Quote:
|
Originally Posted by Sam5
Quote:
|
Originally Posted by Ian Goddard
If a set of points placed at the intersections on a square grid around a central point expand uniquely from that central point n distance per unit of time, the grid structure initially defined by those points will not be maintained (get some graph paper and see). On the other hand, what I described is the case where the points expand apart and the grid structure is maintained, and in that case there is no center of expansion; the expansion behavior favors no point.
|
What you are talking about is a big flat expanding Euclidean plane. What you’ve described still has a center.
If you turn it into 3-D, you’ve got a big expanding cube, with sharp edges on the outside and eight corner points. Even an expanding cube has a center.
If you use polar graph paper, the graph paper still has a center. |
Actually only you've stipulated known edges. And you've switched your counter from saying an expanding finite space must have a "center of expansion" to the irrefutable "it must have a center" -- as if that counters something I said. I believe my last reply provides an actual definition for your initial counter about a
center of expansion that differentiates such from no center of expansion.