Talk:Homothetic transformation
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Unicode has character ∻ ([1]) on this table: http://www.decodeunicode.org/w3.php?ucHex=2200 . Is this character actually in usage to denote "homothetic"? --Abdull 21:42, 28 May 2006 (UTC)
[edit] Self-contradictory introduction
The first few sentences are as follows:
"In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point A called the origin. The number c by which distances are multiplied is called the dilation factor or similitude ratio. Such a transformation is also called an enlargement.
More generally c can be negative; in that case it not only multiplies all distances by | c | , but also inverts all points with respect to the fixed point."
It is absurd to first state that c is the factor by which distances are multiplied (which implies that c is necessarily >= 0) and then go on to say that "c can be negative" -- which is utterly nonsensical, in that it completely removes any meaning to what the number c is.
Why not get it right the first time? And by the way, the phrase "more generally" in this case does nothing to mitigate the nonsense. The phrase "More generally, c can be negative . . ." makes no sense regardless, since the meaning of "c" is entirely unclear.Daqu 05:38, 14 April 2007 (UTC)
The definition is clear as is. The definition contains two parts: (i) a usual meaning (when c is >=0) and (ii) a natural extension when c < 0. The action of c as described imply the structure of the space it acts on; such as metric, vector, etc. Definitions of concepts need not explicitly define every aspect of the universe they live in. Else, many concept would require infinitely long definitions which is not practical to human epistemic pursuits. —Preceding unsigned comment added by 130.22.48.2 (talk) 14:15, 19 September 2007 (UTC)
