New Perspectives in Science Education

In math classes orthogonal trajectories are mostly presented as a purely mathematical issue: curves where at every cross point the tangent lines are perpendicular to each other. Mathematical software however can offer an alternative and more appealing way to introduce orthogonal trajectories: a visual approach guarantees a deeper understanding of the mathematical theory. Moreover mathematical software offers the opportunity to incorporate the topic at different levels: introductory in a more narrative way, intermediary by a programming code to generate the graphical solution or mathematically advanced by a mathematical analysis based on differential equations that can be solved by mathematical software. This makes it attractive for a varied use by the mathematics teacher of a first year calculus course in higher education for students with or without programming experience. Our students, who were part of an experience with this approach, witnessed that computer code and theoretical mathematical analysis can go together and even reinforce each other by confirming the results. We also want to show that this approach to discussing orthogonal curves is suited within interdisciplinary engineering education as it is related to different application fields, e.g. finding the path of the steepest ascent, wire grid representations, ordinary differential equations...