Conclusion
In our fascination with the ubiquitous nature of
spirals, we noticed that they are most prevalent in mollusks'
shells. We therefore decided to use these animal's shells to
investigate spirals. This was both a biological and mathematical
research paper, since we investigated the math behind the spirals
as well as the creatures found in the shells. What is the
definition of a spiral? Why are they so common in nature and
especially among the shells of mollusks? Why would a shell prefer
a spiral shape over any other? Are shells in fact perfect
spirals? These are a few of the questions we asked ourselves as
we began our journey into the land of spirals.
During the previous pages, we managed to satisfy
our objective by answering these questions. We also had the
opportunity to explore Maple's many functions, especially in the
field of plotting graphs. Thanks to this project, we expanded our
overall knowledge on mollusks, shells and spirals. We also
learned about Archimedes' spiral ( ![[Maple Math]](images/conclu1.gif)
) and the
logarithmic (Bernoulli, equiangular) spiral ( ![[Maple Math]](images/conclu2.gif)
). We then verified
these laws by collecting data off concrete shells and
transforming these values into graphs that we curve fitted.
Annex 1
Archimedes
Archimedes of Syracuse, an outstanding Greek
mathematician, flourished in Sicily during the second century
before Christ. His numerous contributions to the world of science
have made him one of the most celebrated mathematicians of
ancient times. Many of his discoveries have played a lasting
impact on our society and have thus enabled us to understand the
world we live in. Indeed, it was he who discovered the formula
allowing us to compute the volume of a sphere: ![[Maple Math]](images/conclu3.gif)
.
Bernoulli
Daniel Bernoulli, one of the many scientists who
dedicated his life to the progress of Calculus, was born in
Groningen on January 29, 1700. Although he was certified in the
field of medicine, he instead became a professor of Mathematics
in St-Petersburg, Russia and expanded his expertise to teach
experimental philosophy, anatomy and botany in Switzerland in the
following years. Bernoulli concentrated his energy in studying
the flow of fluids and formulated the following principle: the
pressure exerted by a fluid is inversely proportional to its rate
of flow. He died on March 17,
1782 in Basle.
Annex 2
3-d Plot:
> restart:with(plots):
> animate3d((1.3)^x *
sin(u*y),x=-1..2*Pi,y=0..Pi,u=1..8,coords=spherical);
![[Maple Plot]](images/conclu4.gif)
Home
Introduction
Plot #1
Plot #2
Conclusion