Approximating physical quantities by idealised mathematical shapes
is a commonly used tool in mathematical biology. By thinking about
these issues and categorising the shapes, students will learn that
various shapes occur both naturally and frequently in nature.
Students will intuitively have some concept as to how 'good' an
representation might be; by explicitly discussing the concepts,
understanding of the strengths and limitations of these
representations will grow.
This question could be posed individually or for group discussion.
This problem also works effectively when students are given time to
reflect. Ask the question and let students consider it over, say, a
week. What shapes have they noticed in nature? This results might
make an effective display.
- How reasonable is the mathematical idealisation?
- Are there any objects which are particularly well represented
by a certain shape?
- What order of magnitude checks could you make to test that your
answer is sensible?
Can students think of good evolutionary reasons for the shapes that
certain organisms take?