Register | Sign In


Understanding through Discussion


EvC Forum active members: 65 (9164 total)
3 online now:
Newest Member: ChatGPT
Post Volume: Total: 916,903 Year: 4,160/9,624 Month: 1,031/974 Week: 358/286 Day: 1/13 Hour: 1/0


Thread  Details

Email This Thread
Newer Topic | Older Topic
  
Author Topic:   Spherical Issues
Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 7.6


Message 2 of 301 (465842)
05-11-2008 2:31 AM
Reply to: Message 1 by IamJoseph
05-11-2008 1:24 AM


IaJ, I'm going to say this in the nicest way I possibly can:
You don't know what you're talking about. A 3rd grade child has a better grasp of nuclear physics than you do of this very simple topic.
So, here's an actual example for you, since you can't seem to work with abstracts:
What is the latitude and longitude of the center of the surface of the Earth? Not the coordinates of the core; what is the latitude and longitude of the center of the surface only?
Is the center of the surface at a point on the equator? The North or South Pole? Chicago Illinois? A random point in the Atlantic?
What is the location of the center of the surface, and what is your reasoning for choosing that specific location?

This message is a reply to:
 Message 1 by IamJoseph, posted 05-11-2008 1:24 AM IamJoseph has replied

Replies to this message:
 Message 4 by IamJoseph, posted 05-11-2008 3:09 AM Rahvin has replied
 Message 5 by lyx2no, posted 05-11-2008 3:23 AM Rahvin has not replied

Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 7.6


Message 18 of 301 (465936)
05-11-2008 10:13 PM
Reply to: Message 4 by IamJoseph
05-11-2008 3:09 AM


The 'surface' is an abstract term, is my point. It's center is thus only in the abstract center of an abstract surface.
The surface of the Earth is not abstract. You're sitting on it, right this very second (unless you live under the sea, in orbit, in an airplane, or in a mine).
Stop equivocating. Either provide the latitude and longitude of the center of the surface of the Earth, or admit that you were wrong. There are no other options.
I agree this is basic 101 logic, and its deficiency has nothing to do with my lack of undertsnading.
Quite to the contrary. If you cannot comprehend of such a simple thing as the fact that the surface of a sphere has no center, then the problem most definitely is your understanding.
Let's try something similar:
A ray is a geometric term referring to a line segment that has a beginning and no end. In other words, this:
*--------------------------->
is a ray. The * signifies the beginning, and the -> refers to an infinite progression in the other direction.
Tell me, IaJ, since "all things have a center," what is the center of this ray? Feel free to simple insert the word "center" into the ray wherever you think the center is.
quote:
What is the location of the center of the surface, and what is your reasoning for choosing that specific location?
What 'location' - your question is an abstract one, because it is based on an abstract surface?! Here, the ony correct answer is, the location of the 'surface' is in the centre of that 'surface'; no location need be pointed to here.
You aren't even making sense. "The location of the surface is in the center of the surface? What? So the location of the surface of my skin is in the center of my body? You must be insane.
If you think you're making sense, you're insane.
The surface of the Earth is not abstract. it is a physical thing, and you are resting on it right this very second.
This is not an abstract question, so stop backpedaling and give us an answer. What is the latitude and longitude of the center of the surface of the Earth? What is your reason for choosing this location?
The centre of a string xyz long = xyz divided by half of xyz.
That definition works for a line segment only, where there are defined "ends." A sphere has no defined end. A ray has only one defined end. A line is infinite in both directions. A plane extends infinitely in two entire dimensions. Where are the centers of these geometric objects?

This message is a reply to:
 Message 4 by IamJoseph, posted 05-11-2008 3:09 AM IamJoseph has replied

Replies to this message:
 Message 20 by IamJoseph, posted 05-11-2008 10:28 PM Rahvin has replied
 Message 21 by IamJoseph, posted 05-11-2008 10:38 PM Rahvin has replied

Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 7.6


Message 22 of 301 (465940)
05-11-2008 10:45 PM
Reply to: Message 20 by IamJoseph
05-11-2008 10:28 PM


You cannot be a rocket scientist by claiming the earth has a center.
You're the one claiming the surface of the Earth has a center, since all objects apparently have one.
Instead, please give us the lats and longs of the surface - therein is the rub. The earth does not impact here whatsover - this is an actual; the surface is a virtual expressionism with no imperical factors. When does the surface if an actual sphear cease being its surface - how far does one have to travel - I mean in actual measurements?
Word salad. Do you speak English? because you sure could have fooled me.
The surface of the Earth is not virtual in any way. it's a physical thing. Again, you're standing on it, right now.
If you really believe the surface of the Earth is "virtual," seek professional help.
Let's take an example - a log of wood which is 1 X 2 X 4. We know the log's cubic mass criteria. Now please tell me the centre, length, breath or height of that log's *SURFACE*?
The surface area of a board is incredibly simple to compute. In your case, the surface area of a 1x2x4 cube would be 28 square feet (assuming your measurements were in feet, though it doesn't really matter).
Where would the center of this surface be, IaJ? You can point to the center of any of the six rectangles that make up the surface, but which do you choose? All six are equally "centers," so there is no true center of the surface of your board, either.
You can calculate the surface area of a sphere, too, you know. The surface area of the Earth is 510,065,600 square kilometers. Where is teh center of the surface, IaJ?

This message is a reply to:
 Message 20 by IamJoseph, posted 05-11-2008 10:28 PM IamJoseph has replied

Replies to this message:
 Message 24 by IamJoseph, posted 05-11-2008 11:05 PM Rahvin has replied
 Message 25 by IamJoseph, posted 05-11-2008 11:20 PM Rahvin has replied

Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 7.6


Message 23 of 301 (465941)
05-11-2008 10:54 PM
Reply to: Message 21 by IamJoseph
05-11-2008 10:38 PM


Do you even realise you have proved my premise here, and made your own the anomoly?
If you believe so, then you either need to re-read my post, or take a beginner's geometry class. A ray has no center. You claim all things have centers.
A ray is viewable, and it's boundaries can be established, qualified by the measuring modes used of course. But a surface is even more virtual and problematic: none can establish its boundaries. A surface is limited/unlimited in accordance with one's free discretion; the circle/sphear is not so.
The surface of a sphere is viewable as well. You can see it any time you pick up a ball or a globe. Can you point to the center of the surface of a ball or glove, IaJ? Pick one, your choice, any spherical object.
At this point my only conclusion is that you are an idiot. Elementary school students can grasp these very basic concepts, and you are failing at every turn.

This message is a reply to:
 Message 21 by IamJoseph, posted 05-11-2008 10:38 PM IamJoseph has not replied

Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 7.6


Message 26 of 301 (465947)
05-11-2008 11:32 PM
Reply to: Message 24 by IamJoseph
05-11-2008 11:05 PM


That's not right at all. You gave only the cubic volume of the earth. The 'surface' hovers it - with indeterminable factors - thus different. One is a known, the other not so - unless specifically qualified. Such perspectives works fine with everyday expressionism - we can go anywhere near or in the midst above the sphear, to denote we are now on the surface of a sphear - it is a discreationary factor. But it cannot be applied mathematically so - unless qualified by empirical measurements where that surface ends.
I didn't give the volume at all, moron. I specifically gave the surface area of the Earth. Note the "square km" units, not cubic.
Do you speak English?
You will find a country on earth has a definite size, but its surrounding water-line, has to be newly given and applied, to determine when we leave that country and get into international waters. Here, that country's water line represents a 'surface' - and an actual measurement - which is not equal to the land size of that country.
Thus, to know the measures of a surface, this has to be arbitratively actualised by the subject. Else it remains in the realm of virtuality. And you have not given the sizes of your 'surface', but eronously applied the measurements of the earth - which no one asked you about.
I gave the full surface area of the Earth. Land and water are treated the same, national boundaries are not considered. Where is the center? It's a real, measurable quantity, as demonstrated because I gave you the freaking measurement.
Where is the center? Give me a location, or retract. No more bullshit, IaJ.

This message is a reply to:
 Message 24 by IamJoseph, posted 05-11-2008 11:05 PM IamJoseph has replied

Replies to this message:
 Message 28 by IamJoseph, posted 05-12-2008 12:12 AM Rahvin has not replied

Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 7.6


Message 27 of 301 (465949)
05-11-2008 11:53 PM
Reply to: Message 25 by IamJoseph
05-11-2008 11:20 PM


My position is clear. I say everything has a centre, else it does not exist. This includes the universe. You applied eronous maths to prove your disposition of mine.
Our math is not erroneous. your comprehension level is simply below that of a child.
I showed you why the circumference is not ACTUALLY infinite when you zoom in and see the reality of it. You are moving from one point to another, without factoring this in. A circle is cyclical - but not so in actuality: after one round, we are passing the same ground again - because of its points trajectory. There is no infinite here, and the center is not negatable by the view on another point.
Nobody said it was infinite - in fact, that was why it was used as an example in the first place!
The surface of a sphere is unbounded, meaning it has no distinct beginning or end, and yet it is finite - its surface area is a measurable quantity. Because it has no beginning or end, it has no center. It is an example of an unbounded, finite object just as the universe is, and such objects do not have a center.
basically, you are applying a virtual expressionism as a math factor, concluding an actual by virtuals.
Bullshit. The surface of the Earth is not virtual, its a physical, real, measurable thing. I have you its surface area. You once again failed to give the center.
This is the glitch in the widespread anomoly and contradiction of the universe seen as having a beginning and also deemed infinite with no center. Both cannot be correct.
The Unvierse is not infinite, it is boundless and finite, like the surface of a sphere. Obviously, you are failing to comprehend.
It is also an anomoly to claim the universe is expanding, thus it has no boundary. I know this is claimed by widespread scientific proclamations. But it is not correct - its a fuzz, as in casino science - a distortion, mostly intional, and then followed by sheep. The expanding universe, like an inflating balloon, does have a boundary - at each instant of time. If you expand the size of your office - it does not mean there is no boundary - even if you keep expanding your office continuously.
You think the surface of a sphere has a center. You think the surface of the Earth is "academic" rather than physical.
You're an idiot, IaJ. I know inanimate objects with more brainpower than you. Go enroll in kindergarten and learn a few things.

This message is a reply to:
 Message 25 by IamJoseph, posted 05-11-2008 11:20 PM IamJoseph has replied

Replies to this message:
 Message 30 by IamJoseph, posted 05-12-2008 12:32 AM Rahvin has not replied
 Message 32 by IamJoseph, posted 05-12-2008 12:56 AM Rahvin has not replied

Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 7.6


Message 47 of 301 (466010)
05-12-2008 11:56 AM
Reply to: Message 46 by IamJoseph
05-12-2008 11:01 AM


Re: Don't Waste Time
quote:
You and I both know that's not what he meant.
I can tell you that is exactly what I meant and said, throughout my postings on this subject. I've no idea what you thought I meant. In any case, it is what I am saying again, namely to determine the surface in actuals, then actual dimensions of the said surface must be included in the question, otherwise the term surface is an abstract quantity.
I gave you the dimensions of the surface of teh Earth, moron. I also gave you the surface area of the piece of wood you used as an example. You have still failed to provide the location ofthe center of the surface for either object.
Let's try with your 12" string example. If we tie the two ends together and make the string into a circle, where is the beginning? Where is the end? Where is the center of the string, and why do you choose that location?
The circle made by the string has no boundary - it has no beginning or end - and yet it is finite - it is still a 12" string - and has no center on the string itself.
quote:
Straggler:
Erm we could however use longditude and lattitude to say where on the surface of the Earth the string actually is.
I think co-ordiantes are an unnecessary distraction. The question is "Where is the centre of the surface of the Earth". A geographical answer would suffice (e.g. In the middle of the Atlantic ocean).
The point being made is that there is no such thing as the centre of the surface of a sphere. It is a meaningless question. Hence the fact that you are unable to answer it.
Here, I doubt a generalised measurement such as the atlantic ocean would suffice, but the latitude and longtitude is the right way to go. Here, actual measurements and locations are given - in contrast with questions such as 'surface of the earth': we all know it hovers the earth - but we don't know to what degree this surface extends.
I've asked you very specifically to give the latitude and longitude of the center of the surface of teh Earth. Repeatedly. "Hovers the Earth" is a meaningless statement - the surface does not "hover" at all, it's simply the outermost edge of the Earth's crust. It's a 2-dimensional structure measured in square kilometers that takes the shape of a rough sphere. The "depth" of the surface is not a meaningful consideration, as a surface has no depth. This is why surface area is measured in square units rather than cubic (which would be a measurement of volume, as you incorrectly identified the surface area of teh Earth when I gave it to you).
While this debate has extended askew, as to a surface having a centre, the original issue was that the universe does have a centre [my position], against the premise I countered, it does not/can not have a center. Now an abstract surface can and does have a center, but this answer will also lie in the abstract. It points the way to all things having a center, including the universe - regardless that we cannot identify it. It is vindicated mathematically, and I am surprised to obtain so much deliberation and negation of this absolute logic.
Shut up with your insane nonsense about abstract vs actual structures. The Universe is an actual structure. The surface of teh Earth is a real structure. Neither are abstract.
I honestly hope Percy bans you expressly for the amount of nonsense contained in each one of your posts in this thread, even though it's in Free For All.
The reason we cannot identify the centre's location can have many reasons, including vastness of size, and that we are actually inside that centre. Based on the BBT, the universe began with a point or singular atom/particle. This means nothing else existed elsewhere. The first point expanded, around itself, harmogenously. This means, the original dot was and is the center, and that it has expanded to the current universe size. And our galaxy is somewhere inside that center. This also means, the original point, namely the BB point, is the center. I cannot see any alternative process or conclusion possible here.
The surface of a sphere example is used becasue it is analogous to the Universe as a whole in that it demonstrates a structure that is finite, yet unbounded, and that such structures have no identifiable center.
You've spent the remainder of the converstation mixing up area for volume, using inccorrect (and not even consistent) definitions for geometry terms, speaking absolute nonsense, and generally making yourself look like a compelte fool as you consistently refuse to actually answer any question posed to you.
So, I will ask again: The Earth being a physical example of a rough sphere, what is the location of the center of its surface? You may give latitude and longitude, or you may give a rough geological location - either is fine. If you cannot identify the location of the center of the surface of a sphere such as the Earth, this will be a tacit admission that you can also not back up your claim that the Universe must have a center.
Put up or shut up, IaJ. We are tired of your nonsense arguments. it's time to either admit that you were wrong, or identify the location of the center of the surface of the Earth.
We're waiting.

This message is a reply to:
 Message 46 by IamJoseph, posted 05-12-2008 11:01 AM IamJoseph has replied

Replies to this message:
 Message 50 by IamJoseph, posted 05-12-2008 11:11 PM Rahvin has replied

Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 7.6


Message 59 of 301 (466071)
05-13-2008 12:15 AM
Reply to: Message 50 by IamJoseph
05-12-2008 11:11 PM


Re: Don't Waste Time
quote:
I gave you the dimensions of the surface of teh Earth, moron.
Correct - dimensions of the earth, and I repeatedly ask: WHY? - why are you giving the earth's dimensions when your asking about the surface dimensions? I repeatedly told you, the earth dimensions are *DIFFERENT* from that of the earth's 'surface'.
WHAT?!
I have you the surface area of the Earth.
SURFACE area.
SURFACE area.
The surface area of the Earth cannot, by fucking definition, be any different from the measurement of the surface! THAT'S WHAT SURFACE AREA MEANS!
This is, without a doubt or exaggeration, the least intelligent conversation I have ever had. I'm not joking, Im not poking fun - you are the least intelligent person I have ever met, including toddlers. Seek help.
Who's the moron?
I'd say that the moron is the person insisting that the surface area is not a measurement of a surface.
I'd say that's one of the dumbest things I have ever heard, ever.
quote:
I also gave you the surface area of the piece of wood you used as an example. You have still failed to provide the location ofthe center of the surface for either object.
Incorrect. I gave you the dimension of the wood - *and the dimensions of the glow* - and I analogised the glow with the surface - to show you these were two different animals from the log and the earth, respectively. But your still at it - educating me how to find the centre of a sphear. Gee, thanks.
WHAT THE FUCK IS GLOW?!
You have stopped referring to reality, and are now trapped in some magic fairy-land.
The measurement of a surface is the suface area. Given a peice of wood cut in a cube with the measurements 1x2x4 as you provided, the surface area, the measurement of the surface, is 28 square units, since you did not include units (not that they matter).
There is no such thing as glow, you imbecile. You fail the most basic thing you learn in geometry. They literally teach this stuff in elementary school, and you make up nonsensical terms like "glow."
5th graders are laughing at you, IaJ.
quote:
Let's try with your 12" string example. If we tie the two ends together and make the string into a circle, where is the beginning? Where is the end? Where is the center of the string, and why do you choose that location?
The beginning and end are the length of the string before you attached the ends. Going over the same ground forever does not mean it is infinite, with no end, beginning or boundary. One can make your office infinite that way, by adjusting the trajectories - my previous example to you. Yet your still dishing out the same casino brilliance. I also showed you, the universe is *NOT* boundaryless - it was not 10 seconds ago. But with the right casino maths, your office chair can be shown to be boundaryless.
You fail to comprehend the difference between "infinite" and "boundaryless." They are different terms that mean compeltely ifferent things, which is the fucking reason I've been using both terms.
A 12" bit of string fashioned into a ring has no beginning or end, no boundary, and yet it is finite. There is still only 12" of string, and will only ever be 12" of string, but there is no boundary to it. Becasue there is no boundary, every single point in the string ring is identical, and it has no center on the string itself.
You most certainly have bnever shown anything about the universe. All you've shown so far is that you lack the most basic of reasoning skills that children can master given very little practice. You've proven to be a loudmouthed idiot of the highest order, capable only of spewing sewage from your fingertips and claiming your waste of forum space has something to do with reality.
You. Are. An. Idiot.
ICANT never grasped the Big bang model after over 4 threads of trying, but he at least responded intelligently even if he was consistently wrong.
You, sir, are so far from the mark that if you were playing darts, your shot wouldn't even be in the same boundaryless-but-finite Universe. The makers of Jackass are more intelligent than you are. I'm shocked and amazed that you seem to have learned how to type, becasue typically those who display this level of a lack of comprehension of basic concepts still can't color inside the lines, and are more likely to eat the crayon!
quote:
The circle made by the string has no boundary - it has no beginning or end - and yet it is finite - it is still a 12" string - and has no center on the string itself.
Then please make your circular string traverse 13"? Fact is, the circular design has no relevence here, but the trajectories of points do: one can perform the same feat with a square, triangle and anything else. What has escaped you is, your circle w/o an end or beginning is academic only, and has nothing to do with reality. Now if you go back to this post, and repeat that manouver when you finish it - you will have a post w/o a beginning or an end. If casino maths turns you on. But I am telling you - you have changed the trajectories is all.
Trajectories are irrelevant when considering surface area, or determining whether a structure has a boundary or center.
What has escaped you is what I had until now always assumed was common sense posessed by every human being without a serious mental handicap. Thank you for lowering my expectations.
quote:
You've spent the remainder of the converstation mixing up area for volume, using inccorrect (and not even consistent) definitions for geometry terms, speaking absolute nonsense, and generally making yourself look like a compelte fool as you consistently refuse to actually answer any question posed to you.
No, I have not. Area or volume serve the same purpose: whether the centre of a 2- or 3-D space is in question.
Volume and area are compeltely different things, cretin. O refer you once again to your fifth grade mathematics textbook. Should I look one up and quote to you exactly why elementary school students know you're full of shit?
quote:
So, I will ask again: The Earth being a physical example of a rough sphere, what is the location of the center of its surface? You may give latitude and longitude, or you may give a rough geological location - either is fine. If you cannot identify the location of the center of the surface of a sphere such as the Earth, this will be a tacit admission that you can also not back up your claim that the Universe must have a center.
Put up or shut up, IaJ. We are tired of your nonsense arguments. it's time to either admit that you were wrong, or identify the location of the center of the surface of the Earth.
There is no alteration in my stance, which has been ever consistant. Either remove the term 'surface' from your question - or allocate your 'surface' dimensions seperately from that of the earth.
This sentence doesn't make sense. Are you atempting to evade because you know you're wrong?
I doubt it. I believe you legitimately think you're right. Sad.
The term "surface" is the fucking point of the question! The surface of a sphere, such as the surface of teh Earth, the surface of a ball, the surface of teh moon, all of these are structures that are finite, yet boundaryless, and which have no center. This is directly contrary to your claim, which makes you wrong.
I gave you examples how and why the glow [and thereby the 'surface'] - are varied from the log and the earth dimensions, respectively. Yet he comes back - like brylcream.
"Glow" is not a term in geometry. you made it up. It has no relevance to the question. Wood, for example, like the bit of wood you wanted to use at one point, does not "glow."
This is why you are an idiot.
quote:
We're waiting.
Here's a better one:
Please give us the volume of your surface of the earth: is it the same as that of the earth?
Waiting.
A SURFACE DOES NOT HAVE A VOLUME, AS VOLUME REQUIRES THREE DIMENSIONS AND THE TERM SURFACE REFERS ONLY TO TWO. THE SURFACE OF THE EARTH HAS NO VOLUME.
the surface of the Earth is measured in square kilometers, as I gave you much earlier.
The surface area of the Earth is 510,065,600 km^2
The volume of the Earth is 1083206246123080894.852 km^3
Note that the units of these two measurements are compeltely different, and that the numbers are also compeltely different. That's becasue volume and surface area are different things.
See, the surface area measures the surface of an object. The volume measures the space displaced by the object. They are different, IaJ, and only fucking surface area is fucking relevant to the fucking question!
Now, IaJ, since you seem to be intellectually incapable of telling the difference between counter space and how much water a given jar holds, I'll answer this insipid little question for you. Let's see if your tiny little mind can keep up.
From Mirriam-Webster:
quote:
Surface
1sur·face
Pronunciation:
\sr-fs\
Function:
noun
Etymology:
French, from Middle French, from sur- + face face, from Old French ” more at face
Date:
circa 1600
1: the exterior or upper boundary of an object or body
2: a plane or curved two-dimensional locus of points (as the boundary of a three-dimensional region)
The surface of the Earth takes the form of a rough sphere. It's surface area is 510,065,600 km^2. It is finite, not infinite. The Earth is only so large. It does not go on forever. And yet, the Earth has no "beginning" point, and no "ending" point. The Earth, being spherical, is not like a line segment. This means the surface has no boundary, despite being finite. These are two different terms. The surface as measured by the surface area, is only the outermost edge of teh Earth, not including the atmosphere - it's literally just the ground you're sitting on and the surface of the oceans. It has no depth, becasue a surface is defined as a two-dimensional term. Because the surface of teh Earth has no beginning point and no ending point, it is impossible to determine what is "halfway" between the beginnign and ending points. This means that there is no center to the surface of the Earth. If you take your finger to a globe and point at the center from any direction, all of the places you touch the surface are equally the center and are indistinguishable from one another. The term center is meaningless when referring to the surface of a sphere.
The surface of a sphere is a finite (it does not go on forever, it has a definite size) yet unbounded (it has no "boundaries," no beginning or ending points) structure that posesses no center.
You. Are. Wrong.
I cannot believe I have participated in such an utterly retarded conversation. I feel dirty in my brain because of your idiocy.

This message is a reply to:
 Message 50 by IamJoseph, posted 05-12-2008 11:11 PM IamJoseph has replied

Replies to this message:
 Message 64 by IamJoseph, posted 05-13-2008 12:41 AM Rahvin has not replied

Rahvin
Member
Posts: 4046
Joined: 07-01-2005
Member Rating: 7.6


Message 62 of 301 (466074)
05-13-2008 12:26 AM
Reply to: Message 60 by ICANT
05-13-2008 12:21 AM


Re: Sphere
I'm a sucker for trick questions but I want to try anyway.
In relation to me the center of the surface of the earth is whereever I am at on the surface of the earth at the moment.
Please correct me if I am wrong.
God Bless,
Actually, close enough. There is no objective center - all points on the surface of a sphere are indistinguishable from one another. They are all equally the center, which is why the word "center" has no meaning whatsoever as it applies to the surface of a sphere.

This message is a reply to:
 Message 60 by ICANT, posted 05-13-2008 12:21 AM ICANT has not replied

Newer Topic | Older Topic
Jump to:


Copyright 2001-2023 by EvC Forum, All Rights Reserved

™ Version 4.2
Innovative software from Qwixotic © 2024