Exploring Egyptian fractions
Julia Plavnik
Faculty Mentor
Julia Plavnik (College of Arts & Sciences)
Project Description
Egyptian fractions are a way of representing rational numbers as the sum of distinct unit fractions (fractions with a numerator of 1). The ancient Egyptians used this method for mathematical calculations, and it's still studied in number theory and recreational mathematics today. This project will focus on solutions to the Egyptian fractions equation with the prime factors of the denominators constrained to lie in a fixed set of primes. For this, we will use algorithms to obtain data and analyze the results.
Technology or Computational Component
In this project, the student will look for solutions to Egyptian fractions with restrictions on the number of prime factors that can appear in the denominators. Important tools to find these solutions and to provide data to be analyzed are the algorithms developed in previous research. There is code available for these algorithms in Sage, Julia, and Maple, and some will be available in a Jupyter notebook that can be found in a GitHub repository. So, finding solutions, analyzing the outputs, and improving the code or developing new code would be part of the components of the project.