О программе:
Графика, алгебра и таблицы связаны между собой и полностью динамичны
Легкий в использовании интерфейс, вдобавок обладает очень мощными возможностями
Вы можете сами создать интерактивный обучающий материал, такие как веб-страницы
Доступна на многих языках для миллионов пользователей по всему миру
Бесплатная программа с открытым кодом

Основные возможности:
Построение кривых
Построение графиков функций;
Построение кривых, заданных параметрически в декартовой системе координат:;
Построение конических сечений: Коника произвольного вида — по пяти точкам.
Окружность: — по центру и точке на ней;
по центру и радиусу;
по трем точкам;
Эллипс — по двум Фокусам и точке на кривой;
Парабола — по фокусу и директрисе;
Гипербола — по двум фокусам и точке на кривой;
3D моделирование
Построение геометрического места точек, зависящих от положения некоторой другой точки, принадлежащей какой-либо кривой или многоугольнику (инструмент Локус).
Вычисления
Действия с матрицами: сложение, умножение;
Транспонирование, инвертирование;
Вычисление определителя;
Вычисления с комплексными числами;
Нахождение точек пересечения кривых;
Статистические функции: вычисление математического ожидания, дисперсии;
Вычисление коэффициента корреляции;
Аппроксимация множества точек кривой заданного вида: полином, экспонента, логарифм, синусоида
Работа с таблицами
Анимация
Много новых команд, например SlopeField, LocusEquation, SurdText
Новые и улучшенные инструменты: Перо, Freehand Формы, Удаление, Жесткий Полигон
Программа позволяет создавать Java-апплеты динамических чертежей для их включения в Веб-страницы
Загрузка готовых шаблонов с официального сайта в формате .ggb
И многое другое ...

Примечания к выпуску GeoGebra 5.0
Новые инструменты
· Plane
· Right prism
· Sphere
· View in front of
Python Window
Общие характеристики
Experimental: typing the decimal comma key on the numeric keypad types a .
· Relative copy in the spreadsheet: GeoText/GeoImage's Position updated (eg A4 -> A5)
· New filling styles: cross-hatch, brick, chessboard, dots, honeycomb
· Bar Charts can have different colors/hatching/filling for each bar
Новые возможности
· Extended types to 3D
· Points
eg A=(5,-2,1)

Vectors
eg u=(5,-2,1)
eg Cross product: a = u •v
· Lines
· Segments
· Rays
· Polygons
· Circles
Новые типы объектов
Surfaces
· eg f(x,y) = sin(x * y)
· eg Function[sin(a * b), a, -5, 5, b, -5, 5]
Planes
eg x + y + z = 1
· Pyramids
· Prisms
· Spheres
· Cylinders
· Cones
3D View
· Applets
· 3D export to applets and GeoGebraTube is not supported at the moment
· Moving objects
· left-drag points in the 3D view. Click on the point to change the mode "along xOy plane" to "along z axis", and so on.
Translation of the scene
· shift+left-drag the 3D view (without pointing on a moveable object)
· use move view tool
Rotation of the scene
· "Rotate 3D graphic view" tool
· right-drag the 3D view (without pointing on a moveable object)
· continue rotation when mouse released
· view in front of an object (toolbar)
Zoom
· use wheel mouse
· use zoom tool
Gridlines
· show/hide axes, grid, xOy plane
Команды
· All commands below works with 2D/3D objects
· Midpoint[ , ]
· Intersect[ , ]
· Intersect[ , ], etc.
· Intersect[, ]
· Intersect[, ]
· Vector[ , ]
· Line[ , ], Segment[ , ], etc.
· Line[ , ], Line[ , ], etc.
· PerpendicularLine[ , ]
(will set output line to undefined if point is on the line)
Circle[ , , ]
Distance[ , ]
Angle[ , , ]
Area[ ], Area[ ]
New Commands
· Spline[ ]
· Spline[ , ]
· Tangent[ , ]
· DensityPlot, syntax to be confirmed. Try DensityPlot[ sin(x)+sin(y) ]
· MatrixPlot, syntax to be confirmed. Try MatrixPlot[{{0.9, 0.08, 0.03}, {0.15, 0.8, 0.05}, {0.25, 0.25, 0.5}}]
· ContourPlot, syntax to be confirmed. Try ContourPlot[x^2+y^2]
· RandomUniform[ , , ]
· AreEqual[ , ]
· AreCollinear[ , , ]
· AreConcurrent[ , , ]
· AreConcyclic[ , , , ]
· AreParallel[ , ]
· ArePerpendicular[ , ]
· Prove[ ]
· ProveDetails[ ]
· UpdateConstruction[ ]
· Min[ , ]
· Max[ , ]
· IntersectPath[ , ]
· IntersectPath[ , ]

3D Commands
General
· IntersectPath[ , ]
· IntersectPath[ , ]
· Rotate[ , , ]
· Rotate[ , , , ]
· Rotate[ , , , ]
Points
· Intersect[ , ] creates the intersection point of a line and a plane, segment, polygon, etc
· Intersect[ , ] creates the intersection point of a plane and segment, polygon, etc
· ClosestPoint[ , ]
· ClosestPoint[ , ]
Lines
· Intersect[ , ]
· PerpendicularLine[ , ]
· PerpendicularLine[ , ]
· Distance[ , ]
Vectors
· OrthogonalVector[ ] creates a vector orthogonal to the plane
· UnitOrthogonalVector[ ] creates a unit vector orthogonal to the plane
Polygons
· Intersect[ , ] creates the polygon(s) intersection of plane and polyhedron
Circles
· Circle[ , ] creates the circle with line for axis and through the point
· Circle[,,] create circle with center, radius, and axis parallel to direction, which can line, vector or plane (in this case : normal vector of the plane)
· Circle[,,] creates a circle with center, through a point, and axis parallel to direction (may be undefined)
· Intersect[ , ] creates the circle intersection of two spheres
Conics
· Intersect[ , ] creates the conic intersection of the plane and the quadric (sphere, cone, cylinder, ...)
Planes
· Plane[ , , ] creates the plane through the points
· Plane[ , ] creates the plane through the point and the line
· Plane[ , ] creates the plane through the point and parallel to the plane
· PerpendicularPlane[ , ] creates the plane through the point and perpendicular to the line
· PerpendicularPlane[ , ] creates the plane through the point and perpendicular to the vector
· PlaneBisector[ , ] create the plane orthogonal bisector between the two points
· PlaneBisector[ ] create the plane orthogonal bisector of the segment
Spheres
· Sphere[ , ] creates a sphere with center and radius
· Sphere[ , ] creates a sphere with center im the first point through the second point.
Cylinders and cones
· Cylinder[ , , ] creates a cylinder of revolution between the two points, and with number for radius
· Cylinder[ , ] (right circular cylinder, "Extrude to Prism/Cylinder" tool : Drag circle, or select circle and enter altitude to create right cylinder)
· Cone[ , , ] creates a cone of revolution between the two points, with disc around first point and of given radius, and with second point for apex
· Cone[ , ] (right circular cone, "Extrude to Pyramid/Cone" tool : Drag circle, or select circle and enter altitude to create right circular cone)
· Bottom[ ] creates the bottom of the limited quadric (e.g. circle for a cylinder)
· Top[ ] creates the top of the limited quadric (e.g. circle for a cylinder)
· Side[ ] creates the side of the limited quadric
Quadrics
· InfiniteCylinder[ , , ] creates a cylinder of revolution around (point,vector) direction, and with number for radius
· InfiniteCylinder[ , , ] creates a cylinder of revolution around (point,point) direction, and with number for radius
· InfiniteCylinder[ , ]creates a cylinder of revolution around line direction, and with number for radius
· InfiniteCone[ , , ] creates a cone of revolution around (point,vector) direction, with point for apex, and with number for angle (half-angle of the cone)
· InfiniteCone[ , , ] creates a cone of revolution around (point,point) direction, with point for apex, and with number for angle (half-angle of the cone)
· InfiniteCone[ , , ] creates a cone of revolution with point for apex, with axis parallel to line, and with number for angle (half-angle of the cone)
· Side [ ]
Polyhedrons
· Pyramid[ , , ... , ] : pyramid
eg Pyramid[A,B,C,D] creates the pyramid with basis ABC and apex D
· Pyramid[ , ] ("Pyramid" tool : select basis + create/select top point)
· Pyramid[ , ] ("Extrude to Pyramid/Cone" tool : Drag polygon, or select polygon and enter altitude to create centered pyramid)
· Prism[ , , ... , , ] : prism
eg Prism[A,B,C,D] creates the prism with basis ABC and top DEF, vectors AD, BE, CF are equal
· Prism[ , ] ("Prism" tool : select basis + create/select first top point)
· Prism[ , ] ("Extrude to Prism/Cylinder" tool : Drag polygon, or select polygon and enter altitude to create right prism)
Кривые, поверхности
· Curve[ , , , , , ]
· Function[ , , , , , , ]
· Surface[ , , , , , , , , ]
Solids
· Icosahedron[ , , ]
· Cube[ , , ]
· Tetrahedron[ , , ]
· Dodecahedron[ , , ]
· Octahedron[ , , ]
· Following commands automatically add xOy plane for direction (first face is contained in xOy plane)
· Icosahedron[ , ]
· Cube[ , ]
· Tetrahedron[ , ]
· Dodecahedron[ , ]
· Octahedron[ , ]
Volume
· Volume[ ], Volume[ ], Volume[ ], Volume[ ]
Turtle Commands
· Turtle
· TurtleForward[ , ]
· TurtleBack[ , ]
· TurtleLeft[ , ]
· TurtleRight[ , ]
New Keyboard Shortcuts
· Ctrl-Shift-Y: Open Python (Scripting) View
• Description of all Keyboard Shortcuts
• New Applet Parameters
• Description of all Applet Parameters
• New Command Line Arguments
If you use command line arguments, make sure you allocate enough memory, eg:
· java -Xms32m -Xmx1024m -jar geogebra.jar --settingsfile=geogebra.properties
· Description of all Command Line Arguments
New jаvascript commands
· registerLoggerListener(functionName), unregisterLoggerListener(functionName) to access Vernier Go!Motion USB Logger
· registerObjectClickListener(String objName, String JSFunctionName);
· unregisterObjectClickListener(String objName);
· registerClickListener(String JSFunctionName);
· unregisterClickListener(String JSFunctionName);
GeoGebra в формате XML-файла