6 papers
On denominators of consecutive -saturated Farey fractions
Jack Anderson, Florin P. Boca, Cristian Cobeli +1
The sequence of -saturated Farey fractions was defined in our previous work by ${\mathscr S}_Q := \{ a/q \in {\mathbb Q} \cap…
On the distribution of -saturated Farey fractions
Jack Anderson, Florin P. Boca, Cristian Cobeli +1
We consider the set of Farey fractions of order with the property that there exists a matrix $\left( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix}…
Arithmetic Polygons and Sums of Consecutive Squares
Jack Anderson, Amy Woodall, Alexandru Zaharescu
We introduce and study arithmetic polygons. We show that these arithmetic polygons are connected to triples of square pyramidal numbers. For every odd , we prove that there…
Angular distribution towards the points of the neighbor-flips modular curve seen by a fast moving observer
Jack Anderson, Florin P. Boca, Cristian Cobeli +1
Let be a fixed non-zero integer. For every and every prime , consider the angles between rays from an observer located at the point on the…
Counterintuitive patterns on angles and distances between lattice points in high dimensional hypercubes
Jack Anderson, Cristian Cobeli, Alexandru Zaharescu
Let be a finite set of integer points in , which we assume has many symmetries, and let be a fixed point. We calculate the distances…
Distribution of angles to lattice points seen from a fast moving observer
Jack Anderson, Florin P. Boca, Cristian Cobeli +1
We consider a square expanding with constant speed seen from an observer moving away with constant acceleration and study the distribution of angles between rays from the observer…