GRACE - a graphical ruler and compass editor
GRACE is a Java applet
that allows the student to specify constructions and their associated
proofs interactively.
GRACE constructions
Some of the main features of the construction editor are:
- Interactive creation of ruler and compass
constructions using the mouse
- Dynamic modification of construction inputs using dragging
- Naming and composition of constructions
- Automatic creation of an associated text representation
GRACE includes most of the dynamic construction capabilities
available in commercial software such to Geometer's SketchPad,
but also includes proof capabilities that are not found in such
software.
GRACE proofs
Some of the main features of the proof system are:
- Graphical display of expressions involving lengths and angles
- Linear constraints involving lengths and angles
- Use of axioms to generate new constraints
- Automatic simplification of constraints
The proof capabilities of GRACE differ from
other proof construction systems in that the student
does not need an understanding of logic.
Proofs are expressed solely in terms of linear algebra constraints
generated by applying axioms of Euclidean geometry.
Meta-goals of this project
The growth of the Internet makes possible an exciting alternative to
the centralized educational system currently in place
in the United States. This new communication technology
frees the student from an educational system tied
to a specific geographic domain. Via the Internet, parents and
students have access to a wide range of educational material
Our goal is to develop quality educational materials for mathematics
and distribute it via the Internet to interested students.
The rapid improvement in computing and communication technology
makes achieving this goal a challenge. One defect in previous
decentralized approaches (such as correspondence courses) was the
lack of significant interactive material. The use of video and
CD-rom technology has remedied this problem to some extent.
However, these technologies do not fully harness the power
of the computer.
The advent of Java makes it possible to deliver fully interactive
computer programs at the click of a button. We intend to harness
this power and create a math curriculum that has at its core
a series of computational environments that allow the student
to explore mathematics interactively. To demonstrate this
idea, we are developing this interactive course in high school
geometry.
Investigators and Other Links
This project is the work of several faculty members in the
Rice Computer Science Department. Each has children and is interested
in taking concrete steps to improve the state of math education
in the United States. They are:
Aaron Hertzmann
did the initial implementation of GRACE in Java. He
entered the NYU CS graduate program in the Fall of 96.
Known Bugs and Java compatibility
Known bugs:
- Selection boxes don't always appear around an expression when it
is selected.
- The library parser does not check if output constraints depend
on intermediate points.
- Some computations may be numerically unstable.
- The pictures will not be accurate when one zooms very far away.
Java programs are supposed to run the same on every computer. In
practice, we have noticed that different browsers on different
computers may give considerably different results. We have run GRACE
successfully on the following systems:
- SunOS 4.1.3 -- Netscape 2.02, Netscape 3.0b7
- Solaris 2.4 -- Netscape 2.02, Netscape 3.0,
HotJava 1.0 preBeta 1
- Irix 5.3 -- Netscape 2.02, Netscape 3.0, Netscape 4.03.
(A long
list of warning messages may appear when the applet is first
started. These can be ignored.)
- Macintosh (680x0 and PowerMac) -- Netscape 2.02,
Netscape 3.0b7
- Windows 95 -- Internet Explorer 3.0, Netscape 3.0
GRACE did not appear to work on some RedHat Linux Java implementations.
Future Work
(To be written.)
Comments and Suggestions
The contact person for GRACE is Joe Warren,
jwarren@cs.rice.edu.
Other links
Back to the GRACE main page