Simple Continued Fractions an Approach for High School Students

TL;DR

This paper introduces high school students to continued fractions, exploring their properties, computation methods, and applications to enhance mathematical understanding and problem-solving skills.

Contribution

It presents an accessible, engaging approach to teaching continued fractions, including their properties, computation, and applications for high school education.

Findings

Students gain understanding of continued fractions and their properties.

The approach enhances problem-solving skills in mathematics.

Students develop appreciation for advanced mathematical concepts.

Abstract

This paper aims to introduce high school students to the intriguing world of continued fractions, a mathematical concept that provides a unique representation of numbers. The study focuses on the exploration and development of the fundamental properties of both Finite and Infinite Continued Fractions. It further delves into the computation of quadratic numbers using given periodic continued fractions and the concept of conjugate quadratic numbers. A significant part of the paper is dedicated to the approximation of real numbers and the convergence properties of continued fractions. The study of continued fractions offers a profound understanding of the intricate relationships within number systems, a key emphasis in contemporary mathematics education. The paper is designed to be engaging and interactive, fostering a fun and stimulating learning environment. By the end of this study, students will have gained a comprehensive understanding of continued fractions, their properties, and their applications, thus enhancing their mathematical proficiency and problem-solving skills. This paper serves as a stepping stone for students to explore more complex mathematical concepts and theories, fostering a deeper appreciation for the subject.