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{\creatim\yr1996\mo10\dy17\hr12\min27}
{\revtim\yr1996\mo10\dy17\hr12\min27}
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{\footer \pard\plain \s242\qr\tqc\tx4252\tqr\tx8504 \f1\fs20\lang2057{\field{\*\fldinst PAGE}{\fldrslt}} }\pard\plain \f1\fs20\lang2057{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Contents}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Contents}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};Contents;}}
\pard \f1\fs20 {\b SISUKORD}
\par
\par {\b {\uldb GEOCON levaade}{\v GEOCON_levaade> main}}
\par 
\par {\b {\uldb Get acquainted with GEOCON}{\v Get_acquainted_with_GEOCON> main}}
\par   
\par {\b {\uldb Start and exit GEOCON}{\v Start_and_exit_GEOCON> main}}
\par   
\par {\b {\uldb Opening a problem}{\v Opening_a_problem> main}}
\par   {\uldb Open LSQ-Menu}{\v Open_LSQ_Menu> main}
\par  
\par {\b {\uldb Solving a construction problem}{\v Solving_a_construction_problem> main}}
\par   {\uldb Admitted Operators}{\v Admitted_Operators> main}
\par   {\uldb Entering a construction step}{\v Entering_a_construction_step> main}
\par   {\uldb Error messages}{\v Error_messages> main}  
\par   {\uldb Exit a problem}{\v Exit_a_problem> main}
\par
\par {\b {\uldb User protocol}{\v User_protocol> main}}
\par   {\uldb Open protocol}{\v Open_protocol> main}
\par   {\uldb Print protocol}{\v Print_protocol> main}
\par   {\uldb Remove protocol}{\v Remove_protocol> main}
\par
\par {\b {\uldb Appendix}{\v Appendix> main}}
\par
\par {\uldb CON-Operators}{\v CON_Operators> main}
\par     {\uldb point}{\v point> main}
\par     {\uldb pointon(Fig)}{\v pointon_Fig_> main}
\par     {\uldb scale(U,V,d)}{\v scale_U_V_d_> main}
\par     {\uldb f # g}{\v f___g> main}
\par     {\uldb point(Ray,Dist)}{\v point_Ray_Dist_> main}
\par     {\uldb center(U,V)}{\v center_U_V_> main}
\par     {\uldb prfl(M,U)}{\v prfl_M_U_> main}
\par     {\uldb orth(Point,Line)}{\v orth_Point_Line_> main}
\par     {\uldb par(Point,Line)}{\v par_Point_Line_> main}
\par     {\uldb par(U,V,d)}{\v par_U_V_d_> main}
\par     {\uldb pbs(U,V)}{\v pbs_U_V_> main}
\par     {\uldb ray(U,V)}{\v ray_U_V_> main}
\par     {\uldb leg(Ray,Alpha)}{\v leg_Ray_Alpha_> main}
\par     {\uldb circle(U,V)}{\v circle_U_V_> main}
\par     {\uldb circleR(Center,Rad)}{\v circleR_Center_Rad_> main}
\par     {\uldb thales(U,V)}{\v thales_U_V_> main}
\par     {\uldb circle(U,V,Alpha)}{\v circle_U_V_Alpha_> main}
\par     {\uldb dist(U,V)}{\v dist_U_V_> main}
\par     {\uldb angle(U,V,W)}{\v angle_U_V_W_> main}
\par
\par {\b {\uldb File handling}{\v File_handling> main}}
\par   {\uldb Working directory}{\v Working_directory> main @ GEOLOG.HLP}
\par   {\uldb Open LSQ-Menu}{\v Open_LSQ_Menu> main}
\par   {\uldb Cut picture}{\v Capturing_a_screen_region> main @ GEOLOG.HLP}
\par
\par {\b {\uldb User interface}{\v User_interface> main}}
\par   {\uldb Tool bar}{\v Tool_bar> main}
\par   {\uldb Windows}{\v Windows> main} 
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}GEOCON_levaade}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}GEOCON levaade}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};GEOCON levaade;}}
\pard \f1\fs20 {\b GEOCON levaade}
\par
\par The problem class supported by GEOCON confines to triangle and quadrilateral construction problems as they can be found in geometry textbooks for secondary schools - and ca be solved by the expert modules of GEOEXPERT. 
\par
\par A construction problem is defined by its {\b goal configuration} (i.e. the relations to be met by the constructed figure). 
\par
\par The goal configuration is represented by a plan figure and a set of relations. The plan figure represents the relations of {\i incidence}, {\i order} and {\i orientation}, the explicit given relations represent the metrical features of the goal configuration. In the definition of the goal configuration of a construction problem, only relations of seven types are admitted (see: {\uldb Structure of relations}{\v Structure_of_relations> main @ GEOEXP.HLP}).
\par
\par A {\b solution} of a construction problem is a {\uldb construction program}{\v Construction_program> main @ GEOLOG.HLP}. But not all of GEOLOG's system 
\par procedures are admitted as operators of GEOCON. Also user defined procedures and macros are excluded. On the other hand, in GEOCON some additional procedures are needed to serve as {\uldb geometric loci}{\v Geometric_Loci> main @ GEOEXP.HLP}.  
\par
\par After entering a program line, GEOCON analyzes the correctness of the step. The program line is rejected, if it does not conform with one of the {\uldb methods}{\v Methods> main @ GEOEXP.HLP}, which the construction expert of GEOCON could have applied in the current problem state. If the student can't find a correct program step, he can ask for help. GEOCON's help systems renders help on different levels. 
\par
\par
\par  
\par  
\par
\par
\par
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Get_acquainted_with_GEOCON}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Get acquainted with GEOCON}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};Get acquainted with GEOCON;}}
\pard \f1\fs20 {\b Get acquainted with GEOCON}
\par
\par Work on the {\uldb tutorial}{\v Tutorial> main @ GEOLOG.HLP},
\par use GEOCONS's {\uldb help file}{\v Help_file> main @ GEOLOG.HLP},
\par use {\uldb interactive help}{\v Interactive_help> main @ GEOLOG.HLP}.
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Start_and_exit_GEOCON}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Start and exit GEOCON}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};Start and exit GEOCON;Exit GEOLOG-WIN;}}
\pard \f1\fs20 {\b Start and exit GEOCON}
\par
\par Starting: GEOLOG-Win always opens with its component GEOLOG. 
\par
\par {\b 1. Starting}: Having started GEOLOG-WIN you get to GEOCON with the menu item GEOCON in menu System. With the same menu item you change to GEOCON from GEOEXPERT and GEOPROOF.
\par
\par {\b 2. Leaving}:
\par With the menu item {\b Exit} in  menu File, you leave GEOLOG-WIN.
\par
\par With the menu items of the menu {\b System}, you change to
\par - {\uldb GEOLOG}{\v Contents> main @ GEOLOG.HLP}
\par - {\uldb GEOEXPERT}{\v Contents> main @ GEOEXP.HLP}
\par - {\uldb GEOPROOF}{\v Contents> main @ GEOPRF.HLP}
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Opening_a_problem}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Opening a problem}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};CON-problem,Opening a problem;}}
\pard \f1\fs20 {\b Opening a problem}
\par
\par To open a {\uldb construction problem}{\v CON_problems> main @ GEOEXP.HLP}:
\par
\par {\b (1)} {\uldb Open the LSQ-Menu}{\v Open_LSQ_Menu> main},
\par   
\par {\b (2)} Click the problem to be opened.
\par
\par {\i Hint}: If you need the file names of the problems, press {\b F5}. Press this key once more, to hide the names again.
\par
\par {\i Results}:
\par - In the plan figure window, the plan figure of the problem is displayed.
\par - In the relations window, the relations of the goal configuration are listed. 
\par
\par {\b (3)} Click \{bmc Ops.bmp\}, to open a list box with all {\uldb Operators}{\v CON_Operators> main @ GEOEXP.HLP} listed, which are admitted for 
\par solving the problem ({\i see} {\uldb Admitted Operators}{\v Admitted_Operators> main}).
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Open_LSQ_Menu}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Open LSQ-Menu}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};LSQ,Open LSQ-Menu;}}
\pard \f1\fs20 {\b Open LSQ-Menu}
\par
\par To open the {\uldb LSQ-Menu}{\v LSQ_Menu> main @ GEOEXP.HLP} with the {\i last used} learning sequence:
\par {\b (1a)} Click \{bmc Lsq.bmp\}.
\par
\par {\i Result}: The LSQ-Menu opens with the last used learning sequence {\i or} Windows dialog for opening files opens. In the latter case go ahead with {\b (2)}.
\par
\par To open the LSW-Menu with a {\i new} learning sequence:
\par {\b (1b)} Click the menu item {\b Open LSQ-Menu} in menu {\b File} to open the Windows dialog for opening files.
\par
\par {\b (2)} Open a folder with CON-Problems and a file of file type {\i LSQ-CON-Problem}.
\par
\par {\b (3)} Double click the file.
\par
\par {\i Result}: The LSQ-Menu opens with the selected learning sequence.
\par
\par  
\par
\par
\par
\par  or if you want to open the LSQ-Menu with another learning sequence
\par
\par To open a learning sequence menu:
\par
\par (1) Open the file dialog by clicking the menu item Open LSQ in menu LSQ.
\par
\par (2) Select the file type
\par - LSQ-CON-Problem (*.lsk)to open a learning sequence with CON-problems.
\par - LSQ-PRF-Problem (*.lsb) to open a learning sequence with PRF-problems.
\par
\par (3) Open a folder with a file of the wanted LSQ type and open it by double clicking.
\par
\par Result: The LSQ window opens with the LSQ-Menu. 
\par
\par Hint: In the following, you can open the LSQ-Menu by clicking .
\par
\par Possible actions:
\par - Click any menu item, to open a problem (see Open problem).
\par - Click LUk (k=1,2,..) left in the line of learning unit LUk, to display the operators, with are admitted to solve the problems of the LU. Double click any of the listed operators to open its info page.
\par - Open a pop-up menu by clicking a menu item with the right mouse key (see LSQ Pop-up menu)
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Solving_a_construction_problem}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Solving a construction problem}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};Solving a construction problem;}}
\pard \f1\fs20 {\b Solving a construction problem}
\par
\par The solution of a {\uldb construction problem}{\v CON_problems> main @ GEOEXP.HLP} is a {\uldb construction program}{\v Construction_program> main @ GEOLOG.HLP} which meets the relations of the {\ul goal configuration}{\v Goal_configuration @ GEOEXP.HLP }. 
\par
\par The solution requires more than one step. In each construction step by applying an {\uldb admitted CON-Operator}{\v Admitted_CON_Operators> main @ GEOEXP.HLP} a program line is generated and an object added to the already constructed figure.
\par  
\par {\i See}
\par {\uldb Entering a construction step}{\v Entering_a_construction_step> main}
\par {\uldb Exit a problem}{\v Exit_a_problem> main}
\par
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Admitted_Operators}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Admitted Operators}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};CON-Oerators,Admitted Operators;}}
\pard \f1\fs20 {\b Admitted Operators}
\par
\par Maximal there are 19 construction {\uldb procedures}{\v Procedure> main @ GEOLOG.HLP} to solve construction problems. In this context they are called {\b operators}. But generally not {\i all} operators are admitted to solve a problem. Which operators are admitted depends on the learning unit from which the problem has been opened ({\i see} {\uldb LSQ-Menu}{\v LSQ_Menu> main @ GEOEXP.HLP}).
\par
\par To get acquainted with the operators admitted to solve the opened problem:
\par {\b (1)} Click \{bmc Ops.bmp\}, to get a list of all construction operators which are admitted to solve the opened construction problem.
\par
\par {\b (2)} Double click any operator in the list box, to open the info page of he theorem with detailed information.
\par
\par {\b (3)} Click the icon once more, to close the list box.
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Entering_a_construction_step}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Entering a construction step}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};CON-problem,Entering a construction step;}}
\pard \f1\fs20 {\b Entering a construction step}
\par
\par {\b Entering a program line}
\par Enter a construction step by either using the Construction menu or by sing the 
\par {\uldb Program editor}{\v Program_editor> main @ GEOLOG.HLP}.
\par
\par {\i {\b Hints}}:
\par {\b a)} After opening a problem from the LSQ-menu, the {\uldb construction menus}{\v construction_menu> main @ GEOLOG.HLP} include only 
\par those {\uldb operators}{\v CON_Operators> main} as menu items, which are admitted for solving the problem.
\par
\par {\b b)} Using a menu item for entering a program line, only {\i figures} (straight lines, rays and circles) and {\i measures} are named automatically. The names of {\i points} always have to be entered by the user.
\par
\par {\b c)} Program lines can't be entered in {\uldb quick mode}{\v Quick_mode> main @ GEOLOG.HLP}, with one exception: The scaling operator {\uldb scale(U,V,Dist)}{\v Scaling_measuring_of_length> main @ GEOLOG.HLP} must always be applied in quick mode, i.e. you have only to enter the single line scale(U,V,Dist).
\par This generates the {\i three} program lines
\par U = point
\par V = point
\par s(U,V,Dist).
\par
\par {\b Monitoring the construction step}
\par If GEOCON judges a program line as {\i faulty}, an error message is send and the step is canceled.
\par {\i See}: {\uldb Error messages}{\v Error_messages> main}
\par
\par {\b Help}
\par In each problem state you get hierarchical help by pressing the function key F1. The first level of help offers only some common hints. In the last level of help, GEOCON performs the step by itself. Learn details about GEOCON's help system by solving some problems.
\par  
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Error_messages}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Error messages}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};Error messages;}}
\pard \f1\fs20 {\b Error messages}
\par
\par Solving a construction problem with GEOCON, each step is monitored by the system. If GEOCON judges the step as faulty, it sends an error message and the step is automatically canceled.
\par  
\par {\b Measuring errors}
\par These can arise with all operators which require a number as measure of a length or an angle. These are the scaling operator scale(U,V,d), the operator point(ray,dist) and the four operators for locus construction: circleR(M,r), par(U,V,d), leg(ray,alpha) and circle(U,V,alpha). A measuring error is sent, if the operator can be applied, but not with the entered measure. The error may be a simple slip or occur if the measure has to be calculated from other measures. The system doesn't discern these cases.
\par
\par {\b Locus errors}
\par These can occur if a straight line, a ray or a circle is entered as a locus for a point to be constructed. Concerned are the operators:
\par - orth(U,g), par(U,g), par(U,V,d), pbs(U,V) to construct a straight line,
\par - ray(U,V), leg(ray,alpha) to construct a ray,
\par - circle(U,V), circleR(M,r), thales(U,V), circle(U,V,alpha) to construct a circle.
\par
\par A {\i locus error} is sent, if there is no point (in the plan figure) to which the constructed figure is a locus - and the error is not a measuring error.
\par
\par {\i Comment}: GEOCON always interprets an entered figure (straight line, ray or circle) as locus of a point occurring in the plan figure. Therefore it is not admitted, that points are constructed which don't belong to the plan figure.
\par  
\par {\b Method error}
\par These can occur if a program line for the construction of a point is entered. In following cases a {\i method error} is sent:
\par
\par P = f # g is entered, but the two loci f and g don't intersect,
\par
\par M = mp(U,V) is entered, but M is not center of the points U and V,
\par
\par P = ps(M,U) is entered, but P is not the result of reflecting the point U at the point M.
\par  
\par P = point(ray,r) is entered, but P is not a point of ray with distance r of the endpoint of ray - and the error is not a measuring error.
\par  
\par P = point is entered, but there is at least one locus to P or the {\uldb degree of freedom}{\v Degree_of_freedom> main @ GEOEXP.HLP} is surpassed by entering the line.
\par
\par P = pointon(f) is entered, but beside of f there is at least one further locus to P or the degree of freedom is surpassed by entering the line.
\par
\par scale(U,V,d) is entered, but the distance of the points U and V is not given and can't be calculated. 
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Exit_a_problem}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Exit a problem}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};Exit a problem;}}
\pard \f1\fs20 {\b Exit a problem}
\par
\par If you want to exit the problem solving process, click \{bmc ExitPrbl.bmp\}.
\par
\par {\i Results}: 
\par {\b a)} If the problem has not been solved completely, you are 
\par asked whether you really want to break off. Otherwise the quality of your solution is evaluated by the system with a score G between 0 and 100:
\par
\par {\b G = 100 * R/(R + F + H)}
\par
\par {\b R} = Number of correct steps
\par
\par {\b F} = Number of faulty steps
\par
\par {\b H} = Number of getting help
\par
\par {\b b)} If you open the LSQ-Menu again, the score is plotted to the menu item. By this way, you always know which problems you have solved already. If the solution of the problem has been broken off, the string $$$ is plotted to the menu item.
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}User_protocol}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}User protocol}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};User protocol;}}
\pard \f1\fs20 {\b User protocol}
\par
\par If a user starts to solve the problems of a learning sequence, after finishing the first problem the user protocol is created as a file in the current working directory. In the user protocol data concerning the users solutions of the problems are gathered. The name of the user protocol differs from the name of the LSQ only by the extension. 
\par
\par Because the name of the user can't be identified from the user protocol, different users always should use different {\uldb working directories}{\v Working_directory> main @ GEOLOG.HLP}.
\par
\par {\i {\b Following dates are saved in a user protocol:}}
\par {\b 1. Evaluation of the solved problems}
\par To each solved problem is recorded:
\par - Date and time of solving the problem,
\par - Learning unit and name of the problem,
\par - Number R of correctly performed steps,
\par - Number F of faulty performed steps,
\par - Number H of asking for help ,
\par - Quality G of the solution in percent: G = R*100/(R+F+H),
\par - Maximal score Pmax of the problem,
\par - Attained score Peff by the user: Peff = Pmax * G.
\par
\par {\b 2. Competence of applying operators}
\par To each operator (CON-operator or theorem) which has been used in any solution of a problem, the following data are recorded:
\par
\par - Total sum R of correct operator applications,
\par - Total sum F of faulty operator applications,
\par - Total sum H of asking for help in applying the operator,
\par - Quality G of applying the operator: G = R*100/(R+F+H).
\par
\par The quality G is a mean value over all solved problems. It does not measure the quality of the present operator application.
\par
\par {\b 3. Frequency of bugs}
\par To each occurring bug its frequency is recorded.
\par
\par {\b 4. Scoring of the users performance if a test sequence has been worked through}
\par
\par Recorded are:
\par - The total score Seff of the user,
\par - the total sum Smax of the scores of problems in the LSQ,
\par - the performance L in percent: L = 100*Seff/Smax.
\par  
\par
\par {\i See also:}
\par {\uldb Open protocol}{\v Open_protocol> main}
\par {\uldb Print protocol}{\v Print_protocol> main}
\par {\uldb Delete protocol}{\v Open_protocol> main}
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Open_protocol}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Open protocol}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};User protocol,Open protocol;}}
\pard \f1\fs20 {\b Open protocol}
\par
\par {\i Result}: Window's file menu opens the folder of the working directory with file type {\b User protocol}.
\par
\par {\b (2)} Double click the file name of a user protocol.
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Print_protocol}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Print protocol}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};User protocol,Print protocol;}}
\pard \f1\fs20 {\b Print protocol}
\par
\par To {\b print} a {\uldb user protocol}{\v User_protocol> main}:
\par
\par {\b (1)} Click the menu item {\b Open protocol} in menu {\b Protocol}.
\par
\par {\i Result}: Window's file menu opens the folder of the working directory with file type {\b User protocol}.
\par
\par {\b (2)} Double click the file name of the protocol.
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Remove_protocol}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Remove protocol}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};Remove protocol;User protocol,Remove protocol;}}
\pard \f1\fs20 {\b Remove protocol}
\par
\par To {\b remove} a {\uldb user protocol}{\v User_protocol> main}:
\par
\par {\b (1)} Click the menu item {\b Open protocol} in menu {\b Protocol}.
\par
\par {\i Result}: Window's file dialog opens with the folder of the working directory and file type {\b User protocol}.
\par
\par {\b (2)} Click the file name of the user protocol with the {\i right} mouse key to open a pop-up menu and delete the file by clicking the menu item {\b Delete}.
\par  
\par  
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Appendix}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Appendix}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};Appendix;}}
\pard \f1\fs20 {\b Appendix}
\par
\par {\uldb User interface}{\v User_interface> main}[b]
\par   
\par {\uldb File handling}{\v File_handling> main}[b]
\par    
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}CON_Operators}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}CON-Operators}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};CON-Operators;}}
\pard \f1\fs20 {\b CON-Operators}
\par
\par {\b Operators for entering or constructing points}
\par {\i See also}: {\uldb Methods}{\v Methods> main @ GEOEXP.HLP}
\par {\uldb point}{\v point> main}
\par {\uldb pointon(Fig)}{\v pointon_Fig_> main}
\par {\uldb scale(U,V,d)}{\v scale_U_V_d_> main}
\par {\uldb f # g}{\v f___g> main}
\par {\uldb point(Ray,Dist)}{\v point_Ray_Dist_> main}
\par {\uldb center(U,V)}{\v center_U_V_> main}
\par {\uldb prfl(M,U)}{\v prfl_M_U_> main}
\par
\par {\b Operators for generating a locus line}
\par {\i See also}: {\uldb Geometric loci}{\v Geometric_loci> main @ GEOEXP.HLP}
\par
\par {\b Straight line as locus of a point} 
\par {\i Hint}: The operator {\b line(U,V)} passing the points U and V is dispensable as a locus, because in each situation an alternate is either ray(U,V) or ray(V,U). 
\par {\uldb orth(Point,Line)}{\v orth_Point_Line_> main}
\par {\uldb par(Point,Line)}{\v par_Point_Line_> main}
\par {\uldb par(U,V,d)}{\v par_U_V_d_> main}
\par {\uldb pbs(U,V)}{\v pbs_U_V_> main}
\par
\par {\b Ray as locus of a point}
\par {\uldb ray(U,V)}{\v ray_U_V_> main}
\par {\uldb leg(Ray,Alpha)}{\v leg_Ray_Alpha_> main}
\par
\par {\b Circle as locus of a point}
\par {\uldb circle(U,V)}{\v circle_U_V_> main}
\par {\uldb circleR(Center,Rad)}{\v circleR_Center_Rad_> main}
\par {\uldb thales(U,V)}{\v thales_U_V_> main}
\par {\uldb circle(U,V,Alpha)}{\v circle_U_V_Alpha_> main}
\par
\par {\b Operators for measuring}
\par {\uldb dist(U,V)}{\v dist_U_V_> main}
\par {\uldb angle(U,V,W)}{\v angle_U_V_W_> main}
\par
\par {\b Procedures for line segments and polygons}
\par {\i Hint}: These procedures don't belong to the CON-Operators. They are not needed for a construction and serve only the transparency of the pictorial representation.
\par {\uldb s(U,V)}{\v Line_segment> main @ GEOLOG.HLP}
\par {\uldb poly(A..Z)}{\v Polygon> main @ GEOLOG.HLP}
\par
\par
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}point}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}point}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};point;}}
\pard \f1\fs20 {\b point}
\par
\par {\b Program line}: P = point
\par
\par {\b Function}: Entering a point arbitrarily.
\par  
\par {\b Error messages}:
\par - There exists a locus of P.
\par - P may not be positioned arbitrarily; try to construct another point.
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}pointon_Fig_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}pointon(Fig)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};pointon(Fig);}}
\pard \f1\fs20 {\b pointon(Fig)}
\par
\par {\b Program line}: P = pointon(f)
\par
\par {\b Function}: Entering a point arbitrarily on a given figure.
\par
\par {\b Error messages}:
\par - f is not a locus of P.
\par - f is indeed locus of P, but you can find a second locus of P.
\par  
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}scale_U_V_d_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}scale(U,V,d)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};scale(U,V,d);}}
\pard \f1\fs20 {\b scale(U,V,d)}
\par
\par {\b Program line}: scale(U,V,d)
\par
\par {\b Function}: Entering of two points U and V, drawing the line segment s(U,V) and scaling the measurement of length to UV = d.
\par  
\par {\b Hints}:
\par - The operator can only be used in the first programming step. 
\par - In GEOCON the operator can only be used in quick-modus. It produces the three program lines:
\par U = point
\par V = point
\par scale(U,V,d)
\par
\par {\b Error messages}:
\par - Line segment UV unsuitable as basic line segment. Its length is neither given nor may it be calculated.
\par - Line segment UV has not length d.
\par  
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}f___g}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}f # g}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};f # g;}}
\pard \f1\fs20 {\b f # g}
\par
\par {\b Program line}: P = f # g
\par
\par {\b Function}: Drawing P as intersection of loci f and g.
\par
\par {\b Error message}:
\par - P is not point of intersection of f and g.
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}point_Ray_Dist_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}point(Ray,Dist)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};point(Ray,Dist);}}
\pard \f1\fs20 {\b point(Ray,Dist)}
\par
\par Program line: P = point(h,d)
\par
\par {\b Function}: Drawing P as point on ray h with distance d to the endpoint of h.
\par
\par {\b Error message}:
\par - P is not a point of ray h with given distance to the endpoint.
\par - P is a point of ray h, but not with distance d to the endpoint.
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}center_U_V_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}center(U,V)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};center(U,V);}}
\pard \f1\fs20 {\b center(U,V)}
\par
\par {\b Program line}: P = center(U,V)
\par
\par {\b Function}: Drawing P as center of points U and V.
\par
\par {\b Error message}:
\par - P is not center of line segment s(A,B).
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}prfl_M_U_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}prfl(M,U)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};prfl(M,U);}}
\pard \f1\fs20 {\b prfl(M,U)}
\par
\par {\b Program line}: P = prfl(U,V)
\par
\par {\b Function}: Drawing P by reflecting U on center M.
\par
\par {\b Error message}:
\par - One does not get P by reflecting Q on center M.
\par  
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}orth_Point_Line_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}orth(Point,Line)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};orth(Point,Line);}}
\pard \f1\fs20 {\b orth(Point,Line)}
\par
\par {\b Program line}: f = orth(U,g)
\par
\par {\b Function}: Draws the perpendicular to straight line g passing point U. 
\par
\par {\b Attribute as a locus}: orth(U,g) is locus of all points P for which the line(P,U) is perpendicular to g.
\par
\par {\b Error message}:
\par - f is not locus of a point to be constructed.
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}par_Point_Line_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}par(Point,Line)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};par(Point,Line);}}
\pard \f1\fs20 {\b par(Point,Line)}
\par
\par {\b Program line}: f = par(U,g)
\par
\par {\b Function}: Draws the parallel to straight line g passing point U.  
\par
\par {\b Attribute as a locus}: par(U,g) is locus of all points P for which the line(P,U) is parallel to g.
\par  
\par {\b Error message}:
\par - f is not locus of a point to be constructed.
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}par_U_V_d_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}par(U,V,d)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};par(U,V,d);}}
\pard \f1\fs20 {\b par(U,V,d)}
\par
\par {\b Program line}: f = par(U,V,d)
\par
\par {\b Function}: Draws to the left of ray(U,V) the parallel to line(U,V) with distance d.
\par
\par {\b Attribute as a locus}: par_abst(U,V,d) is locus of all points P on the left side of ray(U,V) with distance d to line(U,V).
\par
\par {\b Error messages}:
\par - f is not locus of a point to be constructed. 
\par - f is not locus of a point to be constructed. A wrong value for the length of d has been entered.
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}pbs_U_V_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}pbs(U,V)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};pbs(U,V);}}
\pard \f1\fs20 {\b pbs(U,V)}
\par
\par {\b Program line}: f = pbs(U,V)
\par
\par {\b Function}: Draws the perpendicular bisector to points U and V.
\par
\par {\b Attribute as a locus}: pbs(U,V) is locus of all points P, for which PU = PV.
\par
\par {\b Error message}: 
\par - f is not locus of a point to be constructed.
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}ray_U_V_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}ray(U,V)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};ray(U,V);}}
\pard \f1\fs20 {\b ray(U,V)}
\par
\par {\b Program line}: f = ray(U,V)
\par
\par {\b Function}: Draws the ray with endpoint U passing V.
\par
\par {\b Attribute as a locus}: ray(U,V) is locus of all points P, which are collinear with U and V and for which P between U and V or V between U and P holds. 
\par
\par {\b Error message}: 
\par - f is not locus of a point to be constructed.
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}leg_Ray_Alpha_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}leg(Ray,Alpha)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};leg(Ray,Alpha);}}
\pard \f1\fs20 {\b leg(Ray,Alpha)}
\par
\par {\b Program line}: f = leg(h,alpha)
\par
\par {\b Function}: Draws the ray which includes the angle alpha with ray h and is situated
\par - left of h, if alpha > 0,
\par - right of h, if alpha < 0.
\par
\par {\b Attribute as a locus}: ray(h,alpha)is locus of all points P, for which 
\par - angle(P,A,B) = alpha holds, if alpha > 0,
\par - angle(P,A,B) = - alpha holds, if alpha < 0.
\par
\par {\b Error message}:
\par - f is not locus of a point to be constructed. A wrong value for the measure of alpha has been entered.
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}circle_U_V_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}circle(U,V)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};circle(U,V);}}
\pard \f1\fs20 {\b circle(U,V)}
\par
\par {\b Program line}: f = circle(U,V)
\par
\par {\b Function}: Draws the circle with center U and passing V.
\par
\par {\b Attribute as a locus}: circle(U,V) is locus of all points P, for which UP = UV holds.
\par
\par {\b Error message}:
\par - f is not locus of a point to be constructed.
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}circleR_Center_Rad_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}circleR(Center,Rad)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};circleR(Center,Rad);}}
\pard \f1\fs20 {\b circleR(Center,Rad)}
\par
\par {\b Program line}: f = circleR(M,r)
\par
\par {\b Function}: Draws the circle with center M and radius r.
\par
\par {\b Attribute as a locus}: circleR(M,r) is locus of all points P, for which MP = r holds.
\par
\par {\b Error messages}:
\par - f is not locus of a point to be constructed.
\par - f is not locus of a point to be constructed. A wrong value for the length of d has been entered.
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}thales_U_V_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}thales(U,V)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};thales(U,V);}}
\pard \f1\fs20 {\b thales(U,V)}
\par
\par {\b Program line}: f = thales(U,V)
\par
\par {\b Function}: Draws the circle which has the line segment s(U,V) as diameter. 
\par
\par {\b Attribute as a locus}: thales(U,V) is locus of all points P, for which line(P,U) is perpendicular to line(P,V).
\par
\par {\b Error message}:
\par - f is not locus of a point to be constructed. 
\par  
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}circle_U_V_Alpha_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}circle(U,V,Alpha)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};circle(U,V,Alpha);}}
\pard \f1\fs20 {\b circle(U,V,Alpha)}
\par
\par {\b Program line}: f = circle(U,V,alpha)
\par
\par {\b Function}: Draws the circle with s(U,V) as cord and with inscribed angle alpha to the left of ray(U,V). 
\par  
\par {\b Attribute as a locus}: The circular arc of circle(U,V,alpha) to the left of ray(U,V) is locus of all points P, for which angle(U,V,P) = alpha holds. 
\par
\par Error messages:
\par - f is not locus of a point to be constructed.
\par - f is not locus of a point to be constructed. A wrong value for the measure of alpha has been entered.
\par
\par
\par
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}dist_U_V_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}dist(U,V)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};dist(U,V);}}
\pard \f1\fs20 {\b dist(U,V)}
\par
\par {\b Program line}: g = dist(U,V)
\par
\par {\b Function}: Generating the number g by measuring the distance of the points U and V.
\par
\par For some construction problems it is necessary or convenient to enter a program line of the form 
\par a = circle(M,dist(U,V)).
\par This line can be replaced by the two lines:
\par r = dist(U,V)
\par a = circle(M,r).
\par  
\par {\b Error message}: -
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}angle_U_V_W_}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}angle(U,V,W)}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};angle(U,V,W);}}
\pard \f1\fs20 {\b angle(U,V,W)}
\par
\par {\b Program line}: g = angle(U,V,W)
\par
\par {\b Function}: Generating the magnitude g by measuring the angle <UVW with V as vertex and ray(V,U) and ray(V,W) as sides.
\par
\par For some construction problems it is necessary or convenient to enter a program line of the form 
\par a = leg(h,angle(U,V,W)). 
\par This line can be replaced by the two lines:
\par w = angle(U,V,W)
\par a = leg(h,w)
\par  
\par {\b Error message}: -
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}File_handling}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}File handling}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};File handling;}}
\pard \f1\fs20 {\b File handling}
\par
\par {\uldb Working directory}{\v Working_directory> main @ GEOLOG.HLP}
\par {\uldb Open LSQ-Menu}{\v Open_LSQ_Menu> main}
\par {\uldb Cut picture}{\v Capturing_a_screen_region> main @ GEOLOG.HLP}
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}User_interface}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}User interface}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};User interface;}}
\pard \f1\fs20 {\b User interface}
\par
\par {\uldb Tool bar}{\v Tool_bar> main}
\par {\uldb Windows}{\v Windows> main}
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Tool_bar}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Tool bar}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};Tool bar;}}
\pard \f1\fs20 {\b Tool bar}
\par
\par \{bmc ClearAll.bmp\} {\uldb Clear all}{\v Clear_all> main @ GEOEXP.HLP}
\par \{bmc Lsq.bmp\} {\uldb Select problem}{\v Opening_a_problem> main} 
\par \{bmc ExitPrbl.bmp\} {\uldb Exit-Problem}{\v Exit_a_problem> main}
\par \{bmc Delpict.bmp\} {\uldb Delete construction}{\v Delete_construction> main @ GEOLOG.HLP}
\par \{bmc ProgEdit.bmp\} {\uldb Program editor}{\v Program_editor> main @ GEOLOG.HLP}
\par \{bmc UndoLast.bmp\} {\uldb Delete last Step}{\v Delete_program_steps> main @ GEOLOG.HLP}
\par
\par {\i Construction Menu}
\par \{bmc Points.bmp\} {\uldb Points}{\v System_procedures> main @ GEOLOG.HLP}
\par \{bmc Lines.bmp\} {\uldb Straight lines}{\v System_procedures> main @ GEOLOG.HLP}
\par \{bmc Rays.bmp\} {\uldb Rays}{\v System_procedures> main @ GEOLOG.HLP}
\par \{bmc Circles.bmp\} {\uldb Circles}{\v System_procedures> main @ GEOLOG.HLP}
\par \{bmc Segment.bmp\} {\uldb Line Segments}{\v System_procedures> main @ GEOLOG.HLP}
\par \{bmc Numbers.bmp\} {\uldb Numbers}{\v System_procedures> main @ GEOLOG.HLP}
\par
\par \{bmc Repeat.bmp\} {\uldb Repeat last operation}{\v Repeat_last_operation> main @ GEOLOG.HLP}
\par \{bmc Ops.bmp\} {\uldb Admitted CON-operators}{\v Admitted_CON_Operators> main @ GEOEXP.HLP}
\par \{bmc Info1.bmp\} {\uldb Interactive help}{\v Interactive_help> main @ GEOLOG.HLP}
\par \{bmc Help.bmp\} {\uldb Help}{\v Help_file> main @ GEOLOG.HLP}
\par\pard\plain \page
{\up6 #{\footnote \pard\plain \s245 \lang2057 {\up6 #}Windows}}{\up6 ${\footnote \pard\plain \s245 \lang2057 {\up6 $}Windows}}{\up6 K{\footnote \pard\plain \s245 \lang2057 {\up6 K};Windows,Rearrange windows;}}
\pard \f1\fs20 {\b Windows}
\par
\par The {\b Drawing window} serves to display the figural representation of a construction 
\par
\par The {\b Number window} (topmost line of the drawing window) serves to display the numeric values of measures and terms.
\par
\par The {\b Program window} serves to edit and display a construction program. The window is opened and closed by clicking \{bmc ProgEdit.bmp\}.
\par
\par The {\b Plan figure window} serves to display the plan figure of a CON-problem.
\par
\par The {\b Relations window} serves to display the relations which must hold for the constructed figure.
\par\pard\plain \page
}