Geometry Expressions is an Interactive Symbolic Geometry System.

Geometry Expressions draws figures that can be defined by either Symbolic Constraints or numeric locations. Calculations can be made from these constraints and are presented numerically and also symbolically as mathematical expressions. All of the usual constructions are available, along with powerful new symbolic constraints.

Geometry Expressions can be used as a stand-alone program or in conjunction with your favorite (computer) algebra system (CAS)

Computer algebra system

A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...

 via MathML

MathML

Mathematical Markup Language is an application of XML for describing mathematical notations and capturing both its structure and content. It aims at integrating mathematical formulae into World Wide Web pages and other documents...

 input and output. Expressions and Calculations can also be copied and pasted into the following CAS systems: Derive, Maple

Maple (software)

Maple is a general-purpose commercial computer algebra system. It was first developed in 1980 by the Symbolic Computation Group at the University of Waterloo in Waterloo, Ontario, Canada....

, Mathematica

Mathematica

Mathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing...

, Maxima, MuPAD

MuPAD

MuPAD is a computer algebra system . Originally developed by the MuPAD research group at the University of Paderborn, Germany, development was taken over by the company SciFace Software GmbH & Co...

, or Ti-Nspire. This allows for convenient incorporation of Geometry Expressions into other math-related projects.

Drawing Shapes

You can draw and constrain the following objects by using the icons in the Draw tool panel:

• Points
• Line Segments
• Infinite Lines
• Vectors
• Polygons
• Circles
• Conics
  Conic section
  In mathematics, a conic section is a curve obtained by intersecting a cone with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2...
  
  :
  • Ellipse
  • Parabola
  • Hyperbola
• Arcs (on circles and conics)
• "N-gons
  Regular polygon
  A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
  
  "
• Curve Approximations
• Functions

The Draw tool panel also inserts text, pictures and expressions.

Constraints

You can make the following constrains by using the icons in the Constrain (Input) tool panel:

• Length/Distance
• Radius
• Perpendicular
• Angle
• Direction
• Slope
• Coordinates
• Coefficients
• Tangent
• Incident
• Congruent
• Parallel
• Implicit Equation
• Point Proportional along curve

You can only make these constraints on the appropriate objects. For example, you can't constrain a line segment's radius. The software automatically displays only the logical options for the item(s) selected to simplify the process for the user.

Constructions

You can construct a variety of objects in Geometry Expressions. Constructions differ from constraints because they create more objects while constraints change the positioning of existing objects. The following constructions are available from the Construct tool panel:

• Midpoint
• Intersection
• Perpendicular

manikanta

• Angle Bisector
• Parallel
• Perpendicular
• Tangent
• Polygon (this is especially useful because it can include arcs)
• Transformations:
  • Reflection
  • Translation
  • Rotation
• Dilation (scaling)
  Scaling (geometry)
  In Euclidean geometry, uniform scaling is a linear transformation that enlarges or shrinks objects by a scale factor that is the same in all directions. The result of uniform scaling is similar to the original...
  
  
• Locus
  Locus (mathematics)
  In geometry, a locus is a collection of points which share a property. For example a circle may be defined as the locus of points in a plane at a fixed distance from a given point....
  
  
• Trace (of locus, curve, etc. along a proportional point)

As with constraints, you can only make these constructions on the appropriate objects. For example, you can't construct a tangent to a line segment. Again, the software automatically displays only the logical options for the item(s) selected to simplify the process for the user.

Calculations

You can make many of the same calculations as the constraints, with the addition of things like area and perimeter. Calculations can be made in both symbolic and real notation so when you use variables you calculation can be in terms of those variables or a decimal of the numbers represented by the variables. When not using variables, symbolic calculations give an exact output and real calculations give an approximate output. Here is a complete list of the available calculations:

• Length/Distance
• Radius
• Angle
• Direction
• Slope
• Coordinates
• Coefficients
• Area
• Perimeter
• Parametric Equation
  Parametric equation
  In mathematics, parametric equation is a method of defining a relation using parameters. A simple kinematic example is when one uses a time parameter to determine the position, velocity, and other information about a body in motion....
  
  
• Implicit Equation

Like with the other features, calculations these can be made only on the logical objects, so the area of a line cannot be calculated.

Variables

When constraints are made symbolically, Geometry Expressions can drag or even animate variables that are incorporated in the constraints. Functions can also be input symbolically in constraints, and then changed from the variables tool panel.

Other

There is also an annotation feature and a Symbols tool panel which inserts Greek letters, exponents, fractions and more.

Formatting/Display Options

• Control of color, style, thickness and transparency of all objects drawn/constructed
• Option to show with or without axis, with or without a grid
• Ability to show/hide all drawn objects and toggle between shown and hidden

Books

Several books have been written to go with geometry expressions. Most teach or discuss some mathematical concepts and can teach a novice user how to use the software effectively. This table gives the details of each:

Title	Author(s)	Brief Summary
Exploring with Geometry Expressions in High School Mathematics	Ian Shepard	Activities with geometry expressions that aid discovery of the link between geometry and algebra.
Function Transformations	Tim Brown	Students are familiarized with function transformations through investigations of the function families with parents of y=x2, y=1/x and y=sin(x).
Connecting Algebra through Geometry and Technology: Applying Geometry Expressions in the Algebra II and Pre-Calculus Classrooms	Jim Wiechmann	The "playground" of Geometry Expressions facilitates students' discovery and ownership of mathematics with this book, showing that mathematics are created, not just a set of facts.
Using Symbolic Geometry to Teach Secondary School Mathematics – Geometry Expressions Activities for Algebra 2 and PreCalculus	Irina Lyublinskaya & Valeriy Ryzhik	Eight problems of varying difficulty whose main focus is on development of the students' ability to make connections between different representations of the same object.
101 Conic Sections Examples using Geometry Expressions	Philip Todd	This book's goal is to demonstrate what you can do with the powerful conic sections tools in Geometry Expressions; however, it is not intended to teach conics or how to use Geometry Expressions.
101 Symbolic Geometry Examples Using Geometry Expressions	Philip Todd	By giving 101 examples of symbolic geometry in Geometry Expressions, this book hopes to provide a starting point for the reader to pursue their own discoveries.
Developing Geometry Proofs with Geometry Expressions	Irina Lyublinskaya, Valeriy Ryzhik, Dan Funsch	The problems in this book were created to reflect content of a standard high school curriculum, from a collaboration of American and Russian educators, while also using Geometry Expressions to engage students while learning geometry.
The Farmer and the Mathematician: using Geometry Expressions and Google Earth to investigate crop circles	Larry Ottman	The design and implementation of crop circles provides an example of mathematics in action while introducing important mathematical concepts that are adaptable for students in a range of courses from Pre-Algebra through Calculus.

Images

Animations

External links

• Geometry Expressions Home Page
• Geometry Expressions Books
• Saltire Software