On Oresme Numbers and Their Geometric Interpretations.

In this study, we examined the Oresme sequences defined by Nicole Oresme. We examined the geometric interpretation of Oresme sequences with rational coefficients which are defined by A.F. Horadam as 0n+2= 0n+1- 1/40nwith initial conditions and 00 = 0 and 01 = 1/2. We defined the the vector of the Oresme sequence. We calculated the area and volume. We gave the general solution for four squares equation involving Oresme vectors. We calculated the Heron Formula of Oresme sequences. We defined the angle value between these sequences. We also obtained a relationship between the Oresme sequence and the generalized Fibonacci sequence in vector space. We calculated the area and volume of these sequence. We obtained important definitions and theorems for these sequences. [ABSTRACT FROM AUTHOR]