How do you find a continuous fraction?

How do you find a continuous fraction?

To calculate a continued fraction representation of a number r, write down the integer part (technically the floor) of r. Subtract this integer part from r. If the difference is 0, stop; otherwise find the reciprocal of the difference and repeat. The procedure will halt if and only if r is rational.

Who found continued fraction?

The Rogers–Ramanujan continued fraction is a continued fraction discovered by Rogers (1894) and independently by Srinivasa Ramanujan, and closely related to the Rogers–Ramanujan identities. It can be evaluated explicitly for a broad class of values of its argument.

What happens in Chapter 3 of continued fractions?

Chapter 3 deals with the expansion of irrational numbers into infinite continued fractions, and includes an introductory discussion of the idea of limits. Here one sees how continued fractions can be used to give better and better rational approximations to irrational numbers.

Why are continued fractions a subject of study?

It turns out, however, that fractions of this form, called “continued fractions”, provide much insight into many mathematical problems, particularly into the nature of numbers. ‘ Continued fractions were studied by the great mathematicians of the seventeenth and eighteenth centuries and are a subject of active investigation today.

Which is less significant 9 or 9 continued fractions?

At first glance nothing seems simpler or writing a number, for example 9, in the form less significant than It turns out, however, that fractions of this form, called “continued fractions”, provide much insight into many mathematical problems, particularly into the nature of numbers.

Why are continued fractions considered a creative art?

Mathematicians often think of their subject as a creative art rather than as a science, and this attitude is reflected in the pages that follow. Chapter 1 shows how continued fractions might be dis- covered accidentally, and then, by means of examples, how rational fractions can be expanded into continued fractions.