Circular reasoning
Posted by Glen in on 23 Apr. 2003, 3:31 pm
The “solution” to this puzzle has been bothering me. It states that “the circle is NOT the only shape with constant diameter,” but I say the circle IS the only [2D] shape with constant diameter! Lots of other shapes can satisfy the “manhole” problem, but only the circle has constant diameter — defined as “a chord passing through the center of a figure or body” (Webster). The problem with any non-circular manhole shape is that its constant-length “diameters” do not all pass through the geometric center. Because this puzzle was posted in a .edu domain and due to the fact that I’ve seen similar claims elsewhere on sciency websites, I feel the need to set the record straight. Please correct me if I’m missing something.
Sorry, I just had to get that off my chest.
Comment from EYC on 23 Apr. 2003, 4:47 pm :
They get away with a technicality - when people think of ’shape’, they assume a regular shape. Stoopid people… I think that you should write to them and threaten them with Danica McKellar (whatever happened to her, anyway?).
Comment from Glen on 23 Apr. 2003, 4:55 pm :
No, but that’s not the issue. Their shapes, no matter how odd (no pun intended, since the number of sides must be odd), do just fine as manhole covers. The issue is their use of the word “diameter”. So I’m catching them on a technicality.
Comment from EYC on 23 Apr. 2003, 6:47 pm :
Okay, I see. Regardless, they’re whack.
Comment from Mike on 24 Apr. 2003, 2:03 am :
I assume this was brought on by this review?
This sounds like a good read actually… I may pick it up.
Comment from Kanishka on 24 Apr. 2003, 7:48 am :
What about a 2-d torus? Or is that just a variation on a theme of circle?
Comment from Em on 24 Apr. 2003, 9:22 am :
Gwendolyn, did you click on “Danica McKellar’s Website” on the solution page? Some bad things happened, and I may no longer be employed….
Comment from Nick on 24 Apr. 2003, 10:34 am :
You are absolutely correct. The general definition for diameter is “A line passing from side to side of any body through the centre” (ref. OED). The ‘definiton’ they’re working with is false.
Comment from Glen on 24 Apr. 2003, 12:26 pm :
Mike: Damn, you’re good.
Kanishka: I should have been more specific and specified a 2D convex shape.
Em: Yes, and the results were unfortunate.
Nick: That’s what I’m saying!