Abstract:
In order to make any type of exploration, some tools are necessary. The fraction 5/3 is chosen as a tool to make explorations in continued fractions. This thesis mainly consists of the following things. Discussion about the numbers 5/3, 5 and 3 and their significant contributions to the world of mathematics and to the theory of continued fractions in particular. It is to be noticed that 5/3 is the only fraction, when expanded in the form of a continued fraction, that has terms in its expansion whose sum is equal to the average of 5 and 3. Forty theorems in relation to the theory of continued fractions. Also some interesting observations. Famous numbers such as Fibonacci numbers, Theon diameters, et cetera, yield some properties in common to each other when they are studied in the light of continued fractions. A method is explained to get a magic square of order 3 from the magic hexagon of order 3.
