Physical Sciences and Mathematics Commons^™

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 …

The Beauty Of Bézier Curves, Qing Chen, Ariane Masuda

Publications and Research

It is very difficult for ordinary people to become excellent painters like Picasso. In contemporary society, everyone has a computer, but no one associates painting with computers. This project aims to show that one can use computer tools to connect mathematics with art. We use Krita, which is a professional free, and open-source painting program made by artists to create digital art. We demonstrate how the Bezier curve pen tool in Krita can help anyone to ́ draw paintings such as Picasso’s cubist oil paintings on a computer in a relatively short time.

Bézier Curves, Qing Chen, Ariane Masuda

Publications and Research

Drawing on a computer using a mouse is quite different than drawing by hand. It can be challenging to use a mouse to even simply trace a line. If the drawing involves several lines and curves, the task becomes more complicated. The goal of this project is to show how to design beautiful artworks using Bézier curves. A Bézier curve is a smooth parametric curve produced by the coordinates of certain points. To draw a specific curve, one needs to select multiple control points positioned in strategic places. By changing these positions, one can draw different curves to produce the …

Parametric Art, Shaun Pollard, Daanial Ahmad, Satyanand Singh

Publications and Research

Lissajous curves, named after Jules Antoine Lissajous (1822-1880) are generated by the parametric equations ��=��������(����) and ��=��������(����) in its simplistic form. Others have studied these curves and their applications like Nathaniel Bowditch in 1815, and they are often referred to as Bowditch curves as well. Lissajous curves are found in engineering, mathematics, graphic design, physics, and many other backgrounds. In this project entitled “Parametric Art” this project will focus on analyzing these types of equations and manipulating them to create art. We will be investigating these curves by answering a series of questions that elucidate their purpose. Using Maple, which …

U.S. - Canadian Border Traffic Prediction, Colin Middleton

WWU Honors College Senior Projects

Mathematical discussion and analysis of several prediction methods which use real time data to predict traffic flow at the U.S. - Canadian Border crossings.