If a plane has more than 2 principal axes ?

1. Aug 18, 2013

phydis

" If a plane has more than 2 principal axes (axes of symmetry ) through a point, then every axis through that point must be a principal axis "

I can understand above statement regarding a circle, but square also has more than 2 principal axes, how can it be true for every axis of a square or a regular hexagon ?

someone please explain this..

Thank you!

Last edited: Aug 18, 2013
2. Aug 18, 2013

bahamagreen

A "plane" has an infinite number of axes of symmetry through every point.

When you write "plane", I think you must mean more... plane figures, planer bound shapes, polygons?

Since you mention examples of a circle, square, and regular hexagon, if you mean such as that, I'm not sure what the idea means.

For further example, an equilateral triangle has three axes through the center point that are clearly symmetric (bilateral symmetry), but other lines through that midpoint do not show any symmetry.

Are you sure the statement is meant to apply to figures? The statement reads like a mangled and circular definition of a plane itself, or some kind of corollary concerning non-Euclidean geometry...?

What is the context?

3. Aug 18, 2013

SteamKing

Staff Emeritus