In a circle, any diameter is an axis of symmetry, so technically a cirle should have infinitely many axes of symmetry.
This got me thinking about the axes of symmetry of straight lines. A line segment obviously has only one axis of symmetry, but what about an unbounded infinite straight line?
Does it have one axis of symmetry (seems unlikely), infinitely many, none at all? Does it depend on the kind of Geometry we're talking about?
On
A bound line has 2 symmetries. The line itself and a perpendicular line intersecting the midpoint.
An unbound line with a centre point has 2 symmetries. The line itself and a perpendicular line intersecting the centre.
An unbound line without a centre point has 1 symmetry. The line itself. The perpendicular symmetry is undefined.
If the line represents an infinitely large circle, circles have infinite symmetries.
A line segment has two axes of symmetry: the line containing it, and the line perpendicular to it through its midpoint. A line has infinitely many: itself, and every line perpendicular to it.