Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: On redefining reflective symmetry
Replies: 0

 Hagen Schwaß Posts: 8 Registered: 8/1/14
On redefining reflective symmetry
Posted: Aug 1, 2014 4:27 PM

With out loss of generality reflective symmetry of a 3D object is understood as equality of a plane projection of the object to a rotational transformation of that plane with respect to an "reflection" axis about an angle of PI.

In reality a reflection requires two planes. One is a view plane, the other is the reflection plane. For the sake of simplicity let the object be not rotational symmetric in any plane projection. The object equals under transformation of the reflection plane to itself on the view plane in any way, if the reflectionplane is parallel to the view plane. It may equal itself under transformation of the reflection plane if the reflection if orthogonal to the view plane. Considering the understanding of reflectional symmetry as mentioned above, still those transformations are trivial.

"Reflectional" symmetry as mentioned above is not stand alone dependent on a reflection plane! It one and only is denpendent on equality of a rotational transformation of the view plane with respect to an so called "reflection" axis under the angle of PI to the unrotated view plane. There is never a dependency on a reflection transformation.

Best regards
Hagen Schwaß