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Posts from Academy of Sciences of Heroesland

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In reply to Злобный Ящур
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Offline Hermit
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#1006
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Evil Lizard
No, of course not. But he believes that the surface of the Earth is a one-connected, closed, compact, two-dimensional manifold without an edge, homeomorphic to a two-dimensional sphere. :D:D:D
So, that's what I've been living on! :eek:
Всё не так плохо как Вы думаете. Всё намного хуже!
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Offline Небо
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#1007
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Evil Lizard
No, of course not. But he believes that the surface of the Earth is a one-connected closed compact two-dimensional manifold without an edge, homeomorphic to a two-dimensional sphere.:D:D:D
Well, it's spherical. So, do you believe it or not?
Небо – мольбы не ждёт
Небо – угроз не слышит
Небо – ведёт особый счёт
Небо – тебя найдёт

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Offline Злобный Ящур
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#1008
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Ment
I would call it a three-dimensional sphere after all.
No, a three-dimensional sphere is our Universe. More precisely, I heard somewhere that the Universe is a three-dimensional sphere. :D They say Perelman even calculated its "area" (volume). :eek:

Added 2 minutes ago
Ment
on this very sphere we have 2D, but without 3D such a sphere simply cannot exist...
Of course. Therefore, our three-dimensional sphere-Universe is located somewhere in 4D space. ;) Be that as it may, an ordinary sphere is a manifold of dimension 2, not 3. :p

Added 3 minutes ago
Nebо
Zlobny YashchurNo, of course not. But he believes that the surface of the Earth represents a one-connected closed compact two-dimensional manifold without edges, homeomorphic to a two-dimensional sphere. :D:D:D
Well, spherical. So do you believe it or not?Nope. The Earth has the shape of a body whose surface is a one-connected closed compact two-dimensional manifold without edges, homeomorphic to a two-dimensional sphere. This is 100% KNOWLEDGE! :smile08:

Added 1 minute ago
Hermit
So this is what I live on! :eek:
And what did you think you lived on? :D

Ничто не возникает из ничего и ничто не пропадает бесследно.
Если где-то чего-то убудет, то в другом месте добавится.
(Закон сохранения).

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Offline Ment
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#1009
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No, a three-dimensional sphere is our Universe. More precisely, I heard somewhere that the Universe is a three-dimensional sphere.
A four-dimensional one is a sphere that has volume but is described using four dimensions.
This, by the way, is not necessarily true. It is one of two versions derived from General Relativity. The second is that the Universe is an open, infinite space, described by three dimensions (that is, exactly how we see it with our ordinary perspective).
However, an ordinary sphere is a manifold of dimension 2, not 3.
Well, yes, but I don't like this terminology. It is obvious that closure cannot be ensured in two dimensions. Here, what is more important is how such a manifold looks to an observer, and not how it looks to objects inside itself, in my humble opinion. Although I don't argue with the dimension of the manifold; the terminology is accurate here, but with the dimension of the figure – well, yes))
 

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Offline Hermit
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#1010
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Evil Lizard
Did you think it would be something else?:D
It is a geometric locus of points in space equidistant from a given point.
Всё не так плохо как Вы думаете. Всё намного хуже!
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Offline Драккошка
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#1011
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But the Earth is not round, not spherical, and not even ball-shaped; it is actually a geoid.
А, вот почему.

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Online now Heroist
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#1012
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The land is not land.

Whatever
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Offline Небо
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#1013
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Drakkosha
geoid.
Geoid.
Небо – мольбы не ждёт
Небо – угроз не слышит
Небо – ведёт особый счёт
Небо – тебя найдёт

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Online now Arandor
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#1014
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Goreit

Be strong. Believe
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Online now Ple-Sen
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#1015
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Now he’s even started mowing under the planets...
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Offline Злобный Ящур
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#1016
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Ment
The second universe is an open, infinite space described by three dimensions (that is, exactly how we see it with our ordinary perspective).
The first explains expansion (if you take a camera from a ball, draw something on it, and start inflating it, the drawn object will begin to increase, uniformly in all directions, and the larger it is, the faster it increases). All that remains is to understand who the guy with the pump is... And how can expansion be explained using the second one?
Ment
Well, yes, but I don't like that terminology. Obviously, it is impossible to ensure closure in two dimensions. Here, it is more important how such a manifold looks to the observer, and not how it looks to the objects inside itself, in my humble opinion. Although I don't argue about the dimension of the manifold; the terminology is accurate there, but with the dimension of the figure – yes)).
And regarding this, what do you say?:)
Hermit
A geometric locus of points in space equidistant from a given point.
Yes, the surface of the Earth is exactly a sphere. There are no mountains or depressions on it...:rolleyes:
Drakkosha
But the Earth is not round, not spherical, and not even ball-shaped; it is a geoid.
And not even a geoid. It simply resembles it more accurately than other named surfaces.

Added 2 minutes ago
Nebo
Georoid.
Nebooid.
Arandor
Goreit
Arandoroid.

Ничто не возникает из ничего и ничто не пропадает бесследно.
Если где-то чего-то убудет, то в другом месте добавится.
(Закон сохранения).

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Offline Небо
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#1017
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Eviloid Yaschuroid.
Небо – мольбы не ждёт
Небо – угроз не слышит
Небо – ведёт особый счёт
Небо – тебя найдёт

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Online now Ple-Sen
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#1018
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Reptiloid.
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Offline Драккошка
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#1019
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But a geoid, by definition, has the shape of the Earth, right?
А, вот почему.

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Offline Ment
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#1020
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The first explains expansion (if you take a camera from a ball, draw something on it, and start inflating it, the drawn object will begin to increase, and it will increase equally in all directions, and the larger it is, the faster it increases). All that remains is to figure out who that guy with the pump is... And how can we explain expansion using the second one?
Just the initial impulse from the Big Bang.
What do you think about this?
Isn't that what it's saying, or am I hallucinating? Anyway, I looked it up in the wiki n-dimensional sphere
Obviously, for the three-dimensional case, we have a sphere in 3D, not in 4D space.
But a geoid, by definition, has the shape of the Earth, right?
A geoid is a dynamic figure; its definition changes over time (with each volcanic eruption, for example)
 

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