Abstract
This project begins with a look at the history of simple continued fractions and how we have arrived where we are today. We then move through a study of simple continued fractions, beginning first with rational numbers and moving to irrational numbers. Continuing further in the pursuit of joining mathematics and art, we define the specific continued fraction that gives rise to the Fibonacci sequence and the Golden Ratio~ (phi, pronounced 'Jai"). These two notions form a direct link to art and the properties that we hope to examine. I have taken an analytic approach to showing that the Golden Ratio has been a constant presence in art history, probably as an indicator of aesthetic appeal. I collected, measured, and analyzed works of art from various periods to investigate the extent to which ~ is hidden throughout these works. I hope to affirm the hypotheses put forth by others throughout history that yes indeed, those works of art that best exemplify Platonic beauty have instances of the Golden Ratio [Hu] [Li] [Ru] [Ma].
Recommended Citation
Tush, J. (2009). The Beauty of Mathematics and the Mathematics of Beauty: Continued Fractions and the Golden Ratio. Inquiry: The University of Arkansas Undergraduate Research Journal, 10(1). Retrieved from https://scholarworks.uark.edu/inquiry/vol10/iss1/6
Included in
Numerical Analysis and Computation Commons, Other History of Art, Architecture, and Archaeology Commons
