Egyptian fractions meet the Sierpinski triangle
Laura De Carli, Andrew Echezabal, Ismael Morell
TL;DR
This paper investigates the connection between Egyptian fractions and fractal structures, revealing how decompositions of rational numbers into unit fractions can generate fractal patterns, bridging ancient mathematics and modern fractal theory.
Contribution
It introduces a novel link between Egyptian fractions and fractals, demonstrating how rational decompositions can produce fractal structures, a previously unexplored connection.
Findings
Fractal patterns emerge from Egyptian fraction decompositions.
A new mathematical link between ancient and modern concepts.
Potential applications in mathematical visualization and theory.
Abstract
We explore a novel link between two seemingly disparate mathematical concepts: Egyptian fractions and fractals. By examining the decomposition of rationals into sums of distinct unit fractions, a practice rooted in ancient Egyptian mathematics, and the arithmetic operations that can be performed using this decomposition, we uncover fractal structures that emerge from these representations.
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