Metric Properties of Continued Fractions

This project aims to explore the metrical properties of partial quotients in the continued
fractions expansion of real numbers. One of the aims is to study the growth rate of sums of
partial quotients, calculate the Hausdorff dimension of sets of real numbers satisfying this
restriction on their partial quotients. Explore the relevance of this problem in understanding
the long-standing Minkowski’s question mark function problem (1904). Along the way, we
aim to understand the role of metrical theory of continued fractions with metrical theory of
Diophantine approximation.

Lauren White

La Trobe University

Lauren White is a second-year undergraduate student from Bendigo. She is currently studying a Bachelor of Science, majoring in Physics, at the La Trobe University Bendigo Campus. Outside of her major studies in Physics, Lauren has also completed studies in Chemistry, Biochemistry, Quantum Computing and Mathematics (Linear Algebra and Vector Calculus), with these being areas of interest for her. Lauren also enjoys taking on challenges of problem-solving, having participated in the Practera Inspiration Australia program earlier this year. In this program she was part of group of undergraduate students, working with a business to help increase their appeal and reach in developing ways to market virtual tourism. Lauren was accepted as part on the National Youth Science Forum and later acted as a mentor to further applicants. Outside of study, Lauren enjoys running cross-country, playing soccer in the local women’s competition, and training Harness Racehorses with her family.

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