Finding The Splitting Numbers of Tiles

School Name

Governor's School for Science & Mathematics

Grade Level

12th Grade

Presentation Topic

Mathematics

Presentation Type

Mentored

Mentor

Mentor: Gregory Clark, University of South Carolina

Abstract

In this research, the bounds of splitting numbers for finite tiles and their characteristics were analyzed. From prior research by Dr. Cooper, it was proved that the lower bound of splitting numbers is 2, and an upper bound is |T|+1, where |T| is the number of elements in a tile. The main result of this research was proving a tighter upper bound that is |T| for all finite tiles T by the use of an algorithm that can split any |T|-covering without fail. This research also proved that translations, reflections, and scalar multiples of tiles have equal splitting numbers. This allows the tiles to be grouped into categories based on their root tile.

Location

Wall 205

Start Date

3-25-2017 11:00 AM

Presentation Format

Oral and Written

Group Project

No

COinS
 
Mar 25th, 11:00 AM

Finding The Splitting Numbers of Tiles

Wall 205

In this research, the bounds of splitting numbers for finite tiles and their characteristics were analyzed. From prior research by Dr. Cooper, it was proved that the lower bound of splitting numbers is 2, and an upper bound is |T|+1, where |T| is the number of elements in a tile. The main result of this research was proving a tighter upper bound that is |T| for all finite tiles T by the use of an algorithm that can split any |T|-covering without fail. This research also proved that translations, reflections, and scalar multiples of tiles have equal splitting numbers. This allows the tiles to be grouped into categories based on their root tile.