GeoGebra - это бесплатная, кроссплатформенная динамическая математическая программа для всех уровней образования, включающая в себя геометрию, алгебру, таблицы, графы, статистику и арифметику, в одном удобном для использования пакете.
Кроме того, у программы богатые возможности работы с функциями (построение графиков, вычисление корней, экстремумов, интегралов и т.д.) за счёт команд встроенного языка (который, кстати, позволяет управлять и геометрическими построениями). В отличии от других программ для динамического манипулирования геометрическими обьектами, идея GeoGebra заключается в интерактивном сочетании геометрического, алгебраического и числового представления. Вы можете создавать конструкции с точками, векторами, линиями, коническими сечениями, а также математическими функциями, а затем динамически изменять их.
GeoGebra позволяет напрямую вводить уравнения и манипулировать координатами. Таким образом, можно легко составлять графики функций, работать со слайдерами для подбора необходимых параметров, искать символические производные и использовать мощные команды вроде корня и последовательности.
• Построение конических сечений: Коника произвольного вида — по пяти точкам.
• Построение геометрического места точек, зависящих от положения некоторой другой точки, принадлежащей какой-либо кривой или многоугольнику (инструмент Локус).
• Аппроксимация множества точек кривой заданного вида: полином, экспонента, логарифм, синусоида
• Новые и улучшенные инструменты: Перо, Freehand Формы, Удаление, Жесткий Полигон
• Программа позволяет создавать Java-апплеты динамических чертежей для их включения в Веб-страницы
• И многое другое ...
Новые инструменты
· Plane
· Right prism
· Sphere
· View in front of
Python Window
Общие характеристики
· 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
· Линии
· Сегменты
· Лучи
· Полигоны
· Окружности
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
· Пирамиды
· Призмы
· Сферы
· Цилиндры
· Конусы
3D View
Перемещение объектов
· 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)
Маштабирование
· используйте колесо мыши
· использование инструмента "масштаб"
Сетки
· Показать/Скрыть оси, сетки, xOy плоскость
Команды
Улучшенные команды
· DotPlot will work with a list of text eg DotPlot[ {"Red", "Red", "Red", "Blue", "Blue" } ]
· Coefficients can now be used with the output of Fit (if non-polynomial) to get the calculated coefficients for the fit
· These three commands will now work with Conics as well as Curves
· Кривизна[ <Point>, <Object> ]
· CurvatureVector[ <Point>, <Object> ]
· OsculatingCircle[ <Point>, <Object> ]
· All commands below work with 2D/3D objects
· Midpoint[ <Point> , <Point> ], Midpoint[ <Segment> ]
· Intersect[ <Line> , <Line> ]
· Intersect[ <Line> , <Segment> ], etc.
· Intersect[<Line>, <Conic>]
· Intersect[<Conic>, <Conic>]
· Vector[ <Point> , <Point> ]
· Line[ <Point> , <Point> ], Segment[ <Point> , <Point> ], etc.
· Line[ <Point> , <Line> ], Line[ <Point> , <Segment> ], etc.
· PerpendicularLine[ <Point> , <Line> ]
(will set output line to undefined if point is on the line in 3D)
· Circle[ <Point> , <Point> , <Point> ]
· Distance[ <Point> , <Point> ]
· Angle[ <Point> , <Point> , <Point> ]
· Area[ <Polygon> ], Area[ <Conic> ]
· Vertex[ <Polygon> ], Vertex[ <Conic> ]
· Center[ <Conic> ]
Новые команды CAS
· Уравнение Лапласа[ <Function> ]
· Уравнение Лапласа[ <Function>, <Variable> ]
· InverseLaplace[ <Function> ]
· InverseLaplace[ <Function>, <Variable> ]
· SolveCubic[ <Cubic Polynomial> ]
· GroebnerLex[ <List of Polynomials> ]
· GroebnerLex[ <List of Polynomials>, <List of Variables> ]
· GroebnerDegRevLex[ <List of Polynomials> ]
· GroebnerDegRevLex[ <List of Polynomials>, <List of Variables> ]
· GroebnerLexDeg[ <List of Polynomials> ]
· GroebnerLexDeg[ <List of Polynomials>, <List of Variables> ]
· Eliminate[ <List of Polynomials>, <List of Variables> ]
· AngleBisector[ <Line>, <Line> ]
Новые Команды
· Spline[ <List of Points> ]
· Spline[ <List of Points>, <Order •3> ]
· Tangent[ <Point>, <Spline> ]
· RandomUniform[ <Min>, <Max>, <n> ]
· AreEqual[ <Object>, <Object> ]
· AreCollinear[ <Point>, <Point>, <Point> ]
· AreConcurrent[ <Line>, <Line>, <Line> ]
· AreConcyclic[ <Point>, <Point>, <Point>, <Point> ]
· AreParallel[ <Line>, <Line> ]
· ArePerpendicular[ <Line>, <Line> ]
· Prove[ <Boolean Expression> ]
· ProveDetails[ <Boolean Expression> ]
· UpdateConstruction[ <Number of times> ]
· Min[ <List of Data>, <List of Frequencies> ]
· Max[ <List of Data>, <List of Frequencies> ]
· IntersectPath[ <Line>, <Polygon> ]
· Envelope[ <Path Creating Envelope>, <Moving Point> ]
· SetPerspective[ <Options> ]
· Remove[ <List>, <List> ]
· FitImplicit[ <List of Points>, <Order> ]
· DotPlot[ <List of Raw Data>, <Stack Adjacent Dots (optional)>, <Scale Factor (optional)>]
· StartLogging[ "<Sensor>", <Variable>, "<Sensor>", <Variable>, ...] For data logging eg from a phone
· StopLogging[ ] For data logging eg from a phone
· BarChart[ <List of Raw Data>, <Width of Bars>, <Vertical Scale Factor> ]
· FrequencyTable[ <List of Raw Data>, <Scale Factor> ]
· Payment[ <Rate>, <Number of Periods>, <Present Value>, <Future Value (optional)>, <Type (optional)> ] Like the Excel Pmt function
· Rate[ <Number of Periods>, <Payment>, <Present Value>, <Future Value (optional)>, <Type (optional)>, <Guess (optional)> ] Like the Excel Rate function
· Periods[ <Rate>, <Payment>, <Present Value>, <Future Value (optional)>, <Type (optional)> ] Like the Excel NPer function
· PresentValue[ <Rate>, <Number of Periods>, <Payment>, <Future Value (optional)>, <Type (optional)> ] Like the Excel PV function
· FutureValue[ <Rate>, <Number of Periods>, <Payment>, <Present Value (optional)>, <Type (optional)> ] Like the Excel FV function
3D команды:
Основные:
· SetViewDirection[ <Direction> ]
· Rotate[ <Object>, <Angle>, <Axis of Rotation> ]
· Rotate[ <Object>, <Angle>, <Point on Axis>, <Axis Direction> ]
· Rotate[ <Object>, <Angle>, <Point on Axis>, <Plane> ]
· Reflect[ <Object>, <Plane> ] reflects an object about a plane
Points
· Intersect[ <Line>, <Object> ] creates the intersection point of a line and a plane, segment, polygon, etc
· Intersect[ <Plane>, <Object> ] creates the intersection point of a plane and segment, polygon, etc
· ClosestPoint[ <Region>, <Point> ]
· ClosestPoint[ <Line>, <Line> ]
· Corner[3, <Number>] creates a point at one of the 3D view's corners (the number is from 1 to 8)
· Center[ <Quadric> ] creates the center of a quadric (e.g. sphere, cone, etc.)
Lines
· Intersect[ <Plane> , <Plane> ]
· IntersectPath[ <Plane>, <Polygon> ]
· PerpendicularLine[ <Point>, <Line>, <Context> ] <Context> can be a plane or eg "xOy" or "space"
· PerpendicularLine[ <Point>, <Direction>, <Direction> ]
· PerpendicularLine[ <Point>, <Plane> ]
· PerpendicularLine[ <Line>, <Line> ]
· Distance[ <Line>, <Line>]
· PerpendicularBisector[ <Point>, <Point>, <Direction> ]
· Vectors
· PerpendicularVector[ <Plane> ] creates a vector orthogonal to the plane
· UnitPerpendicularVector[ <Plane> ] creates a unit vector orthogonal to the plane
Polygons
· Intersect[ <Plane>, <Polyhedron> ] creates the polygon(s) intersection of plane and polyhedron
· Polygon[ <Point>, <Point>, <Number of Vertices>, <Direction> ] creates a regular polygon with n vertices, and directed by the direction (e.g. a plane to which the polygon will be parallel, if possible)
Circles
· Circle[ <Line>, <Point> ] creates the circle with line for axis and through the point
· Circle[<Point>,<Radius>,<Direction>] 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[<Point>,<Point>,<Direction>] creates a circle with center, through a point, and axis parallel to direction (may be undefined)
· Intersect[ <Sphere>, <Sphere> ] creates the circle intersection of two spheres
Conics
· Intersect[ <Plane>, <Quadric> ] or IntersectPath[ <Plane>, <Quadric> ] creates the conic intersection of the plane and the quadric (sphere, cone, cylinder, ...)
Planes
· Plane[ <Polygon> ]
· Plane[ <Conic> ]
· Plane[ <Point> , <Point> , <Point> ] creates the plane through the points
· Plane[ <Point> , <Line> ] creates the plane through the point and the line
· Plane[ <Line> , <Line> ] creates the plane through the lines (if in the same plane)
· Plane[ <Point> , <Plane> ] creates the plane through the point and parallel to the plane
· PerpendicularPlane[ <Point> , <Line> ] creates the plane through the point and perpendicular to the line
· PerpendicularPlane[ <Point> , <Vector> ] creates the plane through the point and perpendicular to the vector
· PlaneBisector[ <Point> , <Point> ] create the plane orthogonal bisector between the two points
· PlaneBisector[ <Segment> ] create the plane orthogonal bisector of the segment
Углы:
· Angle[ <Line> , <Plane> ]
· Angle[ <Plane> , <Plane> ]
Сферы:
· Sphere[ <Point> , <Number>] creates a sphere with center and radius
· Sphere[ <Point> , <Point> ] creates a sphere with center as the first point through the second point.
Цилиндры и конусы:
· Cylinder[ <Point>, <Point>, <Radius Number> ] creates a cylinder of revolution between the two points, and with number for radius
· Cylinder[ <Circle>, <height> ] (right circular cylinder, "Extrude to Prism/Cylinder" tool : Drag circle, or select circle and enter altitude to create right cylinder)
· Cone[ <Point>, <Point>, <Radius Number> ] 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[ <Point>, <Vector>, <Angle ]
· Cone[ <Circle>, <Height> ] (right circular cone, "Extrude to Pyramid/Cone" tool : Drag circle, or select circle and enter altitude to create right circular cone)
· Bottom[ <Limited quadric> ] creates the bottom of the limited quadric (e.g. circle for a cylinder)
· Top[ <Limited quadric> ] creates the top of the limited quadric (e.g. circle for a cylinder)
· Ends[ <Limited quadric> ] creates bottom and top of the limited quadric (e.g. circles for a cylinder)
· Side[ <Limited quadric> ] creates the side of the limited quadric
Quadrics
· InfiniteCylinder[ <Point> , <Vector>, <Radius Number> ] creates a cylinder of revolution around (point,vector) direction, and with number for radius
· InfiniteCylinder[ <Point>, <Point>, <Radius Number> ] creates a cylinder of revolution around (point,point) direction, and with number for radius
· InfiniteCylinder[ <Line>, <Radius Number> ]creates a cylinder of revolution around line direction, and with number for radius
· InfiniteCone[ <Point> , <Vector>, <Angle Number> ] creates a cone of revolution around (point,vector) direction, with point for apex, and with number for angle (half-angle of the cone)
· InfiniteCone[ <Point>, <Point>, <Angle Number> ] creates a cone of revolution around (point,point) direction, with point for apex, and with number for angle (half-angle of the cone)
· InfiniteCone[ <Point>, <Line>, <Angle Number> ] creates a cone of revolution with point for apex, with axis parallel to line, and with number for angle (half-angle of the cone)
· Axes [ <Quadric> ] create the 3 axes of a quadric
· IntersectConic[ <Plane>, <Quadric> ]
· IntersectConic[ <Quadric>, <Quadric> ]
· Side[ <Quadric> ]
Многогранники:
· Pyramid[ <Point> , <Point> , ... , <Point> ] : pyramid
eg Pyramid[A,B,C,D] creates the pyramid with basis ABC and apex D
· Pyramid[ <polygon>, <top point> ] ("Pyramid" tool : select basis + create/select top point)
· Pyramid[ <polygon>, <height> ] ("Extrude to Pyramid/Cone" tool : Drag polygon, or select polygon and enter altitude to create centered pyramid)
· Prism[ <Point> , <Point> , ... , <Point> , <Point> ] : prism
eg Prism[A,B,C,D] creates the prism with basis ABC and top DEF, vectors AD, BE, CF are equal
· Prism[ <polygon>, <top point> ] ("Prism" tool : select basis + create/select first top point)
· Prism[ <polygon>, <height> ] ("Extrude to Prism/Cylinder" tool : Drag polygon, or select polygon and enter altitude to create right prism)
Платоновы тела:
· Icosahedron[ <Point>, <Point>, <Direction> ]
· Cube[ <Point>, <Point>, <Direction> ]
· Tetrahedron[ <Point>, <Point>, <Direction> ]
· Dodecahedron[ <Point>, <Point>, <Direction> ]
· Octahedron[ <Point>, <Point>, <Direction> ]
Net
· Net[ <Polyhedron> , <Number> ] : create the net for a convex pyramid, convex prism, platonic solid. The number must be between 0 and 1. The net is totally unfold when number value equals 1.
· Net[ <Polyhedron> , <Number>, <Face>, <Edge>, <Edge>, ... ] (just for cube right now, more to come)
Кривые, Поверхности:
· Curve[ <Expression> , <Expression> , <Expression> , <Parameter Variable> , <Start Value> , <End Value> ]
· Function[ <Expression>, <Parameter Variable 1>, <Start Value>, <End Value>, <Parameter Variable 2>, <Start Value>, <End Value> ]
· Surface[ <Expression>, <Expression>, <Expression>, <Parameter Variable 1>, <Start Value>, <End Value>, <Parameter Variable 2>, <Start Value>, <End Value> ]
Following commands automatically add xOy plane for direction (first face is contained in xOy plane)
· Icosahedron[ <Point>, <Point> ]
· Cube[ <Point>, <Point> ]
· Tetrahedron[ <Point>, <Point> ]
· Dodecahedron[ <Point>, <Point> ]
· Octahedron[ <Point>, <Point> ]
Объём:
· Volume[ <Pyramid> ], Volume[ <Prism> ], Volume[ <Cone> ], Volume[ <Cylinder> ]
Высота:
· Height[ <Solid> ], Height[ <Cone> ], Height[ <Cylinder> ] : returns an "oriented" height of the solid
Сценарии:
· SetViewDirection[ <Direction> ] sets the 3D view orientation regarding the direction
Turtle Commands
· Turtle[]
· TurtleForward[ <Turtle>, <Distance> ]
· TurtleBack[ <Turtle>, <Distance> ]
· TurtleLeft[ <Turtle>, <Angle>]
· TurtleRight[ <Turtle>, <Angle>]
Новые Сочетания Клавиш:
· Ctrl-Shift-Y: Open Python (Scripting) View
• Описание всех сочетаний клавиш
• Новый апплет Параметры
• Описание всех параметров
• Новые аргументы командной строки
Если вы используете аргументы командной строки, убедитесь, что выделено достаточно памяти, например:
· java -Xms32m -Xmx1024m -jar geogebra.jar --settingsfile=geogebra.properties
· Описание всех аргументов командной строки
Новые команды JavaScript
· 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
Dec 29 2012, 5:31
4866 
GeoGebra
GeoGebra v4.2.13 (37 Mb)
