order Bertrand mate of a spacelike Bertrand curve with timelike principal normal is always spacelike Bertrand curve with timelike principal normal.