СИММЕТРИИ ПОЛИПОЛЯРНОЙ КООРДИНАЦИИ
Abstract
The polypolar system of coordinates formed by a family of multifocal lemniscates
is introduced, the full gang of which focuses forms its structural beginning. The arbitrary
point of a plane has, as well as in a classical polar system of coordinates, polypolar
coordinates: metric ¥, and angular ϕ, being functions of polar coordinates of rather
each of focuses. The focal representation of the curve form by multifocal lemniscates allows
to adjust a polypolar system of coordinates so that a metric component corresponded
to the form of the given curve. Lemniscate and its focal structure have the same group of
symmetries. The symmetries of polypolar coordination, and also curvilinear symmetries
on multifocal lemniscates are considered
is introduced, the full gang of which focuses forms its structural beginning. The arbitrary
point of a plane has, as well as in a classical polar system of coordinates, polypolar
coordinates: metric ¥, and angular ϕ, being functions of polar coordinates of rather
each of focuses. The focal representation of the curve form by multifocal lemniscates allows
to adjust a polypolar system of coordinates so that a metric component corresponded
to the form of the given curve. Lemniscate and its focal structure have the same group of
symmetries. The symmetries of polypolar coordination, and also curvilinear symmetries
on multifocal lemniscates are considered
References
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