#### Title

Fibonacci numbers and finite continued fractions

#### Date of Publication

1997

#### Document Type

Bachelor's Thesis

#### Degree Name

Bachelor of Science in Mathematics

#### College

College of Science

#### Department/Unit

Mathematics and Statistics Department

#### Abstract/Summary

This research paper deals with the study of the Fibonacci Numbers and Continued Fractions. The Fibonacci Sequence is a sequence in which each term is computed by adding the preceding two terms, the first two terms being 1. The terms of this sequence are called Fibonacci Numbers. Some of the identities involving Fibonacci Numbers are included in this paper. The quotient of two successive Fibonacci Numbers can be expressed as the simple finite continued fraction [1 1,1,...1,1] where the integer 1 appears (n + 1) times. Continued Fractions deal with the resolution of fractions into unit fractions. All the theorems, lemmas and corollaries stated in this research paper are part of the discussion in the book entitled Elementary Number Theory by David M. Burton. The researchers expounded on the subject by giving detailed proofs and examples on the theorems, corollaries and lemmas concerning the said topic. Most of the proofs were presented using the Euclidean Algorithm and Mathematical Induction. Some knowledge about Number Theory was also provided in this paper since it is needed for better understanding of some of the proofs.

#### Abstract Format

html

#### Language

English

#### Format

#### Accession Number

TU08303

#### Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

#### Physical Description

60 leaves

#### Keywords

Fibonacci numbers; Continued fractions; Number theory

#### Recommended Citation

Go, A. G., & Machica, A. S. (1997). Fibonacci numbers and finite continued fractions. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/16443