Last Update 03/ 11/ 2005
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The conic section can either be an ellipse with the semi major axis a and semi minor axis b either a circumference when a and b are equal. The original conic section is drown in blue with a and b as explained above, including the coordinates cx and cy of its center and the rotation angle of the curve in degrees named beta, measured from the positive branch of the cartesian x axis in clockwise sense. The symmetry operators can be enabled by a click on the respective button on the right side of the figure, as described in table 1. The same sequence and orientation of operators was used in the study of triangles and straight lines.
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 |
| A | renews the conical section |
The symbol 2m defines one of the 32 crystal classes (or point groups) in crystallography. The coordinates of the cursor are displayed in the status bar on the bottom of the browser to identify interesting points.
The electrons of atoms can occupy circular or elliptical regions according to the old theory of Niels Bohr (1885-1962) and Arnold Sommerfeld (1868-1951).
Exercises
1) Calculate the area of the conic section.
2) How many symmetry elements can be recognized in class 2m?
3) Calculate the coordinate shift and the respective rotation angle necessary in order to have the ellipse centered on the origin and with its major axis parallel with the y axis.
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Table of subjects.