20th Annual Student Research Conference
Mathematics and Computer Science
The Cut and Project Method in Higher Dimensions
Kensey L. Riley
Dr. David Garth, Faculty Mentor
The cut and project method is a way of generating a point lattice. It is often used to study quasicrystals and tiles of the plane. Formally, it is a projection of the points with integer coordinates in a certain section of an n-dimensional lattice onto a suitable subspace. We studied how to use the Gram-Schmidt process to generate various point lattices and tilings. Specifically we projected vertices of a cube in 3,4, and 5 dimensions onto a plane. We then projected points with integer coordinates in R3 onto a various planes and obtained some interesting tilings. Finally, we extended this to higher dimensions to obtain some additional interesting tilings.
Keywords: Gram-Schmidt, quasicrystals, cut and project
Topic(s):Mathematics
Presentation Type: Oral Paper
Session: 60-2
Location: VH 1232
Time: 3:00 pm