Physical Sciences and Mathematics Commons^™

Solving The Genius Square: Using Math And Computers To Analyze A Polyomino Tiling Game, Noah Jensen

WWU Honors College Senior Projects

This paper investigates if the claim of the game Genius Square is true, that all 62,208 boards that its dice can roll are solvable. The gameboard is a 6 by 6 grid and the objective of the game is to tile a board that has 7 blockers, quasi-randomly placed by the dice, with 9 polyominoes consisting of 1, 2, 3, and 4 squares. In order to implement a model of linear systems created by John Burkardt and M.R. Garvie, code was developed using Python and Matlab. With this code, it was shown that all 62,208 boards are solvable. The number …

Lagrangian Mechanics And The Motion Of A T-Handle, Eric Maurer

WWU Honors College Senior Projects

This paper begins by deriving the equations of motion for the Lagrangian formulation of mechanics. Lagrangian mechanics describes the same thing as the traditional Newtonian mechanics (which is what is taught in most undergrad physics classes), but rather than model the system through forces, it models the system through energy. Energy is conserved in a system, which allows the Lagrangian formulation to model certain types of systems in a more efficient way than the Newtonian formulation.

Next, the paper explores rigid body motion, specifically looking at the motion of the angular momentum. The goal of this part is to explain …