Goals and Methods of Mathematical Visualization
Next: Creating mental models.
Up: Pictures and Mathematics
Previous: Pictures and Mathematics
If graphics is to contribute to mathematics, we must next
What are the principal tasks of mathematical visualization?
Like other visualization domains, it must address
several levels of problems:
These are lofty and difficult goals, as significant mathematical
insights and results are unusual no matter how they are obtained.
- Information Content. Images, animations, and interactive
systems involving displays of mathematical objects must
possess intrinsically non-trivial information content and
reveal this information in some way to the viewer. Since
each viewer sees the world differently, the information
display should also take into account the beliefs, assumptions,
and perceptual preconceptions carried by the viewer.
- Teaching. To carry out effective research, one must
master what has gone before. Worthwhile visualization techniques
attempt to convey a useful and accurate knowledge of the
methods should enhance breadth, depth, and learning
speed compared to standard teaching methods.
- Insight. Visual ways of representing objects that the
viewer has only studied algebraically should offer previously
unattained insights, help expose general principles, and should suggest
- Results. The final objective is to prove interesting new
results, thereby extending the corpus of known mathematics.
Thu Sep 21 19:17:33 CDT 1995