## What
is the Relationship between Molecular Modeling and Mathematics

## (A
MathMol Activity)

## This
activity uses JMol the Chime version is also available here.

_____________________________________

## 1
Dimension, 2 Dimensions, 3 Dimensions...

In this lesson we will
take a look at the 3-Dimensional world we live in. Look at the image below. You
will see two points.

A line has only
one dimension --length. The line has no endpoints and extends forever in both
directions. That is why when a line is drawn, we see arrows at both ends. On the
other hand when we draw a line segment on a piece of paper it has endpoints.

**Question 1:** How many endpoints
does a line segment have?

**Questions 2: **What is the figure below called?

The line, ray and line segment
are all examples of 1-Dimensional objects since they only have length.

On
the other hand a square has both length and height.

**Question 3:** How
many dimensions does a square have?

A square or rectangle is really a plane, a 2-Dimensional object
that has no thickness.

## The
Geometry of 2 Dimensions

When we see a graph on a page we really don't think
in terms of dimensions. But the graph above has only two axis or two dimensions.
It is a plane.

Click
on Graph to see that it only has 2-D

Each
point on the graph is represented by an x and y position. To find the x-position
we count to the right. To find the y-position we count up. Take a look at the
graph below. Angle ABC is represented by three points.

Point B has the coordinates (2,4).
Starting from the origin (0,0) to reach point B we count 2 spaces to the right,
then four spaces up.

**Question 4: **What are the coordinates
of point A?

**Question 5: **What are the coordinates of point
C?

**Questoin 6: **What type of angle is angle ABC (acute,
obtuse, or right)?

## The
Geometry of 3 Dimensions

Compare the graph above (showing the cube) to the one
shown in the above that contains angle ABC. What is different in this graph? Besides
the x-axis and y-axis what do you see?

This graph has another
axis, the z-axis. When we locate a point in three dimensions we need to use three
coordinates. The origin in a two dimension plot is written (0,0).

**Question
7: **How do you write the coordinates for the origin in a 3-dimension plot?

What does all this
have to do with molecules?

##### Molecules
are solid 3 dimensional objects in 3 dimensional space. To describe molecules
accurately we must describe their postion in 3-D space.

Look at the
salt crystal structure above. Each atom is represented on the x,y,z coordinate
axis as a single ball.

In the next section we will look at molecules and their
relationship to mathematics.

GO TO PART II