Geometry Explorer Help

Using the View Menu: Using the Calculator

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The calculator provides for the creation of complex measurements and the evaluation of mathematical expressions.

calculator

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.