Über ebene axialsymmetrische Punktmengen

Summary

The principal results of the present inquiries are: If a plane quantity of points “M” has a finite number of symmetrals “n”, which intersect in a point “S”, these symmetrals form a regular fascicle of straight lines, with an angleπ/n of two subsequent symmetrals. If “α” is the angle between two straight lines with the intersection point “S”, you may or may not supplement them to a regular fascicle of symmetrals of a quantity of points “M”, by adding a finite number of straight lines, according as “α” represents a rational or irrational multiple of 2π. If the angle “α” of two symmetrals of “M” with the intersection point “S” is an irrational multiple of 2π, there will be to every straight line “g” through “S” a symmetral of “M”, which comprises with “g”, a small angle of the size you may choose. If “M” is closed, then in this case every straight line “g” through “S” will be a symmetral of “M”.

The symmetrals of a limited quantity of points will intersect in an exact point.