Visualization, the power of imagination is core of all sciences and technologies. Mathematics is no exception to this golden rule.
Think about ‘a set of points’, geometric figures and diagrams, it may be a simple one or be a complex one. They move, reveal new properties, intersect, combine, form entire families and change their appearance, even sometimes, reshape into unrecognizable forms.
There are a number of problems, ranging from traditional problems in which one has to find and make use of some set of points, to simple inverstigations touching important mathematical concepts and theories. All need some sort of visualization for approaching towards solution aspects. Most of the problems challange for a series of visual interpretation which can be thought of a dynamics of visualization processes.
Most of the times, it is useful to verify and resolve problems in mathematics through experiment; by drawing a diagram or graph, even a series of thoughts mapped into a series of diagrams or graphs. This experimental approach not only helps one to guess the answer and formulate a hypothesis with the aid of visualization processes, but often leads one to a mathematical proof also.
Visualization and interpretation are co-occurring integrated processes that do happen side by side for inference purposes. Reversibility between these two processes, visualization and interpretation, is quite obvious from different perspectives. For instance, visualization to interpretation is usual flow of processes but reversibility of processes, from interpretation to visualization can occur if there be a mapping of interpretation into visualization processes during learning approach as well.