What is GCLC?
GCLC (from "Geometry Constructions->LaTeX converter") is a tool
for visualizing and teaching geometry, and for producing mathematical illustrations.
Its basic purpose is converting descriptions of mathematical objects (written in
the GCL language) into digital figures. GCLC provides easy-to-use support for
many geometrical constructions, isometric transformations, conics, and
parametric curves. The basic idea behind GCLC is that constructions are formal
procedures, rather than drawings. Thus, in GCLC,
producing mathematical illustrations is based on "describing figures" rather
than of "drawing figures". This approach stresses the fact that geometrical
constructions are abstract, formal procedures and not figures. A figure can be
generated on the basis of abstract description, in the Cartesian model of a
plane. These digital figures can be displayed and exported to LaTeX files (or
some other format).
WinGCLC is the Windows version of GCLC and provides a range of additional
7.0/WinGCLC 2007 ((c) 1996-2007 Predrag Janicic); command line version (GCLC) and Windows version (WinGCLC)
with graphical, multi-document interface, support for
animations, traces, export to bitmaps etc. The archive includes manual files,
sample files, LaTeX package gclc.sty, additonal tools etc.
(available since 28.01.2007)
7.0 ((c) 1996-2007 Predrag Janicic);
command line version (GCLC) manual files, sample files, LaTeX package gclc.sty,
(available since 28.01.2007)
Author: GCLC/WinGCLC is
being developed at the Faculty of Mathematics, University of Belgrade, by
Janicic and, in some parts, by Predrag Janicic and his coauthors:
Ivan Trajkovic (University of Belgrade, Serbia)
- coauthor of the graphical interface for WinGCLC;
prof. Pedro Quaresma (University of Coimbra, Portugal) -
coauthor of the theorem prover built into GCLC;
prof. Konrad Polthier and Klaus Hildebrandt (Technical University,
Berlin, Germany) - coauthors of JavaView -> GCLC converter).
prof. Pedro Quaresma (University of Coimbra,
Portugal), Jelena Tomasevic (University of Belgrade, Serbia), Milena
Vujosevic-Janicic (University of Belgrade, Serbia) - coauthors of support for
Scope: Although GCLC was initially built as a tool for converting formal descriptions
of geometric constructions into LaTeX form, now it is much more than that. For
instance, there is support for symbolic expressions, for drawing parametric
curves, for program loops, etc; a built-in theorem prover can automatically
prove a range of complex theorems; the Windows graphical interface makes GCLC a
dynamic geometry tool for teaching geometry, and other mathematical fields as well.
The main purposes of GCLC/WinGCLC:
producing digital mathematical illustrations
of high quality;
use in teaching geometry;
use in studying geometry and as a research tool.
The main features of GCLC/WinGCLC:
support for a range of elementary and
isometric transformations, and other geometrical devices;
support for symbolic expressions, second order curves,
parametric curves, while-loops etc;
user-friendly interface, interactive work, animations, tracing points, watch window ("geometry calculator''), and other
easy drawing of trees;
built-in theorem prover, capable of proving many complex
theorems (in traditional geometry style);
very simple, very easy to use, very small in size;
export of high quality figures into LaTeX, bitmap,
EPS (Encapsualted PostScript), SVG (Scalable Vector Graphics) format;
command line versions for DOS/Windows and Linux and the
MS Windows version;
notice: GCLC/WinGCLC is copyrighted and
cannot be used in commercial purposes. However, you are free to use it in
teaching, studying research and in producing figures and digital illustrations for
If you download and use GCLC package, please let me know by sending an e-mail to
(Predrag Janicic); we
will put you on the GCLC mailing list and inform you about new releases of GCLC/WinGCLC.
Please send us your comments and suggestions to
feedback would be very much appreciated and would help in improving the
future releases of GCLC.
If you used GCLC for producing figures for your
book or a paper, we would be happy to hear about that and to get a copy.
Please send us your GCLC gems and we
will put them on this page.
History: GCLC/WinGCLC programs had several releases since 1996. and they have
been used for producing digital illustrations for a number of books
and journal volumes, and in a number of different courses.
What others said about GCLC/WinGCLC: "... program WinGCLC ... is a very useful, impressive professional
academic geometry program.'' (from an anonymous review for "Teaching
Mathematics and its Applications'')
More on the background of GCLC/WinGCLC can be found in:
P.Janicic and I. Trajkovic: WinGCLC --- a Workbench for Formally
Describing Figures. In Proceedings of the 18th spring conference on
Computer graphics (SCCG 2003), pages 251--256, Budmerice, Slovakia, April,
24-26 2003. ACM Press, New York, USA.
M.Djoric and P.Janicic. Constructions, instructions, interactions. Teaching
Mathematics and its Applications, 23(2):69--88, 2004.
P. Quaresma and P. Janicic. Framework
for the Constructive Geometry. Technical Report TR2006/001, Center for
Informatics and Systems of the University of Coimbra, 2006.
P. Quaresma and P. Janicic. Integrating
dynamic geometry software, deduction systems, and theorem repositories. In J.
Borwein and W. Farmer, editors, Mathematical Knowledge Management (MKM-2006),
volume 4108 of Lecture Notes in Arti cial Intelligence, pages 280-294.
P. Janicic and P. Quaresma. System
description: GCLCprover + GeoThms. In U. Furbach and N. Shankar, editors,
International Joint Conference on Automated Reasoning (IJCAR-2006), volume
4130 of Lecture Notes in Artificial Intelligence, pages 145-150. Springer-Verlag,
P. Janicic. GCLC - A Tool for
Constructive Euclidean Geometry and More than That. In N. Takayama, A.
Iglesias, and J. Gutierrez, editors, Proceedings of International Congress of
Mathematical Software (ICMS 2006), volume 4151 of Lecture Notes in Computer
Science, pages 58-73. Springer-Verlag, 2006.
I am grateful to
Prof. Mirjana Djoric for the initial discussion
which led to the first version of GCLC (1996);
Prof. Neda Bokan and other members of the Group for
geometry, education and visualization with applications (mostly based at the
Faculty of Mathematics, University of Belgrade) for their invaluable support in
developing the WinGCLC package (2003);
Ivan Trajkovic, the main author of the graphical
interface in WinGCLC (2003);
DAAD (Germany) for funding my visit to Konrad
Polthier's group at Mathematical Institute of TU Berlin (2003), which I used for
making a JavaView->GCLC converter. I also thank Konrad Polthier and Klaus
Hildebrandt for their hospitality and their collaboration in developing this
CIM/CISUC (University of Coimbra) for funding my
visit to the Department of Mathematics, University of Coimbra (2005), which I
used for developing the geometry theorem prover built into GCLC. I also thank
prof. Pedro Quaresma for his warm hospitality and his collaboration in
developing this prover;
Prof. Pedro Quaresma (University of Coimbra), Jelena Tomasevic,
and Milena Vujosevic-Janicic, coauthors of the xml support for GCLC (2006);
Buchberger (RISC, University of Linz), for kindly inviting me to visit RISC
and to present GCLC there (2006).
James Fry (New Albany, Indiana, USA) for careful
revision of the GCLC/WinGCLC manual file and many useful insights and comments
Aleksandar Samardzic for his help in making Linux
release of GCLC (2003/2005);
Colleagues which gave contributions and suggestions
in earlier stages of development of WinGCLC: Nenad Dedic, Milos Utvic, Nikola
Begovic, Ivan Elcic, Jelena Grmusa, Aleksandra Nenadic, Marijana Lukic, Goran
Terzic, Milica Labus, Srdjan Vukmirovic, and Aleksandar Gogic (1999/2003);
Konrad Polthier (TU Berlin), Zach (Temple
University, USA), Vladimir Baltic (University of Belgrade), Hristos Bitos
(Greece), Aleksandar Gogic (DTA, Belgrade), Bob Schumacher (Cedarville
University, Ohio, USA), Biljana Radovanovic (University of Belgrade) for useful feedback and suggestions on different versions
All GCLC/WinGCLC users for their
support, feedback and suggestions.