Euclidean geometry is the 2 dimensional study of regular orders of
form. Triangles, circles, length and area, etc, It is the study of
rigid but imaginary objects. Historically, the space in this geometry
was defined in terms of the properties of the objects. The imaginary
objects in this frame are built by ranging dimensionless points into
lines, either curved or straight. If we project Euclidean geometry
onto a Cartesian co-ordinate system, we only have a frame consisting
of rigid objects in a space that allows these objects to exist. This
is nevertheless a unique co-ordinate frame.

Keplerian space differs from Euclidean geometry space. In Keplerian
space we study the kinematic properties that describe regular orders
of form. The orders of form are built by applying motion to an
imaginary point. The moving point is an abstraction that can represent
real world object motion. One can represent Keplerian space by
replacing the static dimensionless point in Euclidean geometry space
with a moving dimensionless point. Projecting Keplerian Space onto a
Cartesian C/S allows us the study of motion, time and space.

Newtonian space differs from Keplerian space in that the imaginary
moving, or dimensionless point, is replaced by a point of substance.
One can insert the quantity mass to replace the Keplerian imaginary
moving point to create the Newtonian coordinate frame. Newtonian space
can be projected onto a Cartesian C/S providing us the study of force
and momentum as well as time and space.

Historically these three frames have been collectively regarded as a
single Euclidean frame. For the purpose of this paper, I have split
the Euclidean space into the three spaces outlined above. To avoid
confusion that might result from the terminology, I will refer to
these frames as Frame 1, Frame 2, and Frame 3, in the body of this
paper. The numbers correspond to the order of presentation.

Frame 1
[2pir/pir^2] is the definitive efficiency ratio of a circle. This
reduces to [2/r]. This shows that the area enclosing efficiency of the
circle, varies with [r]. For my Kepler take, the mathematics consists
of setting a Frame 1 circle [circumference to area] ratio, equal to
the Frame 1 circle [arc to radially enclosed area] ratio. We have:
[2pir/pir^2 = s/(rs/2)], where s is the metric length of the
infinitessimal arc. This reduces to [2/r = 2/r] and shows that the
definitive efficiency ratio is constant for any proportional part of a
given Frame 1 circle. This aspect of the Euclidean circle is very
simple, and rather mundane. It obviously follows from the spatial
symmetry of the circle.

Frame 2
If the planet orbits were perfect spatial circles when viewed in terms
of Frame 1, the orbital velocity and the period of the planets would
also be uniformly constant in Frame 2. In such a case, Kepler's Law of
Areas would be redundant. The law would follow from the property of
the circle itself. The planet orbits when viewed in terms of Frame 1
are ellipses. What we have for these orbits in Frame 2 are "circles in
time" as indicated by Kepler's Law of Areas.

Consider. In this context of Keplerian space, instead of [2pir/pir^2],
we have the period [T/pir^2], as the first efficiency ratio. The
second efficiency ratio is an arc interval [t] of the period [T], with
respect to any radially swept out area accompanying [t]. We have:
[T/pir^2] = [t/(rs/2)], where [t] is the infinitessimal interval, and
[s] is the length of the infinitessimal arc, traveled during that
interval. This reduces to [2t/rs = 2t/rs], and shows that the
definitive efficiency ratio is constant for any proportional part of a
given time-space circle. Kepler called this phenomenon the Law of
Areas.

[2/r = 2/r], defines the proportionally symmetrical, consistent,
efficiency property of the circle in Frame 1. Where [2t/rs = 2t/rs]
represents the equivalent, efficiency ratio in Frame 2. Note the ratio
[t/s]. It is the ratio of time and distance and the inverse to
velocity. So that [t/s = 1/v]. Substituting, we have the simpler
Frame 2 ratio: [2/rv], which is mappable to the Frame 1 ratio, [2/r].

My conclusion here is that [2/rv] and [2/r] are equivalent ratios that
derive from the efficiency properties of a circle from the perspective
of two different C/S's. With respect to the two C/S's so far
described, the Frame 2 conic is equivalent to the Frame 1 conic in
terms of the efficiency ratios: [2/rv and 2/r]. Note that the Frame 2
efficiency ratio applies to any closed conic section that represents
planet orbits. This shows that Kepler's Law of Areas is a least action
function, rather than a special case of angular momentum.

The Repuglicans wasted some 4 years futzing over Bill Clinton's penis.
What made you think they could run the country?

"johnlawrencereed" wrote in message
om...

This shows that Kepler's Law of Areas is a least action
function, rather than a special case of angular momentum.


I didn't read the message, but there doesn't have to be a difference.

"johnlawrencereed" wrote in message
om...
Euclidean geometry is the 2 dimensional study of regular orders of
form.

No - it is the study of the axioms of Euclidian geometry.

Triangles, circles, length and area, etc, It is the study of
rigid but imaginary objects.

Well the axiom of rigidity is not usually specified in Euclid's axioms - but
physically they are assumed to be.

Historically, the space in this geometry
was defined in terms of the properties of the objects. The imaginary
objects in this frame are built by ranging dimensionless points into
lines, either curved or straight. If we project Euclidean geometry
onto a Cartesian co-ordinate system,

Project Euclidian geometry on Cartesian co-ordinate system? That such a
system exists follows form the axioms.

we only have a frame consisting
of rigid objects in a space that allows these objects to exist. This
is nevertheless a unique co-ordinate frame.

It can reside at any point and take any orientation - hardly unique.


Keplerian space differs from Euclidean geometry space. In Keplerian
space we study the kinematic properties that describe regular orders
of form. The orders of form are built by applying motion to an
imaginary point. The moving point is an abstraction that can represent
real world object motion. One can represent Keplerian space by
replacing the static dimensionless point in Euclidean geometry space
with a moving dimensionless point. Projecting Keplerian Space onto a
Cartesian C/S allows us the study of motion, time and space.

What a load of crap. Keplers laws a fully compatible with Newton's.


Newtonian space differs from Keplerian space in that the imaginary
moving, or dimensionless point, is replaced by a point of substance.
One can insert the quantity mass to replace the Keplerian imaginary
moving point to create the Newtonian coordinate frame. Newtonian space
can be projected onto a Cartesian C/S providing us the study of force
and momentum as well as time and space.

What a load of crap. Both Newton an Kepler implicitly or explicitly assume
inertial frames that conform to Euclid's axioms.


Historically these three frames have been collectively regarded as a
single Euclidean frame. For the purpose of this paper, I have split
the Euclidean space into the three spaces outlined above. To avoid
confusion that might result from the terminology, I will refer to
these frames as Frame 1, Frame 2, and Frame 3, in the body of this
paper. The numbers correspond to the order of presentation.

Frame 1
[2pir/pir^2] is the definitive efficiency ratio of a circle.

The efficiency ratio of a circle?

If you actually wish to communicate your ideas I suggest you stick to
standard terminology.

Rest of unintelligible rubbish mercifully snipped.
Bill

"Mark Palenik" wrote in message
...

"johnlawrencereed" wrote in message
om...

This shows that Kepler's Law of Areas is a least action
function, rather than a special case of angular momentum.


I didn't read the message, but there doesn't have to be a difference.



BTW, I still didn't read the message, because it reaked of kookdom, and the
few sentences I did read didn't make much sense, but I'd like to add that
the equal areas isn't a special case of angular momentum. It always holds
true about any point when angular momentum is conserved.

And undoubtedly, if you were to use the Lagrangian to come up with equations
of motion via the least action principle, one of them would be dl/dt = 0
(where l is angular momentum).

"Bill Hobba" wrote in message ...
"johnlawrencereed" wrote in message
om...
Euclidean geometry is the 2 dimensional study of regular orders of
form.

No - it is the study of the axioms of Euclidian geometry.

Triangles, circles, length and area, etc, It is the study of
rigid but imaginary objects.

Well the axiom of rigidity is not usually specified in Euclid's axioms - but
physically they are assumed to be.

Historically, the space in this geometry
was defined in terms of the properties of the objects. The imaginary
objects in this frame are built by ranging dimensionless points into
lines, either curved or straight. If we project Euclidean geometry
onto a Cartesian co-ordinate system,

Project Euclidian geometry on Cartesian co-ordinate system? That such a
system exists follows form the axioms.

we only have a frame consisting
of rigid objects in a space that allows these objects to exist. This
is nevertheless a unique co-ordinate frame.

It can reside at any point and take any orientation - hardly unique.


Keplerian space differs from Euclidean geometry space. In Keplerian
space we study the kinematic properties that describe regular orders
of form. The orders of form are built by applying motion to an
imaginary point. The moving point is an abstraction that can represent
real world object motion. One can represent Keplerian space by
replacing the static dimensionless point in Euclidean geometry space
with a moving dimensionless point. Projecting Keplerian Space onto a
Cartesian C/S allows us the study of motion, time and space.

What a load of crap. Keplers laws a fully compatible with Newton's.

jr writes Your elementary analysis has culminated in your high
reaching conclusion. I make it very easy for ng readers to avoid my
"crap". Just put johnreed in your kill file and niether of us have to
waste our time.

Newtonian space differs from Keplerian space in that the imaginary
moving, or dimensionless point, is replaced by a point of substance.
One can insert the quantity mass to replace the Keplerian imaginary
moving point to create the Newtonian coordinate frame. Newtonian space
can be projected onto a Cartesian C/S providing us the study of force
and momentum as well as time and space.

What a load of crap. Both Newton an Kepler implicitly or explicitly
assume
inertial frames that conform to Euclid's axioms.

jr writes:
Empty your colostomy bag Bill. It is the assumptions that I strive to
eliminate.
Historically these three frames have been collectively regarded as a
single Euclidean frame. For the purpose of this paper, I have split
the Euclidean space into the three spaces outlined above. To avoid
confusion that might result from the terminology, I will refer to
these frames as Frame 1, Frame 2, and Frame 3, in the body of this
paper. The numbers correspond to the order of presentation.

Frame 1
[2pir/pir^2] is the definitive efficiency ratio of a circle.

The efficiency ratio of a circle?

jr writes:
Uh... this is a big one huh Bill? What is it about a circle that is
efficient Bill? Can we,,,, say, use ratios for purposes of scaling? If
this stopped you it is indeed senseless to continue.
(snip to save the space)
jr

"johnlawrencereed" wrote in message
om...
"Bill Hobba" wrote in message
...
"johnlawrencereed" wrote in message
om...
Euclidean geometry is the 2 dimensional study of regular orders of
form.

No - it is the study of the axioms of Euclidian geometry.

Triangles, circles, length and area, etc, It is the study of
rigid but imaginary objects.

Well the axiom of rigidity is not usually specified in Euclid's axioms -
but
physically they are assumed to be.

Historically, the space in this geometry
was defined in terms of the properties of the objects. The imaginary
objects in this frame are built by ranging dimensionless points into
lines, either curved or straight. If we project Euclidean geometry
onto a Cartesian co-ordinate system,

Project Euclidian geometry on Cartesian co-ordinate system? That such a
system exists follows form the axioms.

we only have a frame consisting
of rigid objects in a space that allows these objects to exist. This
is nevertheless a unique co-ordinate frame.

It can reside at any point and take any orientation - hardly unique.


Keplerian space differs from Euclidean geometry space. In Keplerian
space we study the kinematic properties that describe regular orders
of form. The orders of form are built by applying motion to an
imaginary point. The moving point is an abstraction that can represent
real world object motion. One can represent Keplerian space by
replacing the static dimensionless point in Euclidean geometry space
with a moving dimensionless point. Projecting Keplerian Space onto a
Cartesian C/S allows us the study of motion, time and space.

What a load of crap. Keplers laws a fully compatible with Newton's.

jr writes Your elementary analysis has culminated in your high
reaching conclusion. I make it very easy for ng readers to avoid my
"crap". Just put johnreed in your kill file and niether of us have to
waste our time.

Newtonian space differs from Keplerian space in that the imaginary
moving, or dimensionless point, is replaced by a point of substance.
One can insert the quantity mass to replace the Keplerian imaginary
moving point to create the Newtonian coordinate frame. Newtonian space
can be projected onto a Cartesian C/S providing us the study of force
and momentum as well as time and space.

What a load of crap. Both Newton an Kepler implicitly or explicitly
assume
inertial frames that conform to Euclid's axioms.

jr writes:
Empty your colostomy bag Bill. It is the assumptions that I strive to
eliminate.

Thank for reminding me - I forgot how much your drivel gave me the ****s.

Historically these three frames have been collectively regarded as a
single Euclidean frame. For the purpose of this paper, I have split
the Euclidean space into the three spaces outlined above. To avoid
confusion that might result from the terminology, I will refer to
these frames as Frame 1, Frame 2, and Frame 3, in the body of this
paper. The numbers correspond to the order of presentation.

Frame 1
[2pir/pir^2] is the definitive efficiency ratio of a circle.

The efficiency ratio of a circle?

jr writes:
Uh... this is a big one huh Bill? What is it about a circle that is
efficient Bill? Can we,,,, say, use ratios for purposes of scaling? If
this stopped you it is indeed senseless to continue.
(snip to save the space)

What is it about your brain that refuses to learn standard terminology -
probably the same thing that gives me ****s.

Bill

jr

"Bill Hobba" wrote in message
...

"johnlawrencereed" wrote in message
om...
"Bill Hobba" wrote in message
...
"johnlawrencereed" wrote in message
om...
Euclidean geometry is the 2 dimensional study of regular orders of
form.

No - it is the study of the axioms of Euclidian geometry.

Triangles, circles, length and area, etc, It is the study of
rigid but imaginary objects.

Well the axiom of rigidity is not usually specified in Euclid's
axioms -
but
physically they are assumed to be.

Historically, the space in this geometry
was defined in terms of the properties of the objects. The imaginary
objects in this frame are built by ranging dimensionless points into
lines, either curved or straight. If we project Euclidean geometry
onto a Cartesian co-ordinate system,

Project Euclidian geometry on Cartesian co-ordinate system? That such
a
system exists follows form the axioms.

we only have a frame consisting
of rigid objects in a space that allows these objects to exist. This
is nevertheless a unique co-ordinate frame.

It can reside at any point and take any orientation - hardly unique.


Keplerian space differs from Euclidean geometry space. In Keplerian
space we study the kinematic properties that describe regular orders
of form. The orders of form are built by applying motion to an
imaginary point. The moving point is an abstraction that can
represent
real world object motion. One can represent Keplerian space by
replacing the static dimensionless point in Euclidean geometry space
with a moving dimensionless point. Projecting Keplerian Space onto a
Cartesian C/S allows us the study of motion, time and space.

What a load of crap. Keplers laws a fully compatible with Newton's.

jr writes Your elementary analysis has culminated in your high
reaching conclusion. I make it very easy for ng readers to avoid my
"crap". Just put johnreed in your kill file and niether of us have to
waste our time.

Newtonian space differs from Keplerian space in that the imaginary
moving, or dimensionless point, is replaced by a point of substance.
One can insert the quantity mass to replace the Keplerian imaginary
moving point to create the Newtonian coordinate frame. Newtonian space
can be projected onto a Cartesian C/S providing us the study of force
and momentum as well as time and space.

What a load of crap. Both Newton an Kepler implicitly or explicitly
assume
inertial frames that conform to Euclid's axioms.

jr writes:
Empty your colostomy bag Bill. It is the assumptions that I strive to
eliminate.

Thank for reminding me - I forgot how much your drivel gave me the ****s.

Historically these three frames have been collectively regarded as a
single Euclidean frame. For the purpose of this paper, I have split
the Euclidean space into the three spaces outlined above. To avoid
confusion that might result from the terminology, I will refer to
these frames as Frame 1, Frame 2, and Frame 3, in the body of this
paper. The numbers correspond to the order of presentation.

Frame 1
[2pir/pir^2] is the definitive efficiency ratio of a circle.

The efficiency ratio of a circle?

jr writes:
Uh... this is a big one huh Bill? What is it about a circle that is
efficient Bill? Can we,,,, say, use ratios for purposes of scaling? If
this stopped you it is indeed senseless to continue.
(snip to save the space)

What is it about your brain that refuses to learn standard terminology -
probably the same thing that gives me ****s.

Bill


And isn't 2*pi*r/(pi*r^2) just 2/r? For those that may be a little slow,
yes it is. How does 2/r make the circle efficient? If I switch from meters
to millimeters, does the circle become less efficient? Some day I hope to
make a circle with radius zero, 'cause that'd be, like, the most efficient
circle ever!

BTW, the "efficiency ratio", cannot only be written as 2/r (the best way)
and 2*pi*r/(pi*r^2), but also
4*pi*epsilon_naut*gamma^3/(2*pi*r*epsilon_naut*gamma^3) and
4e^(pi*i)hbar^2/(-2hbar^2*r).

I hope that clears some stuff up.

"Mark Palenik" wrote in message
...

"Bill Hobba" wrote in message
...

"johnlawrencereed" wrote in message
om...
"Bill Hobba" wrote in message
...
"johnlawrencereed" wrote in message
om...
Euclidean geometry is the 2 dimensional study of regular orders of
form.

No - it is the study of the axioms of Euclidian geometry.

Triangles, circles, length and area, etc, It is the study of
rigid but imaginary objects.

Well the axiom of rigidity is not usually specified in Euclid's
axioms -
but
physically they are assumed to be.

Historically, the space in this geometry
was defined in terms of the properties of the objects. The
imaginary
objects in this frame are built by ranging dimensionless points
into
lines, either curved or straight. If we project Euclidean geometry
onto a Cartesian co-ordinate system,

Project Euclidian geometry on Cartesian co-ordinate system? That
such
a
system exists follows form the axioms.

we only have a frame consisting
of rigid objects in a space that allows these objects to exist.
This
is nevertheless a unique co-ordinate frame.

It can reside at any point and take any orientation - hardly unique.


Keplerian space differs from Euclidean geometry space. In
Keplerian
space we study the kinematic properties that describe regular
orders
of form. The orders of form are built by applying motion to an
imaginary point. The moving point is an abstraction that can
represent
real world object motion. One can represent Keplerian space by
replacing the static dimensionless point in Euclidean geometry
space
with a moving dimensionless point. Projecting Keplerian Space onto
a
Cartesian C/S allows us the study of motion, time and space.

What a load of crap. Keplers laws a fully compatible with Newton's.

jr writes Your elementary analysis has culminated in your high
reaching conclusion. I make it very easy for ng readers to avoid my
"crap". Just put johnreed in your kill file and niether of us have to
waste our time.

Newtonian space differs from Keplerian space in that the imaginary
moving, or dimensionless point, is replaced by a point of substance.
One can insert the quantity mass to replace the Keplerian imaginary
moving point to create the Newtonian coordinate frame. Newtonian
space
can be projected onto a Cartesian C/S providing us the study of
force
and momentum as well as time and space.

What a load of crap. Both Newton an Kepler implicitly or explicitly
assume
inertial frames that conform to Euclid's axioms.

jr writes:
Empty your colostomy bag Bill. It is the assumptions that I strive to
eliminate.

Thank for reminding me - I forgot how much your drivel gave me the
****s.

Historically these three frames have been collectively regarded as a
single Euclidean frame. For the purpose of this paper, I have split
the Euclidean space into the three spaces outlined above. To avoid
confusion that might result from the terminology, I will refer to
these frames as Frame 1, Frame 2, and Frame 3, in the body of this
paper. The numbers correspond to the order of presentation.

Frame 1
[2pir/pir^2] is the definitive efficiency ratio of a circle.

The efficiency ratio of a circle?

jr writes:
Uh... this is a big one huh Bill? What is it about a circle that is
efficient Bill? Can we,,,, say, use ratios for purposes of scaling? If
this stopped you it is indeed senseless to continue.
(snip to save the space)

What is it about your brain that refuses to learn standard terminology -
probably the same thing that gives me ****s.

Bill


And isn't 2*pi*r/(pi*r^2) just 2/r? For those that may be a little slow,
yes it is. How does 2/r make the circle efficient? If I switch from
meters
to millimeters, does the circle become less efficient? Some day I hope to
make a circle with radius zero, 'cause that'd be, like, the most efficient
circle ever!

Good luck with your quest. Just one suggestion - mind not posting about it
until you have accomplished this marvelous feat?


BTW, the "efficiency ratio", cannot only be written as 2/r (the best way)
and 2*pi*r/(pi*r^2), but also
4*pi*epsilon_naut*gamma^3/(2*pi*r*epsilon_naut*gamma^3) and
4e^(pi*i)hbar^2/(-2hbar^2*r).

I hope that clears some stuff up.

Back when I did my degree in math such concepts were not part of the
syllabus. But then again the institute I attended may have been backward or
part of more advanced courses. So I did a little internet search. Seems
'efficiency ratio' is not a concept usually applied to circle or even conic
sections - http://www.krellinst.org/UCES/archive/resources/conics/.

May I suggest you keep your private terminology just that - private.

Bill

"Mark Palenik" wrote in message ...
"johnlawrencereed" wrote in message
om...

This shows that Kepler's Law of Areas is a least action
function, rather than a special case of angular momentum.


I didn't read the message, but there doesn't have to be a difference.

jr writes
Sorry for the delay. I get an hour on the computer each day and must
ration my time. True. There doesn't have to be a difference and in
fact according to the current paradigm there is none. The quantity
mass is deemed to generate the inverse square laws, which are least
action functions, as well. Its a chicken and egg thing.

The repuglicans wasted some 4 years worrying about Bill Clinton's
penis. What made you think they could run the country?

"Mark Palenik" wrote in message ...
"Mark Palenik" wrote in message
...

"johnlawrencereed" wrote in message
om...

This shows that Kepler's Law of Areas is a least action
function, rather than a special case of angular momentum.


I didn't read the message, but there doesn't have to be a difference.



BTW, I still didn't read the message, because it reaked of kookdom, and the
few sentences I did read didn't make much sense, but I'd like to add that
the equal areas isn't a special case of angular momentum. It always holds
true about any point when angular momentum is conserved.

And undoubtedly, if you were to use the Lagrangian to come up with equations
of motion via the least action principle, one of them would be dl/dt = 0
(where l is angular momentum).

jr writes Yes, if planet-star attractors acted on mass and did not
act on atoms, then all you write is true. But, if the planet attractor
acts on our constituent atoms and not on our mass, then the entire
paradigm must be re-evaluated. All atoms fall to the earth at the same
rate. Mass can be isolated as a conserved quantity because of this.

There are kook theories everywhere. They use the math to show how
nothing falls and everything expands... In fact, the math can show
just about anything if used in one least action scheme or another.
Witness Ptolemy, Gel Mann and Minkowski. Often the language the quacks
use is minimally different from the accepted duck language used by the
above.

The planet-star attractors act on atoms, not on mass. To show this I
have to reach far, far, down the line. Its a major job. I plug slowly
at it.

The repuglican wasted some 4 years worrying about Bill Clinton's
penis. What made you think they could run the country?