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curvature reversal
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Jon
Mar 30, 2012, 1:09:00 PM3/30/12
to
The radius of a sphere increases to infinity until its surface becomes a
perfect plane. Then the curvature reverses and the sphere converges on
another center.
http://mypeoplepc.com/members/jon8338/math/id44.html
perfect plane. Then the curvature reverses and the sphere converges on
another center.
http://mypeoplepc.com/members/jon8338/math/id44.html
biofilm
Mar 31, 2012, 12:45:39 AM3/31/12
to
"Jon" <intr...@bellaire.tv> wrote in message
news:DfqdnZ4d1bo3dejS...@earthlink.com...
Frederick Williams
Mar 31, 2012, 11:05:36 AM3/31/12
to
Jon wrote:
>
> The radius of a sphere increases to infinity until its surface becomes a
> perfect plane. Then
'Then'?
>
> The radius of a sphere increases to infinity until its surface becomes a
> perfect plane. Then
> the curvature reverses and the sphere converges on
> another center.
>
> http://mypeoplepc.com/members/jon8338/math/id44.html
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
Curlytop
Apr 1, 2012, 3:09:24 PM4/1/12
to
biofilm set the following eddies spiralling through the space-time
continuum:
It starts growing again, but the outside is now on the inside. There again,
it could vanish up its own imaginary axis.
--
ξ: ) Proud to be curly
Interchange the alphabetic letter groups to reply
continuum:
it could vanish up its own imaginary axis.
--
ξ: ) Proud to be curly
Interchange the alphabetic letter groups to reply
Ken Pledger
Apr 1, 2012, 4:54:00 PM4/1/12
to
In article <DfqdnZ4d1bo3dejS...@earthlink.com>,
Picturing things like that doesn't prove anything, but it can be
quite helpful to the imagination. No less a person than Kepler
visualized conics as a continuous family, in his "Ad Vitellionem
Paralipomena" (1604).
Ken Pledger.
"Jon" <intr...@bellaire.tv> wrote:
> The radius of a sphere increases to infinity until its surface becomes a
> perfect plane. Then the curvature reverses and the sphere converges on
> another center....
> The radius of a sphere increases to infinity until its surface becomes a
> perfect plane. Then the curvature reverses and the sphere converges on
Picturing things like that doesn't prove anything, but it can be
quite helpful to the imagination. No less a person than Kepler
visualized conics as a continuous family, in his "Ad Vitellionem
Paralipomena" (1604).
Ken Pledger.
Jon
Apr 1, 2012, 7:14:24 PM4/1/12
to
What is the 4-dimensional equivalent to 3-dimensional volume?
How many gallons of water does it take to fill up a:
*hypercube
*hypersphere
*hyper-parallelpiped
and what are the formulas for their volumes?
2-space requires 2 basis vectors for constructions such as A & B (x,y) &
(-y,x)
3-space requires 3 basis vectors for construction such as A, B & AxB
(x,y,0), (-y,x,0), (0,0,z)
4-space requires 4 basis vectors for construction such as A, B, C & the 4x4
determinant of (A,B,C)
If a 4-dimensional plane collapses into 3-dimensions, does it form a volume
rather than a surface? What is the transformation equations between the two
that show this?
How many gallons of water does it take to fill up a:
*hypercube
*hypersphere
*hyper-parallelpiped
and what are the formulas for their volumes?
2-space requires 2 basis vectors for constructions such as A & B (x,y) &
(-y,x)
3-space requires 3 basis vectors for construction such as A, B & AxB
(x,y,0), (-y,x,0), (0,0,z)
4-space requires 4 basis vectors for construction such as A, B, C & the 4x4
determinant of (A,B,C)
If a 4-dimensional plane collapses into 3-dimensions, does it form a volume
rather than a surface? What is the transformation equations between the two
that show this?
Jon
Apr 1, 2012, 8:37:36 PM4/1/12
to
The particle accelerators celebrated by science to promise new discoveries;
may blow up half of the world by creating a black hole bomb by forcing two
particles to occupy the same space at the same time. The scientists play
down the risks but they are not immune to making mistakes. What is our
world to them, a giant laboratory for experiment?
may blow up half of the world by creating a black hole bomb by forcing two
particles to occupy the same space at the same time. The scientists play
down the risks but they are not immune to making mistakes. What is our
world to them, a giant laboratory for experiment?
Jon
Apr 2, 2012, 12:18:41 AM4/2/12
to
Notice that if your vision were everywhere normally inward from the inside
surface of the outer circle looking at the blue curve, the perspective would
be the same as the undefiled pure rotating red parabola as seen from the
center of the circle. http://mypeoplepc.com/members/jon8338/math/id40.html
(the outer circle is merely (0,0,0) expanded into a circle, while on its way
rotating its environment by 180 degrees). This occurs by virtue of the
transformation equations,
P'(x',y') = r*P(x,y)/|P(x,y)| - P(x,y)
P(x,y) = r*P'(x',y')/|P'(x',y')| - P'(x',y')
surface of the outer circle looking at the blue curve, the perspective would
be the same as the undefiled pure rotating red parabola as seen from the
center of the circle. http://mypeoplepc.com/members/jon8338/math/id40.html
(the outer circle is merely (0,0,0) expanded into a circle, while on its way
rotating its environment by 180 degrees). This occurs by virtue of the
transformation equations,
P'(x',y') = r*P(x,y)/|P(x,y)| - P(x,y)
P(x,y) = r*P'(x',y')/|P'(x',y')| - P'(x',y')
biofilm
Apr 2, 2012, 11:01:58 AM4/2/12
to
"Curlytop" <pvstownse...@ntlworld.com> wrote in message
news:jla957$cs8$1...@dont-email.me...
> biofilm set the following eddies spiralling through the space-time
> continuum:
>
>>
>> "Jon" <intr...@bellaire.tv> wrote in message
>> news:DfqdnZ4d1bo3dejS...@earthlink.com...
>>> The radius of a sphere increases to infinity until its surface becomes a
>>> perfect plane. Then the curvature reverses and the sphere converges on
>>> another center.
>>>
>>> http://mypeoplepc.com/members/jon8338/math/id44.html
>>
>> what happens when the radius is 0 ?
>
> It starts growing again, but the outside is now on the inside. There
> again,
> it could vanish up its own imaginary axis.
> --
nope,
> continuum:
>
>>
>> "Jon" <intr...@bellaire.tv> wrote in message
>> news:DfqdnZ4d1bo3dejS...@earthlink.com...
>>> The radius of a sphere increases to infinity until its surface becomes a
>>> perfect plane. Then the curvature reverses and the sphere converges on
>>> another center.
>>>
>>> http://mypeoplepc.com/members/jon8338/math/id44.html
>>
>> what happens when the radius is 0 ?
>
> It starts growing again, but the outside is now on the inside. There
> again,
> it could vanish up its own imaginary axis.
> --
At r = 0, it becomes a point, with no surface, no volume.
a good learning lesson for you.
-Azba Zuggith
Michael Stemper
Apr 2, 2012, 12:37:09 PM4/2/12
to
In article <weydnXQIn6vMfOXS...@earthlink.com>, "Jon" <intr...@bellaire.tv> writes:
>What is the 4-dimensional equivalent to 3-dimensional volume?
Hyper-volume.
>What is the 4-dimensional equivalent to 3-dimensional volume?
>How many gallons of water does it take to fill up a:
>
>*hypercube
make this clear to you.
Let's start with one dimension: a line segment. You can measure its
length in meters (or yards if that's what turns your crank). Pretty
straight-forward.
Now, we'll jump up from one dimension to two dimensions. We'll move
that line segment sideways, so that it sweeps out a square, which is
a nice, simple, two-dimensional figure. Asking "how long is a square?"
isn't really a meaningful question. There are some lengths associated
with a square, such as the length of an edge (side), the length of a
diagonal, or the length of its perimeter.
Asking "how long a piece of string does it take for a square?" doesn't
make sense. What might make sense in its place would be "how big a piece
of paper does it take to cover a square?" would make sense. That is, of
course, the *area* of a square.
Now, we'll move the square parallel to itself, so that it sweeps out
a cube. This bumps us up to three dimensions. A cube, like a square,
has some lengths associated with it: edge, diagonal of a face, diagonal
of the cube. It also has some areas associated with it. Primary among
these are the area of a single face, and the area of its entire surface.
So, "how long a piece of string does a cube take?" and "how big a piece
of paper does a cube take?" aren't really useful questions. But, one
could meaningfully ask "how much water does it take to fill a cube?"
Going from three to four dimensions is a little bit tricky, since we
can't visualize moving a cube parallel to itself in all three dimensions.
But, even if we can't see it, we can reason about it.
A hypercube is going to have many lengths and areas associated with it.
So, we can't ask "how long a piece of string?" or "how big a piece of
paper?" It's also going to have different volumes, so we can't really
answer a question like "how many gallons of water?"
What it does have that's unambiguous is its hypervolume. A line with
length s obviously has a length of s. A square with edges of length
s will have an area of s^2 (s squared). A cube with edges of length
s will have a volume of s^3. A hypercube with edges of length s will
have a hypervolume of _______.
For your further amusement:
A point has 1 vertex (because it *is* a vertex).
A line segment has 1 edge (because it is an edge) and 2 vertices
(its endpoints).
A square has 1 face (because it is a face), 4 edges (its sides), and
4 vertices (its corners).
A cube has 1 volume, 6 faces (look at a die), 12 edges, and 8 vertices.
A hypercube has:
___ hypervolumes
___ volumes
___ faces
___ edges
___ vertices
(It might help to arrange this all in a table.)
--
Michael F. Stemper
#include <Standard_Disclaimer>
The FAQ for rec.arts.sf.written is at:
http://www.leepers.us/evelyn/faqs/sf-written
Please read it before posting.
sanebow
Apr 2, 2012, 2:07:56 PM4/2/12
to
news:weydnXQIn6vMfOXS...@earthlink.com...
> What is the 4-dimensional equivalent to 3-dimensional volume?
>
> How many gallons of water does it take to fill up a:
>
> *hypercube
do you have 3 or 4 dimensional Water ?
>
> How many gallons of water does it take to fill up a:
>
> *hypercube
Shmuel Metz
Apr 2, 2012, 4:46:53 PM4/2/12
to
In <jlckjl$nd$1...@dont-email.me>, on 04/02/2012
--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply to
domain Patriot dot net user shmuel+news to contact me. Do not
reply to spam...@library.lspace.org
at 04:37 PM, mste...@walkabout.empros.com (Michael Stemper) said:
>A hypercube has:
>___ hypervolumes
1 hypervolume
>A hypercube has:
>___ hypervolumes
--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply to
domain Patriot dot net user shmuel+news to contact me. Do not
reply to spam...@library.lspace.org
Frederick Williams
Apr 3, 2012, 7:29:37 AM4/3/12
to
Curlytop wrote:
>
> biofilm set the following eddies spiralling through the space-time
> continuum:
>
> >
> > "Jon" <intr...@bellaire.tv> wrote in message
> > news:DfqdnZ4d1bo3dejS...@earthlink.com...
> >> The radius of a sphere increases to infinity until its surface becomes a
> >> perfect plane. Then the curvature reverses and the sphere converges on
> >> another center.
> >>
> >> http://mypeoplepc.com/members/jon8338/math/id44.html
> >
> > what happens when the radius is 0 ?
>
> It starts growing again, but the outside is now on the inside. There again,
> it could vanish up its own imaginary axis.
Coxeter [1] writes
>
> biofilm set the following eddies spiralling through the space-time
> continuum:
>
> >
> > "Jon" <intr...@bellaire.tv> wrote in message
> > news:DfqdnZ4d1bo3dejS...@earthlink.com...
> >> The radius of a sphere increases to infinity until its surface becomes a
> >> perfect plane. Then the curvature reverses and the sphere converges on
> >> another center.
> >>
> >> http://mypeoplepc.com/members/jon8338/math/id44.html
> >
> > what happens when the radius is 0 ?
>
> It starts growing again, but the outside is now on the inside. There again,
> it could vanish up its own imaginary axis.
Long before the time of Gauss, it was suggested by J. H. Lambert
(1728-1777) that, if a non-Euclidean plane exists it should
resemble a sphere of radius i. [...] Its full significance did
not appear till Minkowski (1864-1909) discovered the geometry of
space-time, which provided a geometrical basis for Einstein's
special theory of relativity.
[1] Introduction to geometry, Wiley, 2nd edition,
near end of section 16.5.
Jon
Apr 4, 2012, 9:24:59 AM4/4/12
to
Here is my treatment of zero and infinity. They are interchangeable and
equivalent.
http://jons-math.bravehost.com/zeroinfinity.html
equivalent.
http://jons-math.bravehost.com/zeroinfinity.html
Pfs...@aol.com
Apr 4, 2012, 10:10:52 AM4/4/12
to
Jon
Apr 5, 2012, 1:14:23 PM4/5/12
to
....as if you knew math?
I doubt it
wrote in message news:vilon7d35t1i7qdd7...@4ax.com...
I doubt it
wrote in message news:vilon7d35t1i7qdd7...@4ax.com...
Jon
Apr 5, 2012, 1:16:54 PM4/5/12
to
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
wrote in message news:vilon7d35t1i7qdd7...@4ax.com...
Pfs...@aol.com
Apr 5, 2012, 2:30:30 PM4/5/12
to
>I doubt it\
Have a Phd -- Alabama --- 1964
Have a Phd -- Alabama --- 1964
Jon
Apr 9, 2012, 4:45:51 AM4/9/12
to
at x=hell, y=an orange
at x=anxiety, y=a shovel
.... these instances and more too in the futility of numbers and their
irrelevancy to describe any goddamned fucking thing at all:
http://jons-math.bravehost.com/zeroinfinity.html
Jon
at x=anxiety, y=a shovel
.... these instances and more too in the futility of numbers and their
irrelevancy to describe any goddamned fucking thing at all:
http://jons-math.bravehost.com/zeroinfinity.html
Jon
Jon
Apr 9, 2012, 5:27:36 AM4/9/12
to
I developed this a little further and seem to have hit on something. It all
goes to show that no matter from what angle you look at a tree, the tree is
still a tree; don't let anything fool you. I have also annihilated the
utility of numbers to describe anything at all. Since a zero can be an
infinity, a 7 can be a 47 and so on and so forth. I think I've attained my
objective for the weekend
"Jon" wrote in message
news:JoKdnUBMCb5dPB_S...@earthlink.com...
goes to show that no matter from what angle you look at a tree, the tree is
still a tree; don't let anything fool you. I have also annihilated the
utility of numbers to describe anything at all. Since a zero can be an
infinity, a 7 can be a 47 and so on and so forth. I think I've attained my
objective for the weekend
"Jon" wrote in message
news:JoKdnUBMCb5dPB_S...@earthlink.com...
Jon
Apr 9, 2012, 11:43:34 AM4/9/12
to
River of pure water of life
River of crude oil of death
pure water is used as drink for life
oil is made from compacted death
silver shiny
camouflaged black
I own the two: BOTH.
left tit, right tit: try and change that.
River of crude oil of death
pure water is used as drink for life
oil is made from compacted death
silver shiny
camouflaged black
I own the two: BOTH.
left tit, right tit: try and change that.
Pfs...@aol.com
Apr 12, 2012, 9:48:38 AM4/12/12
to
On Mon, 9 Apr 2012 05:27:36 -0400, "Jon" <intr...@bellaire.tv> wrote:
>I developed this a little further and seem to have hit on something. It all
>goes to show that no matter from what angle you look at a tree, the tree is
>still a tree; don't let anything fool you. I have also annihilated the
>utility of numbers to describe anything at all. Since a zero can be an
>infinity, a 7 can be a 47 and so on and so forth. I think I've attained my
>objective for the weekend
>
This makes absolutely no sense at all. That stuff you're snorting
>I developed this a little further and seem to have hit on something. It all
>goes to show that no matter from what angle you look at a tree, the tree is
>still a tree; don't let anything fool you. I have also annihilated the
>utility of numbers to describe anything at all. Since a zero can be an
>infinity, a 7 can be a 47 and so on and so forth. I think I've attained my
>objective for the weekend
>
is going to finish the brainn scrambling that has obviously started.!
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