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_ _Where's the Math in Mathmol?_
    
 Table of Contents
  Introductory Comments
  What is Molecular Modeling?
  Why is Molecular Modeling Important?
  What do some common molecules look like?
  Where's the Math?
  Carbon 3 Ways
  Carbon Compounds
  Water and Ice
  Water and Ice pt.II
  How to view structures in class or at home
  MathMol Library of Structures.
  Tutorial 1: 1-Dimension, 2-Dimensions, 3-Dimensions...
  Tutorial2: The Geometry of 2 Dimensions..
  Tutorial3: The Geometry of 3- Dimensions
  Tutorial4: The Geometry of Molecules.
  Appendix1: Scientific Notation
  Appendix 2: Mass
  Appendix3: Volume
  Appendix4: Density
 

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.

  To rotate object hold left mouse button down and slide cursor arrow over object

Below is shown the molecule Benzene. Click off the hydrogens. What geometric pattern do you see?

  To rotate object hold left mouse button down and slide cursor arrow over object
 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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