Last Update 10/ 03/ 2005
in English/ in Esperanto/ in Portuguese
The original blue triangle defined by a random selection of the coordinates of its vertices can be displaced by a click on one of the buttons in the figure. Each option is described in table 1. The mirror planes and rotation axes contain the origin of the cartesian plane and are perpendicular to the xy plane.
Table 1. Symbols on the buttons and description.
| Symbols | Description |
| m | mirror plane perpendicular to x |
| m | mirror plane perpendicular to y |
| 2 | binary axis |
| 3 | triad axis |
| 4 | tetrad axis |
| 6 | hexad axis |
| 2m | mirror plane containing a binary axis |
| C | coordinates of vertices |
A click on button C will show coordinates of vertices. The symbol 2m defines a crystal class. See the coordinates of the cursor as truncated integers on the bottom of the browser to identify vertices and to follow symmetry operations. A click close to the blue triangle will show in blue the area (su), edge length (AC, BC and AB) and the coordinates of the 3 vertices. Changing sequences on coordinates study during the presented symmetry operations, clicking back and forth will enhance perception of beginners. These symmetry elements are a subset of the studied in crystallography or in crystal structure analysis.
The obtained figures can be copied and conveniently colored in order to obtain artistic motifs for panels, icons and tea shirts. The known coordinates allow drawings in diverse scales.
Exercises
1) Use the coordinates to calculate the area of the triangle
2) How many symmetry elements can be recognized in the class 2m?
3) Calculate the coordinates of some vertices to learn about symmetry operations.
Please send your comments.
Table of subjects.