Date of Graduation
2003
Document Type
Thesis
Degree Type
MS
Committee Chair
Michael Mays
Abstract
Minkowski defined the question mark function ?(x) in 1904 as a map from the rational numbers in the interval [0,1] onto the dyadics in [0,1]. The map can be extended over the entire interval. In providing an historical survey of this function, I review basic results concerning Farey fractions and continued fractions. Then I examine Minkowski’s definition and its extension, and I give a new proof of a basic fact about the extension. By stepping through the literature, I outline the known properties of ?(x) and state some generalizations of the function. Finally, I present an interesting connection to a simple combinatorial problem.
Recommended Citation
Conley, Randolph M., "A survey of the Minkowski ?(x) function." (2003). Graduate Theses, Dissertations, and Problem Reports (ETD). 10757.
https://researchrepository.wvu.edu/etd/10757