Translation by a vector in the coordinate plane is first introduced in precalculus and connects to the basic theory of vector spaces in linear algebra. In this article, we explore the topic of collision detection in which the idea of a translation vector plays a significant role. Because collision detection has various applications in video games, virtual simulations, and robotics (Garcia-Alonso, Serrano, and Flaquer 1994; Rodrigue 2012), using it as a motivator in the study of translation vectors can be helpful. For example, students might be interested in the question, “How does the computer recognize when a player's character gets hit by a fireball?” Computer science provides a rich context for real-life applications of mathematics-programmers use mathematics for coding an algorithm in which the computer recognizes two objects nearing each other or colliding. The Minkowski difference, named after the nineteenth century German mathematician Hermann Minkowski, is used to solve collision detection problems (Ericson 2004). Applying the Minkowski difference to collision detection is based on translation vectors, and programmers use the algorithm as a method for detecting collision in video games.
Younhee Lee, firstname.lastname@example.org, is a PhD student in mathematics education at Pennsylvania State University in State College. Her research focuses on connections between college mathematics and school mathematics and the use of technology in teaching mathematics.
Qi Lu, email@example.com, is a PhD student in computer science at the University of New Mexico. He is interested in autonomous robotics, self-organizing systems, and swarm robotics and enjoys connecting mathematics to computer programming.
Woong Lim, firstname.lastname@example.org, is an assistant professor of mathematics education at the University of New Mexico. His research interests include using computing and digital technology to support teaching and learning and mathemat ical discourse.