[QUOTE=Shalmanese]
What would you call the intersection of two edges, like in the roof of this picture?
It doesn’t seem to fit the definition of either an edge or a corner.
[/QUOTE]
The centre of that roof would seem to me to be the intersection of 6 edges (2 edges being the lines at the tops of the ridges, which continue through the point, and 4 edges being the lines at the bottom of the valleys going up to that centre point). I’d call it a corner.
[QUOTE=Really Not All That Bright]
The main face of a cylinder isn’t a plane, though.
[/QUOTE]
Well, maybe not exactly. But how is that relevant? If you took a cube and inflated it a bit so that the faces all curved slightly outward, thus failing to be exact planes, I think the natural propensity would still be to distinguish between 8 corners and 12 edges.
[QUOTE=Indistinguishable]
Well, maybe not exactly. But how is that relevant? If you took a cube and inflated it a bit so that the faces all curved slightly outward, thus failing to be exact planes, I think the natural propensity would still be to distinguish between 8 corners and 12 edges.
[/QUOTE]
Good point. If we went by the OP’s definition then a cube would have 12 corners.
[QUOTE=Really Not All That Bright]
The main face of a cylinder isn’t a plane, though.
[/QUOTE]
Substitute “surface” for “plane”, as the definition in the OP includes “surface”.
[QUOTE=Indistinguishable]
Well, maybe not exactly. But how is that relevant? If you took a cube and inflated it a bit so that the faces all curved slightly outward, thus failing to be exact planes, I think the natural propensity would still be to distinguish between 8 corners and 12 edges.
[/QUOTE]
Right, but mathematically they’d no longer technically be corners as they wouldn’t be the confluences of 3+ planes. In reality, they’re still basically pointy bits that we’d look at and say, “Corners!” (new expletive!), but they wouldn’t really be corners.
Just like a kid looks at a zebra and says, “Stripey horse!”, even though a zebra isn’t a horse. Even the poster Zebra isn’t a horse.
*yes, I am actively campaigning for the title of worst analogist (anologizer?) ever - why do you ask?
[QUOTE=Santo Rugger]
If you called them corners, what would you call the part on a cube where three planes meet, since you’d be calling the edges (where two planes meet) of the cube “corners”?
[/QUOTE]
Well, according to OED…
[QUOTE=Concise OED]
corner
• noun 1 a place or angle where two or more sides or edges meet.
[/QUOTE]
…the edges, or places where two planes meet, are, in fact, corners.
[QUOTE=Hampshire]
Good point. If we went by the OP’s definition then a cube would have 12 corners.
[/QUOTE]
If the planes of a cube were considered two at a time, there are 18 corners.
Well, also according to OED…
bolding mine
This seems a more accurate description of the are being described.
“the position at which two lines, surfaces, or edges meet and form an angle”. Therefore, it seems to me that each edge where the top and bottom circles meet the plane curve can be described as corners.
Wrong. You’re thinking of a “cylinder” as if it had some thickness. A mathematical cylinder has none.
[QUOTE=Really Not All That Bright]
Right, but mathematically they’d no longer technically be corners as they wouldn’t be the confluences of 3+ planes.
[/QUOTE]
Only if you adopt a definition of a corner as the confluence of 3+ planes (with this meaning exact planes, not mere surfaces). But my whole point is that this is a silly definition to adopt, at least if our goal is to characterize the intuitive concept of a corner. Nothing in math compels this definition; math is flexible, it can handle all kinds of definitions.
So, to quote wolfstu, who got it so right that it’s a wonder this thread needs to go on:
[QUOTE=wolfstu]
In math, most everything is a matter of definitions, and definitions are generally only valid insofar as they are useful.
[/quote]
[QUOTE=maroci]
“the position at which two lines, surfaces, or edges meet and form an angle”. Therefore, it seems to me that each edge where the top and bottom circles meet the plane curve can be described as corners.
Wrong. You’re thinking of a “cylinder” as if it had some thickness. A mathematical cylinder has none.
[/QUOTE]
I’m not even sure what you mean by this. What did he say that invoked thickness?
[QUOTE=hajario]
Let’s say an ant is walking along the length of a cylindar and comes to the end. If he then goes around and starts to walk across one of the caps, wouldn’t you say that the ant had turned a corner?
[/QUOTE]
Only if he admitted he had become powerless over alcohol.
Seems to me Wolfstu nailed it, and with superb clarity. Bravo, Sir.
IMO, the LSLGuy Linguistic Uncertainty Principal applies here & quoting duelling dictionary entries attempting to define technical terms is pointless.
After that, all we can bicker about is the colloquial use of the terms “edge” and “corner” when spoken by a probably-not-very-bright 3rd grade teacher speaking to typical 8 year-olds.
YMMV.
[QUOTE=maroci]
“the position at which two lines, surfaces, or edges meet and form an angle”. Therefore, it seems to me that each edge where the top and bottom circles meet the plane curve can be described as corners.
Wrong. You’re thinking of a “cylinder” as if it had some thickness. A mathematical cylinder has none.
[/QUOTE]
I’m not sure what you mean by this either. But note that it is correct to refer as a “cylinder” to the solid, as opposed to the surface (of no thickness) bounding that solid, which would be a cylindrical surface. cite
And all of the preceeding posts just prove why the Oval Office is a pain in the ass to vacuum.
