4 citations · 14 across the 16 of their papers we have counts for
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On second order linear sequences of composite numbers
Dan Ismailescu, Adrienne Ko, Celine Lee +1
In this paper we present a new proof of the following 2010 result of Dubickas, Novikas, and Siurys: Let and let be the sequence defined by…
On the polygon determined by the short diagonals of a convex polygon
Jacqueline Cho, Dan Ismailescu, Yiwon Kim +1
Let be a convex pentagon in the plane and let be the pentagon bounded by the diagonals of . It has been conjectured that the maximum of the ratio between the areas of…
Dense Packings with Nonparallel Cylinders
Dan Ismailescu, Piotr Laskawiec
A \emph{cylinder packing} is a family of congruent infinite circular cylinders with mutually disjoint interiors in -dimensional Euclidean space. The \emph{local density} of a cy…
The Hadwiger-Nelson problem with two forbidden distances
Geoffrey Exoo, Dan Ismailescu
In 1950 Edward Nelson asked the following simple-sounding question: \emph{How many colors are needed to color the Euclidean plane such that no two points distance $1…
The chromatic number of the plane is at least 5 - a new proof
Geoffrey Exoo, Dan Ismailescu
We present an alternate proof of the fact that given any 4-coloring of the plane there exist two points unit distance apart which are identically colored.