How to write zeta function as an ascending continued fraction? You can find the answer in the fourth paragraph.

Note that it’s similar to Gaussian summation. 277 more words

How to write zeta function as an ascending continued fraction? You can find the answer in the fourth paragraph.

Note that it’s similar to Gaussian summation. 277 more words

Iterations and their continued fraction forms

How can we interpret this iteration to get the next continued fraction?

I denote the number of iterations with . 219 more words

Most introductory books on number theory have at least one section on the theory of continued fractions. I suggest

394 more wordsWilliam Stein.

Elementary number theory: primes, congruences, and secrets.

In the preceding post in this series, we saw a connection between the Fibonacci numbers and the golden ratio α = (1+√5)/2. I am going to look at this from a different perspective, that of continued fractions. 1,294 more words

Something has happened to calculators while I wasn’t using them. I am hoping somebody reading this will know more about it than I do.

The story begins with the number theory course I am teaching this year, and a link-up between continued fractions (which form a significant part of the course), Euclid’s algorithm, and the Pythagorean proof of the irrationality of √2. 660 more words

This term, Summer Hansen is taking a reading course with me on Pell’s equation. Our basic reference is:

- Jacobson and Williams,
**Solving the Pell equation…** 1,240 more words

This term, Summer Hansen is taking a reading course with me on Pell’s equation. Our basic reference is:

- Jacobson and Williams,
**Solving the Pell equation…** 1,240 more words