You can also use spreadsheets to model phenomena that can be described by a mathematical equation. You can then plot the equation and study the behavior under different conditions. You can change the values of the constants that might be present in the equation in order to see the effect of that parameter. This use of spreadsheets will be our primary focus in this course. Used properly, such modeling enables the scientist to visualize better the phenomena he or she is studying.

The tool palette on the left side of the *Wingz* window gives you access
to the presentation capabilities of the program. These include the ability
to create text boxes and charts and line, arc, oval, rectangle and polygon
drawing tools. The top tool, the block plus sign, is the tool that must be
activated for normal spreadsheet functions. The second tool, the cross-hairs,
is the tool used to manipulate objects like text boxes or charts. The third
tool is the button tool that allows you to activate a script (a pre-programmed
series of commands) from the spreadsheet. Of these tools we will only be
using the chart tool (unless, of course, you want to get fancy on your own).

**Text Entry**- Used mainly for labels. By default text is left justified; the font is Geneva, the size is 10, and the style is Plain. These defaults can be altered with commands in the**Format**menu.**Number Entry**- By default numbers are right justifed; the font, size and style are the same as for text entries and can also be changed. Numbers are given as decimals with two digits shown to the right of the decimal point. The number of digits shown to the right of the decimal point can also be altered with**Precision...**command in the**Format**menu. Other number formats can be used: including scientific notation, various date notations and various time notations.**Formula Entry**- In*Wingz*formula entries always begin with an equal sign. For example, to multiple the value of cell**A1**by 2 and add 10 to it, you would write the formula =A1*2+10 into a cell (other than**A1**).*Wingz*uses the "*" as the sign for multiplication and "^" as the sign for taking the exponent. The order of operations in*Wingz*is exponentiation, then sign changes, then multiplication and division, and finally addition and subtraction. If the value of**A1**was 15.00, the cell that you wrote the formula in would display 40.00.*Wingz*also has a number of built-in functions that can be included in formulas. These range from simple mathematical functions such as SQRT() or EXP() to spreadsheet specific type functions such as SUM() or AVG(). The functions can be accessed via the**Go, Paste Function...**command.

This feature is especially useful with the kind of modeling that we will be doing. For example, in column A we could place a column of numbers that are the independent variable in our mathematical equation. In column B we could write some function that depends on the independent variable. If the formula refers to the first cell in column A, then when you copy and paste the formula into the other cells of column B the reference to the independent variable is automatically changed. The end result is two columns of numbers: the first, the independent variables and the second, the value of the function at each independent variable. The second column can be plotted as a function of the first to represent the function graphically. (See the next introductory document, Tips to XY Plotting with Wingz.

Sometimes it is necessary to override this default feature of spreadsheets, for
example, if there was a constant in your formula, but the value of the constant
was located in another cell. Suppose you were plotting a straight line with
with the formula y = mx + b, where m is the slope of the line and b is the
y-intercept. In column A write a series of numbers for x, the independent
variable. Cell **B1** will contain the value for m, the slope and **B2**
will contain
the value for b, the y-intercept. In column C write the following formula:
=B1*A1+B2. If this formula is copied down in all the cells of column C, then
because of relative cell referencing, not only will **A1** be changed to
**A2** to **A3**,
etc. as desired, but **B1** will be changed to **B2** to **B3**, etc.
and **B2** will be
changed to **B3** to **B4**, etc. Of course, this is not what we want
since **B1** and **B2** are constants for the equation. One solution is
to put the value for
m and b explicitly into the formula. Sometimes this is the best solution.
Another solution is to use absolute cell references. An absolute cell
reference is not changed during a copy and paste action. In *Wingz* an
absolute cell reference is made by using the dollar sign ($) symbol. Thus, a
reference to **B1** would be $B$1. (It is possible to keep only the
column of the cell reference absolute by placing the $ before the letter in
the reference
($B1) or to keep only the row of the cell reference absolute by placing the
$ before the number in the reference (B$1). The proper formula in the previous
example is =$B$1*A1+$B$2. Now if the formula is copied down column C only
the reference to cell **A1** is changed.

Terry M. Gray

*grayt@calvin.edu*

*Last modified on November 11, 1995*