Submit an Article
Become a reviewer
Vol 3
Pages:
321-333
Download volume:
RUS
Research article
Articles

Symmetry of linear sets of curves of the 2nd order (conoprims)

Authors:
E. S. Fedorov
Date submitted:
1912-06-19
Date accepted:
1912-08-05
Date published:
1912-12-01

Abstract

It is clear that the complete set, that is, the fifth of conoprims, has the highest possible symmetry, that is, circular symmetry. The symmetry of quarts is completely determined by the symmetry of one conoprim, because from it it is completely and unambiguously derived. Therefore, in the general case, such a set has a double axis of symmetry and two perpendicular planes of symmetry (rhombic type of symmetry on a plane). In the special case of a parabola, only the plane of symmetry remains (the hemirhombic type of symmetry). The circle has absolutely exceptional symmetry, and therefore there are linear quarts that have circular symmetry. From here we conclude that if, to define a linear quart, we take an arbitrary conoprime and a fivefold axis of symmetry, from which five equal ones are derived, then we obtain a quart with circular symmetry. All the curves contained in it in all positions are arranged in continuous circles of equal elements.

Go to volume 3

References

  1. -

Similar articles

On the issue of determining the useful action of a compressor
1912 A. A. Lebedev
Crystallization of some similar organic cobaltammines
1912 D. N. Artem'ev
Petrographic observations in the vicinity of the Miass plant
1912 A. N. Zavaritskii
Enigmatic facets of quartz
1912 E. S. Fedorov
Several simplified techniques for graphically solving crystallography problems
1912 E. S. Fedorov
On a simple method for measuring the affinity between a solvent and a soluted body
1912 P. P. von-Weymarn