Skateboarding in 4 Dimensions: Exploring Quaternions Systems Using Computer Simulations

Quaternions are a number system extended to four dimensions. It is used to describe the movement of physical objects in 3D space. This concept is widely applied in fields such as computer vision, robotics, and game design. However, the mathematics involved can be unintuitive, and the notation is often confusing for beginners. In this demonstration, I will use skateboarding, a popular sport among young people, to illustrate Quaternion concepts through a series of interactive computer simulations. I will show how skateboarding tricks like spins, flips, and shuvits can be elegantly represented and modeled using Quaternions and explain why some tricks are more complex than others. This tool is valuable for students interested in 3D graphics, game development, robotics, or computer vision, where Quaternions are foundational concepts. Additionally, it benefits visual and kinesthetic learners by grounding complex mathematical ideas in the familiar and engaging context of skateboarding. It is suitable for middle or high school students or undergraduate students in formal and informal learning settings.