| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 62.1 | | METOO::YARBROUGH | | Mon Apr 30 1984 15:58 | 13 |
| Since my dictionary defines a sphere as,
"A three-dimensional surface, all points of which are equidistant from a
fixed point", the opposite of a sphere must be:
1) not 3-d
2) not a surface
3) not empty, but with a finite number of points at different distances
from a fixed point.
I suggest "two points in different E-spaces" as the opposite of a sphere.
(Only if they are in different spaces can no n-dimensional sphere be found
that passes through all of them!)
Lynn Yarbrough
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| 62.2 | | TURTLE::GILBERT | | Mon Apr 30 1984 21:53 | 4 |
| Any plane figure.
Of all objects placed on an inclined plane, the sphere minimizes the slope
required for it to start it rolling. A plane figure maximizes the slope.
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| 62.3 | | TURTLE::WIECHMANN | | Tue May 01 1984 16:16 | 3 |
|
Also, a sphere maximizes the ratio of volume to surface area.
Wouldn't a plane figure minimize the ratio of volume to surface area?
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| 62.4 | | AURORA::HALLYB | | Wed May 02 1984 17:51 | 5 |
| I take the point-set-theoretical approach: a non-sphere of radius r
is the set of all (x,y,z) satisfying:
2 2 2 2
x + y + z \= r
|
| 62.5 | | TURTLE::GILBERT | | Fri May 04 1984 14:27 | 4 |
| Another sphere!
If the "opposite" is a reflection in a plane, we get another sphere.
If the "opposite" is a reflection through a point, we get another sphere.
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| 62.6 | Postnikov spaces | BERN01::ADDOR | | Tue Apr 07 1987 11:08 | 10 |
| What do you mean by "the opposite"? Is the dual the same as the
opposite? Then it is clear what "the opposite" of a sphere is.
It is well known that a CW-space is built by spheres and attaching
mappings. The dual of a CW-space is a Postnikov tower which is built
by Postnikov spaces and Postnikov invariants (the dual of the attaching
maps). Thus, the opposite of a sphere is a Postnikov space!
Regards, Peter
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| 62.7 | What about the fish? | BUFFER::SWARTZ | In the Castle Aaaaaaaaaaaa... | Thu Jun 08 1989 16:23 | 6 |
| Has noone considered a topological view to this question? In other
words, what do you get when you turn the surface of a sphere *inside-out*,
topographically. I think this has been something of a curiosity for
quite some time.
-- kms
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| 62.8 | What's a Postnikov space? | AITG::DERAMO | Daniel V. {AITG,ZFC}:: D'Eramo | Thu Jun 08 1989 19:06 | 6 |
| re .6
What are CW-spaces, Postnikov towers, Postnikov spaces,
Postnikov invariants, attaching maps, and duals? :-)
Dan
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| 62.9 | And what does "perestroika" have to do with Postnikov | POOL::HALLYB | The Smart Money was on Goliath | Sat Jun 10 1989 22:21 | 1 |
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| 62.10 | | ARTMIS::MILLSH | Is there any Tea on this spaceship? | Thu Aug 03 1989 12:26 | 5 |
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Re .8:
I don't know, but they sound good!
HRM
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| 62.11 | Hyperbolic plane | NOEDGE::HERMAN | Franklin B. Herman DTN 291-0170 PDM1-1/J9 | Wed Sep 12 1990 17:31 | 12 |
|
From the differential geometric point of view, the spheres can
be chararactized as the complete surfaces having constant positive
curvature.
So my choice of "opposite" would be the complete surfaces of constant
negative curvature. These are precisely the hyperbolic planes/disks of
non-Euclidean Bolyai-Lobachevskian geometry.
-Franklin
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