A Comprehensive Analysis on Dissections of Continued Fractions

摘要

Continued fraction is one of the form of expressing any numbers or functions. Though the origin of continued fractions is hard to pinpoint, its algorithms were used by mathematicians during 4~(th) century B.C. – 3~(rd) century A.D. But its true foundations were not laid until the late 1600's, early 1700's. Continued fractions became a field in its right, in the beginning of 18~(th) century. In the intervening years, many researchers studied and analyzed Continued fractions in different angles and many researcher papers have appeared in journals. This work is a survey of studies on dissections of continued fractions conducted by different mathematicians from the beginning till the 21~(st) century.