E. Polyak

New York University, Tisch Asia School of the Arts (SINGAPORE)
The aim of this work is to present an active and creative visualization method for mathematical concepts using 3D animation, modeling, simulation and story. The result is a first-hand experience of practical problems that need solutions. The method attempts to motivate investigation and problem solving by inviting the student to experience the problem itself through a creative activity.
Although classic visualization models in mathematics involve three dimensional renderings and interactive animations and have proven to be effective in many situations, often they break down concepts into new concepts and then present segments to the observer. Most interactive models are predefined, driven by limited parameters that are available as a user interface. Many times we can see students wanting to use their creativity to interact instead of becoming the passive observer or operator.
The active visualization method employs a measurable virtual 3D world with a time-line, a modeling tool-set and a physics simulation engine inside a common 3D animation package. The animation process strictly relies on segments controlled by non-linear function curves locked to time and therefore it provides an excellent ground to manipulate transformations without limitations even when those lead to problems. Students will engage in a creative activity that involves a story with a given goal by modeling and animating a phenomenon or group of phenomena that will lead to a problem they do not expect. The students will learn about a mathematical concept that provides the solution to their problem. They will integrate the concept and fix the problem to complete the story.
Although there is a large number of topics and many levels of complexity where the method can be used at, for example modeling geometries to calculate volume or grouping large amounts of particles based on certain attributes, one of the most important elements is the storytelling that connects all participants.
This work presents an example of using quaternion to adjust the rotation of a spaceship to change trajectory in order to fly back to the Earth. The spaceship will be driven to a gimbal lock in Euler angles.