Mathematics and Molecules- A STEM Activity

What is the relationship between molecular modeling and mathematics?

This activity uses Jsmol
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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?

ray

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.

rotating 2D graph 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.

angle A,B,C

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.

-------------->spin on -------->- spin off
------>space fill/cpk -------->stick ----> ball-and-stick

To Rotate the Molecule--->Left Click and Drag

To Zoom-->>Left Click + hold Shift button and Drag Vertically

Jmol Menu --->>Right-Click

PDB File for Salt Molecule click here.

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.