Saturday, 9 January 2010
Constructing Triangles
19:50
Constructing Triangles: Use Sketchpad's Tools
A triangle with two congruent sides is called isosceles and one with three congruent sides is called equilateral. In this tutorial, you’ll use Sketchpad’s tools to construct a triangle, an isosceles triangle, and an equilateral triangle.
You can construct a triangle with Sketchpad by simply drawing three connected segments. Unlike a triangle that you draw on paper, a Sketchpad triangle is “dynamic”—it can move—and can become any triangle at all, just by dragging its vertices to change its size and shape.
Construct a Triangle
.1. Open Sketchpad, or click on the Sketchpad window to make it active. Choose File | New Sketch to open a blank sketch.
2.Choose the Segment tool. Construct a segment using either one of two methods:
- Press and hold, drag, and release.
- Click, move, and click again.
3.
Construct another segment attached to one endpoint of the first segment. Make sure the point is highlighted when you click.
4.If you make a mistake—now or at any other time—choose Edit | Undo (and if you want to redo what you undid, choose Edit | Redo).
5.
Construct a third segment that connects the two free endpoints (check for highlighted points) to complete your triangle.
6.Choose the Polygon tool. Click the triangle’s vertices (points) in order. End by clicking on the point you first clicked.
7.Choose the Arrow tool. Click in empty space to deselect all objects.
8.Drag the different parts of your triangle to see how it behaves. Your triangle should stay a triangle. If not, use Edit | Undo and try again.
Construct an Isosceles Triangle
Now you’ll construct a triangle with two congruent sides. A circle holds the key to building a triangle that stays isosceles no matter how you drag it.
9.Choose the Compass tool. In a blank area of your sketch, construct a circle using either one of two methods:
- Press and hold, drag, and release.
- Click, move, and click again.
The circle has two points—its center and a radius point.
10.Choose the Arrow tool. Drag each point to see how it affects the circle.
11.Choose the Segment tool. Construct a segment from the center to the radius point (check for highlighted points). This is a radius of the circle.
12.
Construct a second radius from the center to the circle. Make sure the circle is highlighted when you construct the second point.
13.
Construct a segment between the points on the circle.
14.Choose the Polygon tool and construct the triangle interior.
Hide an Object
When you construct shapes with Sketchpad, you will often need to construct objects that you don’t want to see in your finished product. For your isosceles triangle, how can you make the circle “go away”?
15.Choose the Arrow tool. Select the circle and choose Edit | Cut (or press Delete).
Why does your triangle also go away? The second segment you constructed was defined by the circle. Without the circle, there is no segment. And without the segment, there is no triangle.
16.
Choose Edit | Undo to restore the circle (and triangle).
17.Instead, select the circle and choose choose Display | Hide Circle. This time, the circle should disappear, but the triangle should remain.
18.
Drag the different parts of your isosceles triangle to make sure your construction stays together. If not, use Edit | Undo and try again.
19.
Why is your triangle isosceles?
Format Your Triangles
You can change the color and appearance of the objects that make up your triangles—points, segments, and polygons—and label them.
To select objects with Sketchpad, use the Arrow tool. When you click an object, the highlighting indicates that the object is selected. To deselect an object, click it again, or click in empty space to deselect everything.
To select objects with Sketchpad, use the Arrow tool. When you click an object, the highlighting indicates that the object is selected. To deselect an object, click it again, or click in empty space to deselect everything.
20.
To change a point’s size, select it and choose Display | Point Style.
21.
To change a segment’s thickness, select it and choose Display | Line Style.
22.
To change the color of any object—point, segment, or polygon—select it and choose Display | Color.
23.Choose the Text tool. Click the points to label them. Click them again to hide the labels, or double-click them to change the labels.
24.Choose the Marker tool. Click on one of the two congruent sides of the isosceles triangle to add a tick mark. Then add a tick mark to the other congruent side. Repeated clicking changes the number of strokes.
Construct an Equilateral Triangle
Constructing an equilateral triangle is similar to constructing an isosceles triangle, but now you’ll use two circles instead of one.
25.Choose the Arrow tool. Drag the first two triangles you made to make room in your sketch.
26.Choose the Compass tool and construct a circle.
27.
Construct a second circle that interlocks with the first—start your new circle at the radius point of the first circle and end it at the center of the first circle. When done, there should only be two circles and two points.
28.Choose the Arrow tool. Drag each point. Both circles should always stay exactly the same size. If not, choose Edit | Undo and try again.
29.Choose the Point tool. Click on one of the intersections formed by the interlocking circles (make sure both circles are highlighted) to construct the third vertex of your triangle.
30.Choose the Segment tool and construct segments between the three vertices.
31.Choose the Polygon tool and construct the triangle interior.
32.Choose the Arrow tool. Drag each point of your triangle to make sure your construction holds together and stays equilateral. If not, choose Edit | Undo and try again.
33.
Hide the circles and format your triangle. Use the Text and Marker tools to add labels and tick marks.
34.
Why is your triangle equilateral?
Explore More
35.
Drag the different parts of your three triangles to see how they behave. Can you make them all look as if they are equilateral? Can you make them all look as if they are right triangles? Why or why not?
36.
Choose File | New Sketch. With the same tools you used to construct your isosceles and equilateral triangles, construct a rhombus or a regular hexagon.
Wednesday, 16 December 2009
Complete LATEX environment on a USB stick
13:18
1. What is it for?
Install a LATEX distribution, Ghostscript, Ghostview software, install a text editor, configure it all … These instructions can be a problem for newbies who then feel lost and discouraged before even starting to discover LATEX.
For other LATEX users, it is frustrating to work on a computer where no LATEX environment is (or perhaps can be) installed.
See also
* This article (in French) about USBTEX on the Framasoft.net website.
* The pack Framakey “LaTeX edition” inspired from USBTeX that provides several softwares and additive documents.
2. USBTEX: LATEX portable environnment
It contains LATEX, Ghostscript, Ghostview and Texmaker, in a portable setup. To make it work:
1. Download and unzip the distribution on a USB stick (or on your hard disk)
2. Run the program — no configuration needed
3. Write and compile your documents!
Admin rights are not required so the software can be run in a normal user Windows session.
3. Download (Version 1.1 updated on 27.11.2008)
Download the USBTEX archive (about 186Mo unzipped):
The self-extracting archive USBTeX.exe (40Mo) (1022 downloads since 05/23/07)
USBTEX gives you:
* MiKTeX 2.7 portable version
* Ghostscript 8.53
* Ghostview 4.7
* SumatraPDF 0.9.3-fr
* Texmaker 1.8
4. Using USBTEX
After downloading, uncompress the archive. The program asks you where you wish to place the folder, choose, for instance, your USB stick. Be patient, it can take several minutes.
Now go to the uncompressed folder.
1. Demarrer: double-click on Demarrer (Start). It will build the paths needed for the software to work.
2. TexMaker: while commnds are executing, double-click on TexMaker and start writing your LATEX document or open the example file located in the Documents folder.
When Demarrer has finished, you can compile your document clicking on the QuickBuild (Compilation rapide) button:
3. Arreter: at the end of your work session, close Texmaker and double-click on Arreter(Stop). You can now unmount your USB stick.
To make it work well, it is important to have a good USB stick, meaning high speed. A lot of data will be read and written to the stick while the software executes. A stick and a computer that are USB-2.0 compliant are highly recommended. For instance, I use Kingston DataTraveler and USBTEX starts in less than 1 min.
5. Add a package
Since 0.9.4 version, MiKTeX_Options works. Start it then click on the tab Packages. Choose your package, install it (clicking on +) and in the tab Général, click on Refresh FNDB, then Update Formats. There you are, your new package is ready to use.
6. How does it work?
MiKTeX can be built as a portable distrinution following the instructions of this HOWTO, which is how I made USBTEX:
http://www.ctan.org/tex-archive/info/MiKTeX+Ghostscript+GSview+USB-drive-HOWTO.txt
7. License
The USBTEX-specific work in the distribution downloadable on this page is placed under GPL license.
The author has no responsibility in case of any problems or damage caused by the use of this distribution.
8. Archives
You will find USBTEX versions on this page.
Source: ExOmatiK.net
The Geometer's Sketchpad® Version 5
13:05
Arc Tool that work with Java Sketchpad
12:39
By using this tool, you can create an arc that work with Java Sketchpad. Simply select the tool and click 3 points to finish. Also, the tool include a free point on the arc. If you want to add more free point on arc, apply this tool again to that 3 points. Bonus: This file include an another tool, name "Dashed segment". This tool create a dashed segment that work with Java Sketchpad.
Dowload here
Dowload here
The magnet tool
12:38
Before using this tool, we prepare the one free point and 3 destination points. Select the tool then click at free point and others in this order. The screen will display a new button. Click the button to active it. Drag free point to place you want.If it near to the one of 3 destinations points, it will be attracted.'
Dowload here
Dowload here
The mini coordinate system
12:28
The mini coordinate system will help you save your Sketchpad documents space, display only what you want, create more than one coordinate system and, of cause, it contains features as the full Sketchpad coordinate system.
Dowload here
Dowload here
Square to Circle and more
12:24
How can we transform a square to a circle, or a circle to a triangle? Is it exist that transformation? Using The Geometer's Sketchpad, we can morph from a triangle to a square to a circle in a quite simple way. First, we create three objects: a square, a circle and a triangle.
Choose a free point A on square using the point tool. We fix a original point from 4 vertex and name it as O. Measure the OA distance. Of cause, there is exist an one-to-one mapping that transform a point on square to a point on circle, so using this map, we can define a point B on circle that correlative with the point A on square.
Using this method, we define a point C on triangle that correlative with the point B on circle. After that, construct triangle ABC and create a free point on it. Chose this free point and the free point A on square, apply Construct | Locus. This loci will look like the square if the free point (named as "drag") is near point A, and so on.
Square to Circle to Triangle
We can change the triangle, circle and square and drag point "drag" to see how it works.
Like to get this model? Please go to Download from Top Menu.
Choose a free point A on square using the point tool. We fix a original point from 4 vertex and name it as O. Measure the OA distance. Of cause, there is exist an one-to-one mapping that transform a point on square to a point on circle, so using this map, we can define a point B on circle that correlative with the point A on square.
Using this method, we define a point C on triangle that correlative with the point B on circle. After that, construct triangle ABC and create a free point on it. Chose this free point and the free point A on square, apply Construct | Locus. This loci will look like the square if the free point (named as "drag") is near point A, and so on.
Square to Circle to Triangle
We can change the triangle, circle and square and drag point "drag" to see how it works.
Like to get this model? Please go to Download from Top Menu.
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