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Explore the mathematical properties of the infinite Fibonacci word through this 36-minute conference talk examining balanced rectangles in Hankel matrices. Discover how the famous Sturmian word 0100101001... maintains its balanced property, where any two blocks of equal length have sums that differ by at most one. Learn about "Fibonacci word rectangles" as blocks within corresponding Hankel matrices and understand their complete characterization using the Walnut software. Examine the results through the lens of distribution modulo 1 theory. Gain insights into this collaborative research with Jeffrey Shallit that advances understanding of word combinatorics and Diophantine approximation. The presentation was delivered during the thematic meeting on "Diophantine approximation and transcendence" at the Centre International de Rencontres Mathématiques in Marseille, France.
