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    • Cabri 3D 3D動態幾何軟體
Cabri 3D 3D動態幾何軟體

本公司皆販售最新版本,目前版本僅供參考
最新版 Cabrilog Cabri 3D v2.2.12
最新版 Cabri II Plus 1.4.5

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  • Cabri 3D
  • 特色
  • Cabri II Plus
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3D幾何教學到現在為止仍是相當困難。複雜的設計與模型,在構想時是相當困難且費時。Cabri 3D將會是您唯一的解決方案,透過使用Cabri 3D,您可以更快掌握幾何構造觀察和操控各種3D空間圖形如直線、平面、圓錐、球體、稜錐…等。Cabri 3D可以創建簡單與複雜的各種動態幾何結構,擁有cabri 3D,就等於擁有了助人學習解答幾何與數學問題的非凡工具。

應用 cabri 3D,可以容易的做出線與面的垂線,線段的中垂面,一個角的角平分面,圓柱,圓錐,球,稜錐,稜柱,多面體(當然包含正正多面體),也就是常用的幾何對象。

當然,還可以對這些對象進行變換,測量,跟蹤等。而且可以做出幾何體與面的交線,比如,圓柱與平面的交線等,正是有了以上基本構件,才得以實現cabri 3D可以完成任意幾何體的制作,而且可以把幾何體表面展開,用打印機打出來,來完成實物模型。當然,更吸引人的,是cabri 3D由於採用了open GL技術,表示立體立體幾何圖形的三維效果,確實令人震撼。

動態幾何的新創舉,第一套實現使用者希望能像GSP或Cabri Geometery II以尺規作圖並拖動幾何物件,而且操作介面非常容易的的動態立體幾何軟體。

過去在GSP或Cabri Geometry II的環境中,想要畫個立體圖形,可是要耗費許多功夫,如果要研究幾個立體幾何物體的關系或模式,那就更困難了,如今Cabri 3D提供了一些基本物件:點、線、面(廣義角度來看這些物件)與一些立體圖形,以及一些關系,如對稱等。如今我們可以聚焦在立體幾何物體間的關系或是某些物件所呈現的模式,如果對照GSP與Cabri Geometery II為平面歐氏幾何(甚至是非歐)所注入的活力,我們當然可以期待Cabri 3D為立體歐氏幾何開拓新的研究領域!



Cabri 3D在中學數學的應用 節錄至台北市立華江中學網站
Cabri 3D圖形簡介 節錄至清大數學系網站


系統需求

System requirements
To use Cabri 3D, users must have a computer with the following minimum requirement:

PC    
Cabri 3Dv2.1 Windows requires Win XP, Vista, 7 or higher

Mac
Recommended: OpenGL compatible graphics card with 64MB RAM or more    Mac OS X 10.3 or higher

Tools for students:

With just a few clicks, students can:

  • Construct 2-D and 3-D figures, from the simplest to the most complex, by combining fundamental geometric objects such as points, angles, segments, circles, planes, solids and transformations.
  • Create expressions using fundamental algebraic concepts, such as numbers, variables and operations.
  • Connect geometry and algebra by measuring length, angles, area and volume and then attaching these numeric values directly to the figure to use them in calculations or in algebraic expressions.
  • Explore a figure’s properties by manipulating its variable elements.
    Observe the effects of dynamic transformations like shrinking and enlarging.
    Make conjectures about algebraic and geometric properties, and then verify relationships among various parts of a figure.

 

Tools for teachers:

The teacher can:

  • Create activities that:
    - facilitate the introduction and understanding of new concepts
    - promote the discovery of theorems, instead of just showing them
    - help model real-life situations.
  • Generate classroom resources by inserting text or pictures in a figure, modifying graphical elements, copying/pasting into other software and producing high-quality printouts.
  • Present activities to students, have them manipulate figures, observe and guide them. Using Cabri allows you to better assess individual student comprehension.
  • Expand online by integrating figures that can be manipulated on web pages or by incorporating Microsoft Office® documents.
  • Have students solve problems directly linked to the NCTM standards with possible interdisciplinary connections to physics, geography and the arts. 

Cabri II Plus is a software recognized by experts in pedagogy, specifically for its simplicity of use and solid educational foundation.

  • Basic tools borrowed from traditional design tools: compass, T-square
  • Advanced tools:

 

place and trace: display the paths of geometric figures when they are distorted.

redefine objects: add or subtract constraints on the relationship between the objects in the figure.

  • Numeric and algebraic tools: coordinate points, equations of lines, graphical representations of functions and tables
  • Save the history of figures: simultaneously follow the work of several students by replaying each of their actions step-by-step.
  • Create your own tools in order to remake frequently used constructions in just a few clicks. Design « black box » tools whose functions are to be discovered by the students.
  • Modify the toolbar to fi t the level of the class or the planned activity.
  • Import/export files between the teacher’s computer and the students’ graphing calculators, from Cabri II Plus to the free application Cabri Jr. (available on TI-83 Plus and TI-84 Plus calculators).

系統需求

System requirements
To use Cabri II Plus, users must have a computer with the following minimum requirement:

PC    
Cabri II Plus requires Win XP, Vista, 7 or higher
Recommended: 800Mhz or higher processor, 256MB RAM, OpenGL compatible graphics card with 64MB RAM or more    

Mac
Mac OS X 10.3 or higher

Dropdown menus, a more user-friendly interface
Simply by right-clicking on an object with the mouse a contextual menu is displayed for rapid choice of an attribute. It shows the type of object, as well as the list of objects used in its construction. The information shown by the cursor during construction is clearer. The left-hand figure shows the contextual dropdown menu of an intersection between a triangle and a straight line. The triangle is thus highlighted (selected in the menu) You can choose a line color, a text color or a fill-in color using the 'Variable Color' or 'Variable Fill Color' attributes. Using the menu you can also change the opacity of objects, noting that opaque objects cannot mix colors with intersecting inferior surfaces.
Improved resolution of ambiguities
When clicking on a location with several superimposed images, a dropdown menu is shown to aid with selection. By running through this menu the various objects associated with the particular construction are highlighted. The right-hand example shows the menu displayed when you point the cursor at the point of intersection between the three bisectors of a triangle.
More attributes
Click on 'Options' and 'Show Attributes', the attributes menu offers even more possibilities. It lets you choose the color of a line, of text, fill-ins, and all the other attributes of an object, including the 'intelligent display' of lines.


Colors
Palette:Cabri II Plus has an extended palette of 36 separate colors and three shades of gray.
Mixtures:The ‘fill-in’ colors mix on-screen depending on the figure and the color synthesis. The example shows a mixture of the three primary colors, cyan, magenta and yellow, giving red, green, blue & black.
Customized:Color can be applied to all objects, lines and surfaces using a customized color by giving, on the worksheet, the intensity value for each component: Red, green and blue. This coloration procedure can be used during optical simulations to represent the various wavelengths of light. It can also be used in the study of scalar or vectorial fields. In the example below, the color corresponds to the values of a scalar field (polynomial in x & y), which applies color to a small disk with an active trace.


Attributes - Fonts and styles
The choice of font, style, size and attributes has been widened. Object names, numbers and equations can be inserted into a text zone and will be automatically updated when the figure is modified.With Cabri Geometry II Plus, every single object can be named.


Images insertion
Images can be attached to points, segment and convex quadrilaterals. Images can be files in the BMP, GIF or JPG format. They can be attached using the object dropdown menu (right-click mouse). The first example shown below shows a planet and its satellite in an elliptical orbit.
The second shows an image of a piston rod attached to a segment of a figure. The whole assembly may be animated to show the moving parts of an engine.


Expressions
Cabri II Plus offers a new type of object: the Expression. The Expression tool allows you to enter in the text form a mathematical expression containing variables (all operators from the calculator can be used). For example, '3*x-2*y+1' is an expression containing variables 'x' and 'y'. The 'Apply an Expression' tool allows you to evaluate the result of an expression by indicating which values on the drawing sheet are to be used for replacement of the variables in the expression. Moreover, if an expression is defined in function of 'x', this tool allows you to graph y=f(x) designating the system of axes of your choice. The opposite example illustrates this possibility with expression 'x^3/5-x^2-x+4'. Expressions have many more applications, like the exploration of scalar or vector fields, defined on the plane, and associated to the locus of a point located on a coordinate system.


Smart lines
Cabri II Plus gives the user the possibility of showing just the significant sections of lines. Lines are intrinsically infinite in length, however, often only a small portion of each line is required to make the figure comprehensible. The rest adds nothing to its understanding. Using the ‘Smart Lines’ option they are thus cut just after the last point on each line in both directions. If you wish, you can add an arrow to each end. The example shows a Simson line for a triangle.


Loci
An intersection with a locus:Cabri II Plus is also capable of representing intersections with loci. The example shows a cardioid, the locus of point p with m varying around the circle.We can thus build the intersections of the curve with a small circle, centered about p, and thus obtain a good estimate of the tangent and normal of the curve p.
Displaying loci:Loci are displayed using a new, adaptive monitoring, algorithm, which returns the optimal resolution for display and printing with no further operator intervention.
A locus from a point on a mark:A construction involving a point on a grid or axe can be used to generate a locus. This locus is the set of points around the target object with the moving point tracing around all points on the grid. Such a locus can be used to explore scalar or vectorial fields.In the following example a point on a grid is associated with a circle, the radius of which is proportional to the value of a polynomial P in x & y. Then the locus of these circles is built and we obtain a visualization of the scalar field corresponding to the polynomial, thus an idea of the shape of the curve P(x,y)=0.
Algebraic Equation Curves:Digital methods as algebraic curves of up to and including degree 6. If the equation of a locus is considered to exceed this functional range, the equation cannot be determined. The calculations are carried out to the precision of the machine itself (64 bits), thus numerical errors may appear.The following example shows the equation of an asteroid in a circle.


Saving a session
‘Session’ is used to save and print stages of a construction, and, therefore to analyze the behavior of offshoots during the resolution of a problem using Cabri II Plus.


Export for calcs
Cabri II Plus is capable of reading and saving drawings in Cabri Jr. format. (Menu ‘File – Open or Export figure for calcs…’) Cabri Jr. interactive geometry software developed by Cabrilog for Texas Instruments is available on the TI-84 Plus and 83 Plus (SE Inclusive).

 

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