Re: Clean Object Class Design -- Circle/Ellipse

nospam_at_newsranger.com (Mikito Harakiri) wrote in <lMBb7.660$NJ6.1929_at_www.newsranger.com>:
>1. {(1234), (3421), (2134), (4312)} is a subgroup of octic (dihedral)
>group. Yet, we want to subclass square (octic group) from rectangle (or
>{(1234), (3421), (2134), (4312)}.

This is all pretty basic stuff, but I'm not an algebra or geometry guy, so this has been a while.

If we number the corners of a rectangle as follows:

1 2

4 3

then I think the symmetry group of that non-square rectangle is isomorphic with

H={(1)(2)(3)(4), (14)(23),(12)(34)}

and that of the square with

G={(1)(2)(3)(4), (14)(23), (12)(34), (1234), (13)(24), (1432)}

and H is a subgroup of G.

Are you saying that since every rectangle is a square you would intuitively expect it to be the other way around?

>2. The other way to express the same idea is to say that subclasses
>inherit symmetries of their ancestors. In that sence we vew subsetting
>on the set of symmetries, not the universe. Reals is simply more
>symmetrical class than integers. (Although, Mark is questioning
>practicality of such conclusion;-)

I'm not sure what symmetries on the reals/integers you are thinking of.

Regards,

Martijn Received on Mon Aug 06 2001 - 23:16:20 CEST