Dynamic Dynamic geometry on pseudospherical surfaces
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9. Examples of using macro constructions in this micro-world

 

1. Home | 2. Lines on PS | 3. First figures | 4. Full rolling-up | 5. Conjugation with KB's model | 6. New conjugation

 

7. Hyperbolic PS | 8. Elliptic pPS | 9. To play on the pseudosphere

Do a short right-clic to use the macros in the figures : it appears like a popup menu (example 3) :

ExemplePopUp

You have also a tool's palet as this one (example 4)

BarreOutilsApplet

The four first tools are : move - point - intersection - segment - locus.
The options are : hide - back - color - thickness points and l ines .

An "how to do" in four examples, one on each approach

 

As it was used for make all provious figures, these macros have many implicit objects, so you have just to show few objects.
From example to send a point from KB to the pseudosphere you have to show only one point, but nine points are implicit.

 

You can reload this page to have the original figures and make a new construction (with example 3 or 4)

 

The files are heavy enough and it take time to be interpreted. It's better to move a point on the pseudoshere and then to move the pseudosphere to be sure that the applet is ready. Then you can use the macros.

Example 1 - Intrinsic geometry on the main sheet of the pseudosphere

In this file, there is only two macro constructions, one for the segments and one for midpoints. In each case, you have to show the latitude uX and the point X. For the midpoint it give the latitude of the point so you can create the triangle and its medians

Example 2 - Intrinsic geometry with full rooling-up on the pseudosphere

 

 

MacrosHowTo2Because of the rolling up, the point A can't give the real longitude, so we have to give the numeric valude. In this file, there is many macros :

 

For the seven first macros you have to give for each point (two or three) the numerical latitude LuX and numrical longidue rdX.

 

The seventh macro give the two constans of the line : c and k2.

 

The four last macro built lines from these constants (four numbers for common perpendiclar line)

 

Becarefull when you use "hide" to comme back to "move"

Exemple 3 - Usign the Klein-Beltrami's model with the pseudosphere

This file is to built the symetric of a triangle. the axis is the line (MN). All has sent onto the KB's disk.

You can use the macros and the tools to :

1. Built the KB's line (M'N') by the macro (KB mine) - Show only the two points M' and N'.

2 Built the symetrics A', B', C' of A, B, C throught (M'N') by macro (show first the KB-line and then the point)

3. Built the side of the triangle A'B'C' by the tool segment.

4. Take a point on each side and send back this point to thepseudosphere by the macro DL Extented to PS. Sho only the point.

5. For each point built on the pseudosphere make the locus of this point when the point on the side move.

Then you have built the symetric of the triangle.

Example 4 - With the hyperbolic pseudosphere (HPS)

 

MacroHowTo4Many KB's disk macros on this file. Like the previous file : you built anything you want (common perpendicluar of altitudes, circumcircle, medians, etc) on KB and you send back to HPS by locus of a point on each segments on circles.

 

One thing to remerber : if you wand to send lines from KB to HPS, you have to send only the part on this line which is on the hyperbolic pseudoshere. So you must cut this KB-line with the limit on the pseudsosphere - the large red equidistance : you make the intersections, hide the KB-line, create a new segment limited by the equidistance. Then you take a point on this new segment and send this point for the locus.

1. Home | 2. Lines on PS | 3. First figures | 4. Full rolling-up | 5. Conjugation with KB's model | 6. New conjugation

 

7. Hyperbolic PS | 8. Elliptic PS | 9. To play on the pseudosphere