Interactive in 3D: Vector fields and Geometry
Wigand Rathmann
Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Department Mathematik
Abstract
Spatial concepts play an important role in the education of engineers. For the understanding of integrals over surfaces different concepts are necessary at the same time.
First is the representation of a parameterized surface in space. From the field of geometry, the triple product is used to calculate the content of the infinitesimal surface piece. For oriented surface integrals, the representation of a vector field on the surface supports the understanding and the interpretation of the integral to be calculated. Since summer 2022 it is also possible to create three-dimensional interactive diagrams with JSXGraph, which allows the realization of diagrams as described at the beginning.
The visualization of vector fields is also helpful for the understanding of ordinary differential equations. For visualization in the planes, the visualization of vector fields has been greatly simplified with version 1.6.0. JSXGraph also includes Runke-Kutta methods so that trajectories through given points can be easily drawn. This is possible in the plane as well as in space.
In my amount I present several applications from these areas.
The work for these graphs was funded by the ERASMUS+ project “Interactive digital assessments in mathematics”.