| Topic: |
Science > Physics |
| User: |
"Don1" |
| Date: |
14 Oct 2005 07:46:36 PM |
| Object: |
Pi = circumference/diameter |
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
Don
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| User: "Dirk Van de moortel" |
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| Title: Re: Pi = circumference/diameter |
15 Oct 2005 04:25:01 AM |
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"Don1" <dcshead@charter.net> wrote in message news:1129337196.364858.89470@g44g2000cwa.googlegroups.com...
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
That is much better already. Mati's Sears Tower seems to
have done its job.
But your statement stills needs some patching. Someone
should try to explain that a ratio *is* a numerical value.
You could just as well have said:
Since the product of 5 and 10 is greater than 20, the
value 5x10 is greater than 20.
Dirk Vdm
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| User: "odin" |
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| Title: Re: Pi = circumference/diameter |
14 Oct 2005 09:18:44 PM |
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Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
Lobachevsky would not agree with you. Lets see a proof of this idiotic
conjecture of yours. Ooops. I forgot... Don1 never proves anything. He just
pulls crap from out of his *****, puts it out on public display, and sits back
with pride. You never get anything right. Idiot.
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| User: "Uncle Al" |
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| Title: Re: Pi = circumference/diameter |
15 Oct 2005 10:08:29 AM |
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Don1 wrote:
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
Hey Dumb Donny *****, (circumference)/(radius) is largest
(unbounded - is that large enough for you, Dumb Donny *****?) on a
hyperbolic plane. Idiot.
Hey Dumb Donny *****, there are **eight** fundamental
simply-connected geometric 3-manifolds with compact quotients: E^3,
S^3, H^3, S^2 x R, H^2 x R, SL_2, Nil, and Sol. Wiggle your Dumb
Donny ***** ***** and tell us what limiting (circumference)/(radius)
is for each of them.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Androcles Androcles@ MyPlace.org" |
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| Title: Re: Pi = circumference/diameter |
15 Oct 2005 01:47:49 PM |
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"Uncle Al" <UncleAl0@hate.spam.net> wrote in message
news:43511B6D.AD618554@hate.spam.net...
[snip crap]
If you follow threads from March 1999 when Androcles posted the
orginal bug in relativity you will see an increasingly hysterical and
vicious collusion of bitter little people who deny the process of
scientific inquiry and are utterly rabid about the disclosure being
done. They literally drool foaming spit.
They don't care about the results. They scream, threaten, and attempt
assassination to prevent the disclosure from ever taking place. What
do they fear? They fear their own exposure as the small people they
are.
The critic trolls and idiot vituperators have lost. Androcles
has all his ducks in a row - raw theory, support, calculation, public
disclosure, and no army. Not even the final result remains.
LITLE PEOPLE LIKE UNCLE SNIPCRAP HATE THAT and will
throw any tantrum and invent any lie to prevent the inevitable.
They cannot prevent the inevitable. The disclosure proceeds and the
final knowledge will be had. A null result is the historic Gold
Standard
of performance, but the truth is a Platinum result. The net result is
the
trivially reproducible falsification of Special Relativity in existing
mathematics
all over the world. Professionals call this "science." We don't care
what
god-fearing witch burners and wog haters call it.
Credit for a successful disclosure cannot be stolen by an unsuccessful
rogue
researcher.
It's happening. Let the universe decide.
Androcles.
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| User: "Uncle Al" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 02:01:03 PM |
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Androcles wrote:
[snip crap]
Androcles <=>Jämmerlichkeit
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Androcles Androcles@ MyPlace.org" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 05:02:07 PM |
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"Uncle Al" <UncleAl0@hate.spam.net> wrote in message
news:4352A36F.3A9CCE7F@hate.spam.net...
| Androcles wrote:
| [snip crap]
|
| Androcles <=>Jämmerlichkeit
|
| --
| Uncle Al
| http://www.mazepath.com/uncleal/
| (Toxic URL! Unsafe for children and most mammals)
| http://www.mazepath.com/uncleal/qz.pdf
Auntie Alice <=> Wanker
Schwartz is *****.
The Chinese told him "*****, you DUMB *****"
They were right.
Androcles
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| User: "Jim Spriggs" |
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| Title: Re: Pi = circumference/diameter |
15 Oct 2005 02:02:58 PM |
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Don1 wrote:
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
The definition [*] of pi has got nothing to do planes, Euclidean or
otherwise.
[* There is more than one definition, but all the good ones are the same
in this respect.]
--
I don't know who you are Sir, or where you come from,
but you've done me a power of good.
.
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| User: "David R Tribble" |
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| Title: Re: Pi = circumference/diameter |
15 Oct 2005 04:25:20 PM |
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Don1 wrote:
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
Greatest, compared to what?
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| User: "Don1" |
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| Title: Re: Pi = circumference/diameter |
15 Oct 2005 06:43:37 PM |
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David R Tribble wrote:
Don1 wrote:
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
Greatest, compared to what?
The value of the ratio of a circle's circumference, divided by its
radius, is generally considered to be pi, and its quotient equals about
3.14159; which is greatest in a flat plane Euclidean surface.
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| User: "Don1" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 06:28:47 AM |
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Don1 wrote:
David R Tribble wrote:
Don1 wrote:
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
Greatest, compared to what?
The value of the ratio of a circle's circumference, divided by its
radius, is generally considered to be pi, and its quotient equals about
3.14159; which is greatest in a flat plane Euclidean surface.
Make that:
The value of the ratio of a circle's circumference, divided by its
_diameter_ , is generally considered to be pi, and its quotient equals
about
3.14159; which is greatest in a flat plane Euclidean surface.
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| User: "" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 06:35:19 AM |
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"I once tried to watch the filming of an episode of Baywatch on Redondo
Beach. A policeman came over and told me I was standing too close to
the action. Later I learned that it was just a Baywatch actor in a
policeman's costume."
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| User: "PD" |
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| Title: Re: Pi = circumference/diameter |
17 Oct 2005 09:00:09 AM |
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Don1 wrote:
Don1 wrote:
David R Tribble wrote:
Don1 wrote:
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
Greatest, compared to what?
The value of the ratio of a circle's circumference, divided by its
radius, is generally considered to be pi, and its quotient equals about
3.14159; which is greatest in a flat plane Euclidean surface.
Make that:
The value of the ratio of a circle's circumference, divided by its
_diameter_ , is generally considered to be pi, and its quotient equals
about
3.14159; which is greatest in a flat plane Euclidean surface.
The statement only makes sense when you are talking about a *unit*
circle, and even then it is wrong, as the wonderful doily example
illustrates. There are *two* ways to make a doily wrong, and the two
results that you get indicate that the value of pi is not an extremal
value of anything. If anything, it is a *central* value.
PD
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| User: "Don1" |
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| Title: Re: Pi = circumference/diameter |
17 Oct 2005 10:33:27 AM |
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PD wrote:
Don1 wrote:
Don1 wrote:
David R Tribble wrote:
Don1 wrote:
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
Greatest, compared to what?
The value of the ratio of a circle's circumference, divided by its
radius, is generally considered to be pi, and its quotient equals about
3.14159; which is greatest in a flat plane Euclidean surface.
Make that:
The value of the ratio of a circle's circumference, divided by its
_diameter_ , is generally considered to be pi, and its quotient equals
about
3.14159; which is greatest in a flat plane Euclidean surface.
The statement only makes sense when you are talking about a *unit*
circle, and even then it is wrong, as the wonderful doily example
illustrates. There are *two* ways to make a doily wrong, and the two
results that you get indicate that the value of pi is not an extremal
value of anything. If anything, it is a *central* value.
PD
Comparing doilies to Euclidean planes is asinine: Doilies have
thickness, Euclidean planes don't, and the best pressed doilies will
still have some thickness and some wrinkles.
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| User: "PD" |
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| Title: Re: Pi = circumference/diameter |
17 Oct 2005 11:02:08 AM |
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Don1 wrote:
PD wrote:
Don1 wrote:
Don1 wrote:
David R Tribble wrote:
Don1 wrote:
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
Greatest, compared to what?
The value of the ratio of a circle's circumference, divided by its
radius, is generally considered to be pi, and its quotient equals about
3.14159; which is greatest in a flat plane Euclidean surface.
Make that:
The value of the ratio of a circle's circumference, divided by its
_diameter_ , is generally considered to be pi, and its quotient equals
about
3.14159; which is greatest in a flat plane Euclidean surface.
The statement only makes sense when you are talking about a *unit*
circle, and even then it is wrong, as the wonderful doily example
illustrates. There are *two* ways to make a doily wrong, and the two
results that you get indicate that the value of pi is not an extremal
value of anything. If anything, it is a *central* value.
PD
Comparing doilies to Euclidean planes is asinine: Doilies have
thickness, Euclidean planes don't, and the best pressed doilies will
still have some thickness and some wrinkles.
Ah, so the buckling of the doily is caused by its *thickness* and not
due to using a greater or lesser number of stitches around the
perimeter than what pi would suggest? Ah.
PD
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| User: "Ron Shepard" |
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| Title: Re: Pi = circumference/diameter |
18 Oct 2005 12:54:32 AM |
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In article <1129563207.753524.162410@g49g2000cwa.googlegroups.com>,
"Don1" <dcshead@charter.net> wrote:
Comparing doilies to Euclidean planes is asinine: Doilies have
thickness, Euclidean planes don't, and the best pressed doilies will
still have some thickness and some wrinkles.
A line drawn with a pencil has a thickness, and the paper on which
it is drawn has thickness, but that does not prevent you from
learning Euclidian geometry with a pencil, paper, straight edge, and
compass. This is the way we have been doing it for 23 centuries.
In a similar way, the thickness of a doily does not prevent you from
learning about curvature in R^n space. In both cases, it is a
matter of applying "common sense", which these days, isn't very
common at all.
$.02 -Ron Shepard
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| User: "David R Tribble" |
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| Title: Re: Pi = circumference/diameter |
17 Oct 2005 03:46:18 PM |
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Don1 wrote:
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
David R Tribble wrote:
Greatest, compared to what?
Don1 wrote:
The value of the ratio of a circle's circumference, divided by its
radius, is generally considered to be pi, and its quotient equals about
3.14159; which is greatest in a flat plane Euclidean surface.
Make that:
The value of the ratio of a circle's circumference, divided by its
_diameter_ , is generally considered to be pi, and its quotient equals
about 3.14159; which is greatest in a flat plane Euclidean surface.
Greatest, compared to what? Other non-Euclidean spaces?
If so, then the ratio C/d is greatest in hyperbolic spaces, and
least in spherical spaces.
But pi = 3.14159265... = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ...,
period.
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| User: "Androcles Androcles@ MyPlace.org" |
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| Title: Re: Pi = circumference/diameter |
17 Oct 2005 07:29:39 PM |
|
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"David R Tribble" <david@tribble.com> wrote in message
news:1129581978.045171.26640@g14g2000cwa.googlegroups.com...
| Don1 wrote:
| >> Scince the ratio of a circle's circumference divided by its radius
is
| >> greatest in a Euclidean plane, the numerical value, or quotient,
must
| >> be greatest there.
| >
|
| David R Tribble wrote:
| >> Greatest, compared to what?
| >
|
| Don1 wrote:
| >> The value of the ratio of a circle's circumference, divided by its
| >> radius, is generally considered to be pi, and its quotient equals
about
| >> 3.14159; which is greatest in a flat plane Euclidean surface.
| >
| > Make that:
| > The value of the ratio of a circle's circumference, divided by its
| > _diameter_ , is generally considered to be pi, and its quotient
equals
| > about 3.14159; which is greatest in a flat plane Euclidean surface.
|
| Greatest, compared to what? Other non-Euclidean spaces?
| If so, then the ratio C/d is greatest in hyperbolic spaces, and
| least in spherical spaces.
|
| But pi = 3.14159265... = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ...,
| period.
|3.142594
3.140593
(the 999th and 1000th terms)
Androcles.
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| User: "Robert Low" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 03:32:03 AM |
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Don1 wrote:
The value of the ratio of a circle's circumference, divided by its
radius, is generally considered to be pi, and its quotient equals about
3.14159; which is greatest in a flat plane Euclidean surface.
Ech. If you want to define pi this way, it is *half* the ratio
of the circumference to the radius, in the limit as the radius
tends to zero. Otherwise 'pi' is always strictly less than
3.14159.... on a surface of positive curvature, and always
strictly greater than that on a surface of negative curvature.
But in the limit of small radius, it's always the same as
it is on the Euclidean plane.
.
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| User: "John Christiansen" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 04:59:32 AM |
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"Robert Low" <mtx014@coventry.ac.uk> skrev i en meddelelse
news:3rehdgFisreuU1@individual.net...
Don1 wrote:
The value of the ratio of a circle's circumference, divided by its
radius, is generally considered to be pi, and its quotient equals about
3.14159; which is greatest in a flat plane Euclidean surface.
Ech. If you want to define pi this way, it is *half* the ratio
of the circumference to the radius, in the limit as the radius
tends to zero. Otherwise 'pi' is always strictly less than
3.14159.... on a surface of positive curvature, and always
strictly greater than that on a surface of negative curvature.
But in the limit of small radius, it's always the same as
it is on the Euclidean plane.
That requires calculus, Don does not believe in that.
.
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| User: "Don1" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 07:09:07 AM |
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Lettuce, turnip and start this thread over again:
For most practical purposes, the ratio of a circle's circumference,
divided by its Diameter is about 3.14159, and is greatest in a Eulidean
flat plane.
The exact value has been carried out many more decimal places, and a
lot of time has been spent doing it. Just as a lot of time is being
wasted on the calculus, there are more important things about physics
that should be sought, than extreme accuracy.
Just because computers can be programmed for virtually unlimited
precision, does not make the old adage "garbage in, garbage out" any
less true.
We've got to get to the roots of the mysteries remaining.
Don
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| User: "Androcles Androcles@ MyPlace.org" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 08:09:55 AM |
|
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"Don1" <dcshead@charter.net> wrote in message
news:1129464547.639188.118860@z14g2000cwz.googlegroups.com...
| Lettuce, turnip and start this thread over again:
|
| For most practical purposes, the ratio of a circle's circumference,
| divided by its Diameter is about 3.14159, and is greatest in a
Eulidean
| flat plane.
Ok...
| The exact value has been carried out many more decimal places, and a
| lot of time has been spent doing it. Just as a lot of time is being
| wasted on the calculus, there are more important things about physics
| that should be sought, than extreme accuracy.
Whoa... easy up... One man's time wasted is another man's time well
spent.
\pi isn't a "thing about physics", it's "a thing about mathematics".
|
| Just because computers can be programmed for virtually unlimited
| precision, does not make the old adage "garbage in, garbage out" any
| less true.
Ok... So your garbage above is still garbage to me, even if it's
pearls of wisdom to you. <shrug>
| We've got to get to the roots of the mysteries remaining.
Which mysteries are you talking about, natural or mathematical?
Androcles
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| User: "Don1" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 09:22:30 AM |
|
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Androcles wrote:
"Don1" <dcshead@charter.net> wrote in message
news:1129464547.639188.118860@z14g2000cwz.googlegroups.com...
| Lettuce, turnip and start this thread over again:
|
| For most practical purposes, the ratio of a circle's circumference,
| divided by its Diameter is about 3.14159, and is greatest in a
Eulidean
| flat plane.
Ok...
| The exact value has been carried out many more decimal places, and a
| lot of time has been spent doing it. Just as a lot of time is being
| wasted on the calculus, there are more important things about physics
| that should be sought, than extreme accuracy.
Whoa... easy up... One man's time wasted is another man's time well
spent.
\pi isn't a "thing about physics", it's "a thing about mathematics".
|
| Just because computers can be programmed for virtually unlimited
| precision, does not make the old adage "garbage in, garbage out" any
| less true.
Ok... So your garbage above is still garbage to me, even if it's
pearls of wisdom to you. <shrug>
| We've got to get to the roots of the mysteries remaining.
Which mysteries are you talking about, natural or mathematical?
Androcles
BOTH!
.
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| User: "Androcles Androcles@ MyPlace.org" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 10:30:29 AM |
|
|
"Don1" <dcshead@charter.net> wrote in message
news:1129472550.642028.4130@g43g2000cwa.googlegroups.com...
| Androcles wrote:
| > "Don1" <dcshead@charter.net> wrote in message
| > news:1129464547.639188.118860@z14g2000cwz.googlegroups.com...
| > | Lettuce, turnip and start this thread over again:
| > |
| > | For most practical purposes, the ratio of a circle's
circumference,
| > | divided by its Diameter is about 3.14159, and is greatest in a
| > Eulidean
| > | flat plane.
| >
| > Ok...
| >
| > | The exact value has been carried out many more decimal places, and
a
| > | lot of time has been spent doing it. Just as a lot of time is
being
| > | wasted on the calculus, there are more important things about
physics
| > | that should be sought, than extreme accuracy.
| >
| >
| > Whoa... easy up... One man's time wasted is another man's time well
| > spent.
| > \pi isn't a "thing about physics", it's "a thing about mathematics".
| >
| > |
| > | Just because computers can be programmed for virtually unlimited
| > | precision, does not make the old adage "garbage in, garbage out"
any
| > | less true.
| >
| > Ok... So your garbage above is still garbage to me, even if it's
| > pearls of wisdom to you. <shrug>
| >
| >
| > | We've got to get to the roots of the mysteries remaining.
| >
| > Which mysteries are you talking about, natural or mathematical?
| > Androcles
|
| BOTH!
One is not a mystery, except on a personal level. Not everyone can
understand
mathematics. I can explain much, but I can't understand for you.
Natural mysteries are a little different.
No single person is responsible for the design and operation of a modern
air-liner, pilots do not fully understand jet engines AND electronics
AND
aerodynamics AND hydraulics AND passenger psychology AND navigation.
Fortunately they do not need to.
If you have a mystery in my own area of expertise I may be able to help,
but I'm not a chemist, biologist, psychologist or geologist, although I
now a little of each. Which mystery are you interested in?
Androcles.
.
|
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| User: "Dirk Van de moortel" |
|
| Title: Re: Pi = circumference/diameter |
16 Oct 2005 10:40:53 AM |
|
|
"Androcles" <Androcles@ MyPlace.org> wrote in message news:pmu4f.129229$RW.110341@fe2.news.blueyonder.co.uk...
"Don1" <dcshead@charter.net> wrote in message
news:1129472550.642028.4130@g43g2000cwa.googlegroups.com...
| Androcles wrote:
[snip]
| > Which mysteries are you talking about, natural or mathematical?
| > Androcles
|
| BOTH!
One is not a mystery, except on a personal level. Not everyone can
understand
mathematics. I can explain much, but I can't understand for you.
Androcles can explain calculations:
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/FALSE.html
Androcles can explain groups:
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/AndroGroups.html
Androcles can explain limits:
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Limit.html
Androcles can explain equations:
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SetSolve2.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Persuasive.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/AndroDistri.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Pythagoras.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ToothlessBite....
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Competent.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/UseTrans.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Sheesh.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SetSolve.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/DivZero.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Think.html
Androcles can explain square roots:
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/STILL.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/CanSpecify.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Nearly.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Quadratic.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/GrowUp.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Tautology.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Material.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/GIVEN.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PythagoRescue....
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SqrtRev.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/NegSqrt.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SqrtAnswers.html
Androcles can explain exclusive ors:
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Gibberish.html
Androcles can explain partial differential equations:
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PartialDiff.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PartialDiff2.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PartialDiff3.html
Dirk Vdm
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| User: "Uncle Al" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 02:04:36 PM |
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Androcles wrote:
[snip crap]
Androcles <=> Jämmerlichkeit
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Androcles Androcles@ MyPlace.org" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 05:01:59 PM |
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"Uncle Al" <UncleAl0@hate.spam.net> wrote in message
news:4352A444.321FAFAD@hate.spam.net...
| Androcles wrote:
| [snip crap]
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| Androcles <=> Jämmerlichkeit
| --
| Uncle Al
| http://www.mazepath.com/uncleal/
| (Toxic URL! Unsafe for children and most mammals)
| http://www.mazepath.com/uncleal/qz.pdf
Auntie Alice <=> Wanker
Schwartz is *****.
The Chinese told him "*****, you DUMB *****"
They were right.
Androcles
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| User: "Ron Shepard" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 10:29:27 AM |
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In article <1129464547.639188.118860@z14g2000cwz.googlegroups.com>,
"Don1" <dcshead@charter.net> wrote:
For most practical purposes, the ratio of a circle's circumference,
divided by its Diameter is about 3.14159, and is greatest in a Eulidean
flat plane.
My grandmother used to crochet doilies. I tried it a few times, and
mine never looked as good as hers. There are two mistakes that you
can make when you do this. One mistake is to not include enough
thread as you work around the outside edge; when you do this the
doily cups up into the shape of a bowl and doesn't lay flat. The
other mistake is to leave too much thread as you work around the
outside edge; when you do this, the edge ruffles up and doesn't lay
flat. If the doily represents a surface, then the first case
corresponds to a positive curvature in which the circumference is
less than pi times the diameter, and the second case corresponds to
negative curvature in which the circumference is more than pi times
the diameter.
If the surface is smooth, then in the mathematical limit of zero
diameter, the ratio of circumference/diameter will approach the
value of pi; on a small enough scale, everything looks flat, and
this is why classical Euclidian geometry has proven so useful over
time even though we live on the curved surface of the planet (and at
lease locally we live in in a 3D space with positive curvature).
But if the surface is not smooth, then that ratio can approach any
value. Consider, for example, a cone; in this case, the
circumference is a constant ratio to the diameter, but that ratio
can be any value less than pi that you choose. Larger values
correspond to "flatter" cones, and smaller values correspond to
"pointier" cones. There are also ruffled doily like shapes that
correspond to constant ratios larger than pi, and those constant
ratios can be any value. In these cases, the point of the cone is
not smooth. There are singularities in 3D space that correspond to
cones, but I don't know if there are singularities in 3D space that
correspond to ruffled doilies.
I think that 50 to 150 years ago, everyone had common everyday
experience about things like crocheted doilies and coiled ropes that
correspond to abstract mathematical ideas. This allowed previous
generations to understand these abstract things at an intuitive
level. This used to be called "common sense". These days, kids
spend their time watching music videos on TV, and they never get a
chance to develop this intuition with their everyday experience. A
surprising number of people these days no longer seem to have that
kind of "common sense".
$.02 -Ron Shepard
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| User: "Al Zenner" |
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| Title: Re: Pi = circumference/diameter |
16 Oct 2005 10:38:03 AM |
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Robert Low <mtx014@coventry.ac.uk> wrote in news:3rehdgFisreuU1
@individual.net:
Don1 wrote:
The value of the ratio of a circle's circumference, divided by its
radius, is generally considered
Skip the word "generally"
to be pi, and its quotient equals about
3.14159; which is greatest in a flat plane Euclidean surface.
Ech. If you want to define pi this way,
http://wordnet.princeton.edu/perl/webwn?s=pi
The definition of pi is fixed, it isn't a matter of choice.
it is *half* the ratio
of the circumference to the radius,
You'll kick yourself over this so no one else really needs to.
in the limit as the radius
tends to zero. Otherwise 'pi' is always strictly less than
3.14159.... on a surface of positive curvature, and always
strictly greater than that on a surface of negative curvature.
Time to kick yourself again.
Be careful who you pick to follow through (perhaps into) the morass.
snip
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| User: "Eric Gisse" |
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| Title: Re: Pi = circumference/diameter |
14 Oct 2005 10:14:11 PM |
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Don1 wrote:
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
This has been known for two thousand years. What the ***** is your
point?
Don
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| User: "Don1" |
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| Title: Re: Pi = circumference/diameter |
15 Oct 2005 05:21:31 AM |
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Eric Gisse wrote:
Don1 wrote:
Scince the ratio of a circle's circumference divided by its radius is
greatest in a Euclidean plane, the numerical value, or quotient, must
be greatest there.
This has been known for two thousand years. What the ***** is your
point?
Don
Just because you've known it for two thousand years, doesn't mean
everybofy knows it; even today.
A lot of people fell for Einsteins curved space, with straight world
lines that are parallel, and criss-cross in curved space. In Euclidean
space two parallel straight lines will never cross.
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