Point Reflection Group
The composition of two point reflections is a translation. Specifically, point reflection at p followed by point reflection at q is translation by the vector 2(q – p).
The set consisting of all point reflections and translations is Lie subgroup of the Euclidean group. It is a semidirect product of Rn with a cyclic group of order 2, the latter acting on Rn by negation. It is precisely the subgroup of the Euclidean group that fixes the line at infinity pointwise.
In the case n = 1, the point reflection group is the full isometry group of the line.
Read more about this topic: Point Reflection
Famous quotes containing the words point, reflection and/or group:
“All our Concord waters have two colors at least; one when viewed at a distance, and another, more proper, close at hand.... Walden is blue at one time and green at another, even from the same point of view. Lying between the earth and the heavens, it partakes of the color of both.”
—Henry David Thoreau (1817–1862)
“With some people solitariness is an escape not from others but from themselves. For they see in the eyes of others only a reflection of themselves.”
—Eric Hoffer (1902–1983)
“No group and no government can properly prescribe precisely what should constitute the body of knowledge with which true education is concerned.”
—Franklin D. Roosevelt (1882–1945)