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Part
I -Geometry
Part
II-Mathematical Relationships
Part
III- Overview of MathMol Tutorials
Numerous connections
are found between mathematics and molecular modeling. Here are
just a few!
Many molecular
structures have the same shape of familiar space figures. Take
another look at the fullerene molecule shown below. The molecule
has the same shape as an icosohedron. Notice that the faces are
composed of hexagons and pentagons.
Below is shown
the molecule Methane.
Try
this.
Notice when
you rotate the methane molecule it is off-center. Click on the
tools pulldown and select 'pickcenter'. Click the center carbon
atom in the methane molecule. Now rotate the methane molecule.
It should rotate around the center carbon atom.
What polyhedral
stucture would you think methane best represents? Click on the
tetrahedral box. Now rotate the object to show how the molecule
fits snugly within the tetrahedron.
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To
rotate object hold left mouse button down and slide
cursor arrow over object |
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Below is shown
the molecule Benzene. Click off the hydrogens. What geometric
pattern do you see?
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To
rotate object hold left mouse button down and slide
cursor arrow over object |
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Do
you know what the interior angle measurements are for a hexagon?
You can measure the angles of the hexagon using the above software.
First click the hydrogens back on. Click on tools --> measures.
Then click with the left mouse button on three consecutive vertex
points. The lower left hand corner will give the angle measurement
of 120 degrees along with several other measures. What is the sum
of the interior angles equal to? At the end of this textbook are
several tutorials which explain in greater detail how to use this
software package and what all those numbers at the lower left mean.
Many
geometric figures display symmetry.
 Image 5K
The equilateral
triangle on the left displays rotational symmetry. Rotating the
figure about about a point formed by the intersection of the three
angle bisectors (the incenter of the triangle) will give the same
appearance. The ammonia molecule on the right also shows symmetry.
It has a 3-fold axis of symmetry. Rotating the molecule 120 degrees
about its axis will give the same appearance.
Go to part II_Mathematical Relationships
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