The calculator provides for the creation of complex measurements and the evaluation of mathematical expressions.
The calculator is organized into four main sections: Input text area, Evaluation text area, KeyPad, and Measurement list.
Input Text Area: The topmost text panel (with scroll bars) is the input area. When one clicks on KeyPad buttons, the resulting text of the expression being constructed is displayed here. The five keys in the lower left side of the KeyPad group control how one can move back and forth among the entries of an expression.
Evaluation Text Area: The text area labeled "value" is where
the result of evaluating an expression is displayed. When an expression
has been built it can be evaluated by hitting the "Evaluate" button on
the bottom of the calculator window. For example if the expression
is
"50!" the result displayed would be
30414093201713378043612608166064768844377641568960512000000000000.
(Note: Geometry Explorer can handle arbitrarily large integer
arithmetic)
KeyPad: The KeyPad is like a traditional calculator keypad, with a few twists. First, the constants pi and e can be input as symbolic expressions which can then be evaluated. Second two functions which take two variables are available - max and min. For example, the expression "max(22,22.1)" gives 22.1.
Note the four keys "(", ")", "^", and "!". Parentheses are
used
for grouping and for function calls. Thus, to evaluate sin(pi) we would
hit the "sin", "(", "pi", and ")" keys and then hit the evaluate
key. The caret "^" is used for powers. Thus, "2^500" would evaluate to
3273390607896141870013189696827599152216642046043064789483291368096133796404
674554883270092325904157150886684127560071009217256545885393053328527589376
The "!" is used to compute factorials (of integers only).
As noted above the five keys in the lower left side of the KeyPad group control how one can move back and forth among the entries of an expression.
Measurement List: Geometry Explorer provides for the
measurement
of geometric quantities such as radius, length, slope, etc. Often
one would like to use these measurements in more complex expressions.
For
example, suppose we wanted to compare the area of a circle to the
formula
for "pi*radius^2". We want to be able use a given measurement in an
expression,
much like we use sin(x) or pi in expressions. The calculator is
the
means by which we can build up such expressions. As measurements are
made
in the canvas, they are automatically added to the list of available
measurements
in the calculator. These measurements can then be selected in the list
and inserted into the Input window by double-clicking on the desired
measurement
in the list. At the top of this page is a screen shot of the calculator
with an expression built from the radius and area of a circle from the
canvas. The expression has been evaluated and the result
is not too surprising!
(Note that the precision of calculations is carried out to the maximum
accuracy of the computer when evaluating
expressions in the Cacluator. This is done to guarantee the most
accuracy of calculation. Thus, in the expression shown,
we see the effect of approximating pi in the final result.)
Adding expressions to the canvas: Once an expression like the one shown above has been evaluated, it is then available to insert into the canvas and will then be a "live" measurement, just like any other measurement. That is, as the geometric objects that are measured change the new complex measurement will also change dynamically.