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# «Geometry Expressions Manual TM Saltire Software PO Box 230755 Tigard, OR 97281 0755 © 2013 Saltire Software. All rights reserved. Information in ...»

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You can click the annotation box and drag it to adjust its placement in the drawing.

Calculations Calculating the Output Geometry Expressions will make calculations in the geometry based on any constraints or constructions you have specified, or just from the sketch. Calculations can be output in Real or Symbolic terms by choosing the appropriate tab.

If you haven't supplied all of the necessary input constraints, the system inserts any missing variables automatically or, for real calculations, bases the value on the sketch.

Some calculations may take longer than you expected. If the calculation isn't immediate, you can stop it and restart it with these buttons on the tool bar.

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You may want to reconsider the problem, add constraints, or just let it continue with the calculation.

The Stop calculations and Start calculations can also be found under Calculate (Output) menu and under the general context menu.

The table below lists all the available calculations and geometry elements which must be preselected. Be careful when selecting geometry objects, if extra things are selected that are not related to the calculation (like other calculations) the calculations will remain inactive. This can happen by mistake, especially when using the selection rectangle.

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Distance / Length Calculation Length calculations may be obtained for any line segment, polygon side or vector. Distance calculations are available between two points, or the perpendicular distance between a point and a line, segment, polygon side,

or vector. Use these steps:

1. Select the line segment, or point and line, or pair of points as described above.

2. Click the tab to switch from Real to Symbolic output or vice versa.

3. Click the Distance / Length tool in the Calculate toolbox or select Distance / Length from the Calculate menu.

Geometry Expressions displays the length, using any relevant parameters you may have specified.

Radius Calculation Geometry Expressions will calculate the radius of any circle. Use these

–  –  –

1. Select a circle.

2. Click the tab to switch from Real to Symbolic output or vice versa.

The equation with real or symbolic terms appears in the diagram.

Angle Calculation Geometry Expressions will calculate any angle between lines in the

geometry. Use these steps to find the angle:

1. Select two line types - any line, segment, vector, or polygon side.

2. Click the tab to switch from Real to Symbolic output or vice versa.

3. Click the Angle tool in the Calculate toolbox or select Angle from the Calculate menu.

The equation with real or symbolic terms appears in the diagram.

You can obtain the angle's supplement by dragging the angle symbol.

Supplementary Angles If it's unclear whether a calculation is requested for the angle or its supplement, you can drag the angle symbol to the correct position.

Here are some examples of playing around with supplementary angles (inputs, outputs and angle annotations all have this feature):

© 2013 Saltire Software 126 Geometry Expressions Manual

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Direction Calculation Geometry Expressions will calculate the direction of lines, segments,

polygon sides, or vectors with these steps:

1. Select a line type.

2. Click the tab to switch from Real to Symbolic output or vice versa.

3. Click the Direction tool in the Calculate toolbox or select Direction from the Calculate menu.

The direction measurement appears in real or symbolic terms.

Slope Calculation Geometry Expressions will calculate the slope of lines, segments, polygon

sides, or vectors with these steps:

1. Select a line type.

2. Click the tab to switch from Real to Symbolic output or vice versa.

3. Click the Slope tool in the Calculate toolbox or select Slope from the Calculate menu.

The equation for the slope with real or symbolic terms appears in the diagram.

© 2013 Saltire Software 128 Geometry Expressions Manual Calculate Coordinates You can calculate the coordinates of any point in your diagram with these

steps:

1. Select a point.

2. Click the tab to switch from Real to Symbolic output or vice versa.

3. Click the Coordinates tool in the Calculate toolbox or select Coordinates from the Calculate menu.

The real or symbolic coordinates appear by the point.

Area Calculation You can obtain the area of any polygon or circle in your diagram.

Note: If your polygon is not filled it is just a group of line segments. To convert them to a polygon, use the Polygon Construction tool, then

proceed with these steps:

1. Select a circle or polygon.

2. Click the tab to switch from Real to Symbolic output or vice versa.

3. Click the Area tool in the Calculate toolbox or select Area from the Calculate menu.

The area is displayed in real or symbolic terms.

–  –  –

Perimeter Calculation You can obtain the perimeter of any polygon or circle in your diagram.

Note: If your polygon is not filled it is just a group of line segments. To convert them to a polygon, use the Polygon Construction tool, then

proceed with these steps:

1. Select a circle or polygon.

2. Click the tab to switch from Real to Symbolic output or vice versa.

3. Click the Perimeter tool in the Calculate toolbox or select Perimeter from the Calculate menu.

The perimeter is displayed in real or symbolic terms.

Calculate Coefficients Use this tool to calculate the coefficients of a vector in the diagram with

these steps:

1. Select a vector.

2. Click the tab to switch from Real to Symbolic output or vice versa.

3. Click the Coefficients tool in the Calculate toolbox or select Coefficients from the Calculate menu.

The real or symbolic coefficients appear by the vector.

© 2013 Saltire Software 130 Geometry Expressions Manual Calculating Parametric Equations Computes parametric equations for a locus or envelope, based on the parameter defining the curve.

You can also calculate parametric equations for a circle or line.

Use these steps:

1. Select any geometry object described above.

2. Click the tab to switch from Real to Symbolic output or vice versa.

3. Click the Parametric Equation tool in the Calculate toolbox or select Parametric Equation from the Calculate menu.

The real or symbolic equations for x and y appear by the geometry.

Calculating Implicit Equation Calculates the implicit equation for the selected circle or a line.

Geometry Expressions will also attempt to calculate the equation of a locus or envelope curve.

1. Select any geometry object described above.

–  –  –

2. Click the tab to switch from Real to Symbolic output or vice versa.

3. Click the Implicit Equation tool in the Calculate toolbox or select Implicit Equation from the Calculate menu.

The real or symbolic equation appears by the geometry.

Output Viewing the Output The Output settings apply to Symbolic Calculations. The general default Output settings are found in the Edit / Preferences menu selection,

–  –  –

Individual outputs can be adjusted in the Display Properties dialog.

Select the output(s), then invoke the dialog in one of two ways:

right click the mouse and select All Properties from the Selection · context menu © 2013 Saltire Software 132 Geometry Expressions Manual from the menu bar, select Edit / Properties · The Output selections specify how the calculations are made and how the output is displayed.

Use Assumptions - applies to equations containing absolute values.

Use Intermediate Variables - can sometimes simplify the output.

The "Show" check boxes control where the output is displayed.

–  –  –

Click the Output selection, and then the drop-down arrow to select the desired state - True or False.

Assumptions With the Use Assumptions selection, Geometry Expressions eliminates the absolute value from expressions and determines from the diagram

whether the value is positive or negative. Try it with these steps:

1. select one or more output calculations

2. right click the mouse and select All Properties from the Selection context menu

3. click anywhere on the Use Assumptions line in the Output box

4. click the drop-down arrow

5. select False or True Obviously, this tool only has an effect when the expression selected contains an absolute value.

Intermediate Variables Substituting intermediate variables can sometimes simplify expressions calculated by the program. Try this option to see how it affects your

output:

1. select one or more output calculations

2. right click the mouse and select All Properties from the Selection context menu

3. click anywhere on the Use Intermediate Variables line in the Output box

4. click the drop-down arrow

5. select False or True If Use Intermediate Variables is False, the Show Intermediate Variables is © 2013 Saltire Software 134 Geometry Expressions Manual inactive.

Note: Intermediate variables are not always used in calculations, in which case this box will have no effect.

Show Output Check Boxes

After you generate an output expression:

1. click the output

2. right click the mouse and select All Properties from the Selection context menu

3. click one of the Output / Show... rows

4. click the drop-down arrow

5. select False or True Show Intermediate Variables - if the system uses intermediate variables, their definitions are displayed in the output window.

Show Name - is a term assigned by the system to the output. This name is zn where n is the sequential number of the output.

–  –  –

You can change the output name by double clicking the output and entering a new name in the box.

Show On Diagram - puts the output expression on the diagram when True.

Show in Output Window - puts the output expression in the Output Window when True. If this value is True, then Show Name becomes True.

Too Big for Diagram - the output expression is moved to the output window when True (Show in Output Window becomes True, Show On Diagram becomes False).

© 2013 Saltire Software 136 Geometry Expressions Manual Symbols Using Symbols The Symbols toolbox lets you easily insert Greek letters into your expressions and constraints. Click the tab to choose from lower case or upper case Greek letters.

The bottom row of buttons in the toolbox lets you insert commonly used math operations. You can either use the icons, or your type them from

–  –  –

Inserting Greek Letters To insert Greek letters into any variable name or expression, click the appropriate tab, Greek Upper (upper case letters) or Greek Lower ( lower case letters) in the Symbols toolbox, and click the letters to be inserted into the data entry box.

Multiplication & Division Editing Tools The Multiplication button inserts a multiplication symbol into the expression.

The Division button makes expressions easier to enter and read.

From the data entry box, enter the numerator of the expression, · highlight it, and then click Division.

The cursor is then positioned in the denominator.

If you click the Division button first, be sure to place the cursor in the · appropriate place before typing the expression.

© 2013 Saltire Software 138 Geometry Expressions Manual Square Root Editing Tool

You can enter square roots in one of these ways:

From the data entry box, enter the expression you want inside the · square root, highlight the terms, and click the Square Root button.

From the data entry box, click the Square Root button, then highlight · the 0 and type the terms.

Use the sqrt() function in the data entry box.

· Subscript / Superscript Editor You can enter superscripts or subscripts for variables in one of these

ways:

From the data entry box, enter the expression you want sub/ · superscripted, highlight the terms and click the Subscript or Superscript button.

From the data entry box, click the Sub/Superscript button and type · the values into the grey boxes.

Note: Make sure the cursor is positioned at the left side of the gray box before typing the sub/superscript.

–  –  –

Using the Piecewise Function A piecewise function or expression can be created using the Piecewise symbol or the built-in function - piecewise({expression1, domain1}, {expression2,domain2}...,{last expression, otherwise}). The reserved word, "otherwise" is an option available for the last condition.

For details see Piecewise Function and Piecewise Parametric Example in the Creating Functions section.

Built-In Functions For including in any expression or constraint, Gx has the following

common functions available:

Trig

–  –  –

tools. These symbols are not used in Geometry Expressions' algebra engine, but may be useful in creating worksheets and tests.

Use the symbols from the data entry window of the Annotate tools.

Simply click the symbol you need as you type.

When you are finished with the annotation, press enter.

© 2013 Saltire Software 142 Geometry Expressions Manual Font trouble - some of the Annotation Symbols may not show up in your drawing, depending on your OS and the default font setting.

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