Contents
C.a.R.

Compasses and Ruler

Computer Aided Geometry

programmed by René Grothmann

Contents

Click here to go to the following topics.

-	Overview

-	The main window

-	The toolbox

-	The Menu

-	Keyboard usage

-	Using macros

-	Reaching the author

-	Answers to Questions

Enjoy this program!


Overview

C.a.R. is a program to help teachers and pupils understand geometric constructions with circles and straight lines. By geometric construction we understand constructions with a pair of compasses and a ruler. I.e., constructions with circles and straight lines. The program is not to be used as a CAD program. It is especially designed for the didactic purpose to teach mathematical ideas about geometry.

A usual construction will start with points, which you place at random. Using these points, you may construct lines, line segments, rays or circles. You will then generate new points by intersection two of these objects, continuing until you reach your final construction goal. There are some additional construction steps available, which shorten the process, but may be replaced by the basic steps.

In contrast to the usual paper method, you will benefit from the computer in many ways. You are now able to

-	undo and retry construction steps,

-	hide construction details,

-	use color to label groups of construction steps,

-	move points and view the resulting construction changes,

-	draw tracks of points, while you move other points,

-	discover constructions by the inspection of these tracks,

-	use macros to speed up the construction process,

-	use macros to learn a basic feel for programming,

-	save your construction in ASCII readable form,

-	paste your construction into other documents,

-	make a high quality print of your construction.

This program is shareware. In the unregistered version, the number of construction steps is limited, as well as the ability to save macros. Prints will be labeled Unregistered Version.


Main Window
The Main Window

The main window pops up after program start above the toolbox dialog. It will display your construction. You can resize the window as usual. Pressing the cursor keys, when the main window has the focus, will move the view to the up, left, down or right. Pressing + or - will zoom in or out.

The window title contains the file name of your construction. If this is a new construction, it will receive a name after it is saved into some file.

The left mouse button is used for most constructions to place or select objects. Additionally, the right mouse button is used to pop up the property dialog of any object (when the button is released). When the mouse is moved with the right button down, a point may be dragged. This is a shortcut to the Move object tool.

All constructions have keyboard shortcuts, consisting of a single letter. Note, that these will only work, if the main window has the keyboard focus. To give it the focus, click on its title bar.

The position and size of the main window are saved at program end, together with the position of the toolbox.


The Toolbox

The toolbox is a dialog, which should pop up under your main window.

On top of the toolbox, the status line displays information about the next awaited step. Furthermore, this dialog contains the various construction tools, a color choice and two other controls. Each tool is also available through the menu and the corresponding keyboard commands.

From left to right:

-	Point: To generate a point. Click on any position on the drawing area.

-	Line: Generates a line through two points. The line is an infinite straight line. Choose the points among all available visible points.

-	Segment: Connects two points with a line segment.

-	Ray: Makes a ray starting at one point through another. Choose the starting point, and then the other point.

-	Circle: Choose the midpoint and then a point on the boundary.

-	Circle (3): Generates a circle by its midpoint and two points. The distance of these points will be the radius of the line. This construction was not basic in ancient constructions, since a collapsing pair of compasses was assumed. However, it can be simulated by basic constructions.

-	Intersection: Intersects two line objects, a line object with a circle or two circles. Thus this construction generates one or two points. Choose both objects in the drawing area. Note, that in C.a.R. you cannot automatically use intersection points, unless you have generated them with this tool.

-	Point on Object: Generate a point, which is bound on to a line or circle. When the circle or line moves, the point will stay on it.

-	Move: Move a point. Not all points are moveable, however. In general, points, which depend on some construction, cannot be moved. Even then, points may be fixed by editing their properties. You can also move a point by dragging it with the right mouse button.

-	Move on Object. The purpose of this construction is to generate tracks of other points. You must first choose a line or circle, then the point to be moved. This point will flip to the line or circle and you can move it on the object with the mouse. This way you are able to study the changes in the construction, when one of the parameter points is moved along a line or circle. Especially, you can track any other points, leading to insights about the dependence of these points.

-	Track: Marks a point as a track point. I.e., any movement of the point will leave a trail. This is a powerful tool to study constructions. Sometimes these trails turn out to be well known geometric objects. To remove the track, use the Delete tracks button on the right of the toolbox, or choose the point anew. You can track more than one point. There is a maximal value for the track length.

-	Middle Point: Generates the middle point between two points. This construction as well as the following constructions are by no means basic. You could replace it with a macro using basic constructions only. However, it is quite handy. To disable these trick constructions, check the corresponding menu point.

-	Vertical Line: Constructs a vertical line from a point to a line. You have to choose the line and then the point. Note, that this constructs a hidden point, which defines the vertical line.

-	Parallel Line: Constructs a line parallel to a given line through a point. Again, you must choose the line first.

-	Angle: This is only for demonstration.  To mark an angle on the screen, choose a point on one of the lines forming the angle, the basis point and then a point on the other line. Angles are drawn in a mathematically positive sense. I.e., you must first choose a point on the left wing of the angle.

-	Edit: Allows you to edit the properties of an object (point, line, circle or angle). You may also set the precise coordinates of a point, or view the length of a line segment. Look into the help text for the various edit dialogs. Clicking with the right mouse button on an object will also open its properties dialog.

-	Hide: Clicking on any object will hide it. To view the hidden objects, use the Show all button on the right of the toolbox. If this is checked and a hidden object is clicked, it will become visible.

To the right of the tools are the color choices. This  choice will be the default color of newly constructed objects. The Show all check button will uncover all hidden objects. Finally, the Delete tracks button removes all tracks on the screen.


The Menu

The menu appears in the main window. It contains the following sub-menus. As usual, a sub-menu can be opened by pressing the ALT-key together with the underlined character in the menu header.

- File

The file menu contains items to load or save your construction. Unless the construction has a name appearing in the window title, saving will prompt for a file name. New will erase the construction and open a new, unnamed construction. C.a.R. uses the *.car extension for construction files. These files are readable ASCII text. They may be used to derive a man readable description of your construction.

- Figures

This menu contains those construction tools, which directly create new objects. The tools are explained in detail in the toolbox section.

- Actions

This menu contains the construction tools, which contain objects, depending on other objects (like intersections) or which modify objects. The tools are explained in the toolbox section.

Delete Tracks will delete all tracks of any points. Delete Objects deleted any chosen object, together with all objects, which depend on it. (The last object can be deleted with the Clear Last menu entry in the options sub-menu.)

Furthermore, Step through Construction allows the step by step execution of your construction. There is a sub-menu available for the various stepping commands. Alternatively, you can use the cursor keys and the page up and down keys. Also, he mouse key will step forward. Note that hidden construction steps are skipped.

- Options

Show all will toggle the display of all hidden objects. This is the same option as in the toolbox. Default Color offers the choice between the six colors of C.a.R. Each newly created object gets this color. Again, this is also available in the toolbox.

Show Grid toggles the display of the grid on and off. Grid Settings opens a dialog to set the grid spacing.

Edit Comment allows the editing of a comment, which is saved with the construction. This comment dialog will pop up after a construction is loaded.

Clear Last deletes the last object, together with hidden construction steps, so that the last previous visible object becomes the last object.

Zoom, Shift and Center allow the positioning of the construction window. Think of the construction on virtual plane. Then your window offers a view to this construction of variable position and size. This view can be enlarged by zooming, or moved by shifting. Usually, this is done with the cursor keys or the +/- key.

Clear all is identical with New from the file menu.

- Macro Setup

Here you can define new macros, delete old macros, save or load macros. Look into the macro section for a description.

- Run Macros

There are two ways to run a macro. First you can click on Run Macro (or press the corresponding key) and choose the macro. Or you can choose the macro in this menu. Each macro will become a new menu point.

- Help

Calls the online help.


Keyboard Shortcuts

All keyboard shortcuts can be seen in the menu bar. However, here is a list.

Key	Function
F1	help contents
F3	edit comment
F4	step through construction
F5	run macro
F6	delete tracks
^F5	define macro parameter
^F6	define macro targets
^F7	complete macro definition
^F9	load macro
^F10	save macro
^L	load construction
^S	save construction
^A	save construction as …
^X	exit program
left	move view left
right	move view right
up	move view up
down	move view down

The following keys select construction tools.

P	point
S	line segment
L	line
R	ray
C	circle
3	circle from midpoint and radius
V	vertical line
1	parallel line
D	middle point
A	angle
O	point on object
I	intersections
M	move point
J	move point on object
T	track of point
E	edit object properties
H	hide object

The last group is only available, when the Step through construction tool is activated.

^down	step forward
^up	step back
^page- down	10 steps forward
^page- up	10 steps back


Macros
Using Macros

Macros serve as shortcuts of complicated constructions. Macros have parameters, which the user is required to choose. You can define a specific prompt string for any parameter. When the last parameter is chosen a macro will go through the defined construction steps, using the chosen parameter objects, and creates the target objects.

When the user runs a macro, he will be prompted for the parameter objects. The macro will then create the target objects automatically, after the last parameter is chosen. All objects are created with predefined attributes (color, style, hidden). One exception are black objects, which will receive the current default color.

Using macros may also provide a first contact to some sort of programming. Macros behave much like subroutines of programs, which have parameters and a function result.

Defining macros is easy. You have to choose the parameter objects first. For each parameter, you may enter a prompt string. Then you must choose the target object, or the target objects. The program must be able to construct the target objects from the parameter objects. Note, that choosing a line as a parameter does not automatically choose the two points, which define the line. After you have fixed the last target, complete the macro definition by setting a name for the macro. A new macro will appear in the macro menu. Use the macro menu to initiate the parameter selection, the target selection and the completion of the macro. Here is an outline of these steps:

1.	Construct a specimen for the macro.

2.	Hide construction details, if you wish.

3.	Choose the parameters for your macro.

4.	Choose the target objects of the macro.

5.	Complete the macro definition.

6.	Save the macro, if you wish.

Macros are save with the *.mac extension. The format is similar to the save format of the construction, but macros do additionally specify the names, types and prompts of the parameters.


The Author

The most recent version will be on the ftp server at am.ku-eichstaett.de with file name car*.zip. Log in as anonymous and enter your Email-address as password. In a net-browser, open the location

ftp://am.ku-eichstaett.de/pub.

Send comments or bug reports to mail address grothm@ku-eichstaett.de, if possible. If you do not have access to E-mail, mail me at

Dr. R. Grothmann

Ahornweg 5a

D-85117 Eitensheim

Germany


Answers to Questions;Frequently asked Questions
Answers to Questions

Why do I have to use the Intersection tool?

When doing paper and pencil constructions, you simply use the constructed points you see. However, in this program you have to construct the intersection points. The reason of this is that an automatic generation of all possible intersection points would be impractical. On the other hand, a check, which intersection is meant, is unhandy and time consuming.

Why does my construction disappear, when I move points?

Constructions may become invalid. Obviously, intersections become invalid, when the intersection is empty. Furthermore, circles of zero radius are invalid, as well as lines, with defining points at the same position. Of course, this is checked with an internal epsilon. So in rare cases, things may become invalid by numerical reasons.

How do I make my construction clearer?

First of all, you can hide construction details. Furthermore, you can explain the construction in the construction comment. Then you can use color to group construction steps. Since it is possible to view only specified colors, this helps a lot. Finally, you could hide unnecessary parts of circles by checking complete circle in the circle properties off.

What is the order of the intersection points?

If a line is intersected with a circle or if two circles intersect, two intersection points are generated. When you use one of them, you wish to control which one is meant. The order of these points depends continuously on the position of the line, or circles respectively. Thus, if the two intersecting circles are interchanged, the order is reversed. Also, each line has an orientation, which depends on the order of the defining points. The intersection points depend on this order as well.

However, there is a special feature in this program, which helps overcome this difficulty. In most cases, a construction will become invalid, when the wrong intersection point is chosen. Especially, a circle may have a zero radius or the two points, defining a line may fall together. If this is the case, the construction will be tried with the other intersection point. This feature helps in most instances.

Why can my macro target not be constructed from my parameters?

The reason may be, that your parameter is a line, and your construction uses the defining points. You must included these in the parameter list, and the user must enter these parameters, when he runs the macro.


Display Colors
Choose displayed Colors

In this dialog, you can choose groups of objects for display. A group is determined by the color of its objects. This will also apply to hidden objects, if Show All is checked.


Object Properties;Edit Object
Edit Object Properties

The properties dialogs vary from object to object. They all contain a line, showing the construction command for the object, as it would be saved in the construction file. Furthermore, the name of any object can be set. Objects get default names, consisting of a type identifier and a unique number. To make your construction file more readable, you may wish to change the name of important objects. Two check boxes are common to all object types: The Hidden checkbox and the Show Name check box. The first is another method to hide the object, and the latter must be checked for the object name to appear in the construction.

Object dialogs contain specific object parameters, like the position of a point, the radius of a circle and the size of an angle. For points, you are able to set the position, unless the point depends on other objects. A fixed point cannot be moved with the mouse. A circle has a complete circle check box, which is on by default. If it is not checked, only relevant parts of a circle are visible.


Parameter Prompt

When the user is running a macro, he will be prompted for the parameters. This dialog lets you enter a text for this prompt. Look into the macro section for more information.


Macro Name

Enter a name for your macro. This may be different from the file name, which you intend to use for the macro. The name is used to identify the macro in the macro selection dialog, and in the toolbox, when the user is prompted for the macro parameters. Look into the macro section for more information.


Select Macro

Select the macro from all available macros. Double click on the macro name should select the macro. Alternatively, select the macro and click OK. Look into the macro section for more information.


File Error
File Error !

The input file contains a syntax error. This should only happen, if you manually changed the file.


Select Object

Select the object from a list of objects. Selection may be by a double click on the object name, of by selecting the object and clicking OK. This dialog pops up, when the choice of objects is not unique with the mouse, because several objects are close to the clicked position. It will also pop up, when the right mouse button is used, or a Move tool is active. In this case, the object will be highlighted (which may not covered by other objects) and a second try will select the object immediately.


Macro Comment
Edit Macro Comment

This comment is saved with the macro and shows up when the macro is loaded.


Edit Comment

The comment is saved with the construction. It will also pop up, when a construction is loaded. In this dialog, you may edit the comment. As in all Windows applications, selection by dragging the mouse works. Use Control-X to cut a selected text to the clipboard, Control-C to copy it to the clipboard, and Control-V to paste text from the clipboard.


Set Printer

Here, you can choose your printer and determine weather comments should be print below your construction. After this dialog, the setup dialog of your printer will pop up.


Set Grid

C.a.R. optionally displays a grid of vertical and horizontal lines, and the x- and y-axes. You can set the grid spacing here, and toggle the axes on or off. There is a fine and a coarse spacing. The computer will only draw 100 space lines in total. To turn the grid on or off, use the menu option or the corresponding key.


Registration

Enter your name and your key. Both must be entered verbally as in your registration information. Spaces do not count, but case does.


Register
How to register

At the moment, the only way to register is to send me cash or a check. Registration fee is 25 Deutsche Mark, or the equivalent of 30 DM in foreign currency. Send the check to

R. Grothmann

Ahornweg 5a

D-85117 Eitensheim

Germany

If you have E-Mail, send a mail to grothm@ku-eichstaett.de and you will get the name and key by email immediately after I got your check. Otherwise, you will get a letter with your key and code with snail mail.