The Farey Sequence of order n is the sequence made up of all non-negative irreducible proper fractions between 0 and 1, arranged in increasing order, with denominators not exceeding n. (Note that in this definition, order does not refer to the size of the sequence). The terms of the Farey Sequence have geometric applications that include the Farey Starburst and Ford Circles. In addition, the sequence can be found within a graphic representation of non-negative rational values called the Farey Tree, which is contained within the Stern-Brocot Tree.
Webb, Alice C., "Extensions of the Farey Sequence and Ford Circles" (2013). Senior Independent Study Theses. Paper 950.
mathematics, number theory, farey sequence, ford circles
Bachelor of Arts
Senior Independent Study Thesis
© Copyright 2013 Alice C. Webb