Norway Spiral : Case reopened - the analysis of an event (Part 2)

reply to post by tauristercus



tauristercus, I will pose this question to you again maybe you have an answer.

If this spiral was not caused by a sonic blast then could this be electron plasma

oscillations called Langmuir waves created by magnetic plasma Flux in space?

^Y^

reply to post by davesidious

Originally posted by davesidious
reply to post by Protector

 

Cruise missiles stay in the atmosphere for their entire journey (hence the wings on the side, and air intake for the jet engine (not rocket).

The "black hole" is just space becoming visible after the white spiral has moved out the way. It's growing at the same speed as the outside of the spiral. As it happened in space, there can not be a shock wave, as a shock wave requires a medium through which to travel, and a vacuum is the very opposite of a medium

I wasn't implying it was a cruise missile. I was implying that it might have a stealth design to be difficult to see a fuselage in an image (or just painted a non-reflective black).

I thought that the "black hole" expanded faster than the spirals were initially created. If that is true, which I'm not guaranteeing that it is, then the explanation could be that the missile burst, or was manually destroyed, and the liquid oxygen rapidly expanded/boiled (creating a pressure wave radiating out in 360 degrees) thereby pushing some of the leaked fuel out of the way. LOX is oxygen + ozone, so it would create an atmospheric like pressure force, even in space, as the O2 and O3 particles collided at high speeds with much of the leaked fuel, thus forcing it to dissipate at a faster rate to the naked eye.

After watching the "black hole" form several times, I believe it is forming faster than the ripples, but is it the result of the camera zoom? Either way, I think there is a reasonable answer.

Hence, every way you look at it, it is a rocket.

[edit on 8-2-2010 by Protector]

Originally posted by davesidious
reply to post by Protector

 

As it happened in space, there can not be a shock wave, as a shock wave requires a medium through which to travel, and a vacuum is the very opposite of a medium

Also, you're wrong about it being a vacuum. The Exosphere extends theoretically half-way to the moon. Which means there is at least partial atmosphere and greatly fluxuating temperatures on the entire flight path the rocket. I'm not certain of its final altitude, but I'm sure it still sits in the upper layers of the atmosphere, albeit with greatly reduced atmospheric conditions.

Wikipedia: Exosphere

Originally posted by PhotonEffect
reply to post by Point of No Return

 

The analysis EM keeps posting is fundamentally flawed.

The OP's maths are approaching it from a different perspective. They are interesting with regards to the values he's arrived at for the dissipation of the spiral. It doesn't suddenly show that a missile wasn't involved.

I also don't think the first part is of any value. The pictures that he's reversed and zoomed in on are open to one's own interpretation... but either way it's completely inconclusive... it's not for or against either theory



[edit on 8-2-2010 by PhotonEffect]

Hey Photon...I'm still waiting for you to translate these supposed fundamental flaws mathematically. www....(nolink)/?myygii2emfm

But, as I said before...because you lack any mathematical skills where you can demonstrate and illuminate these "supposed" fundamental flaws, your opinion of whether it is valid or not is NULL AND VOID. As a matter of fact, I have yet to see you post any evidence on your behalf whatsoever...

Here's where you admitted no mathematical skills.
www.abovetopsecret.com...
By the way, in your post, you said you would get back with me on the mathematics. LOL. Its been a few days now...Tick tock, tick tock....
By the way...math is spelled as such and cannot be made plural unless you use the word mathematics. But, I loved the third grade way that you spelled it. "Maths" It let me know the mentality of what I was dealing with.

So, this should be fun.

Let me see if I can adequately define our situation (its been a hilarious one I might add). You have no mathematical abilities, as you've admitted (smart move by the way, this way you're not expected to think). Therefore, it is impossible for you to be able to even know what the math is saying because you lack the fundamental skills to understand them. It would be the equivalent of me looking at a letter sent to me in Chinese Kanji from the Dalai LLama and then telling the Dalai LLama that his punctuation was wrong. Its impossible for me to know, because I do not speak or understand that language. (Oh, if you need proof that Kanji is actually a writing system, I'll be more than happy to provide that evidence.)

You are in no position to say whether there are flaws or not, because your brain doesn't comprehend the message that the math is speaking. Without the language and the ability to prove your theory mathematically, you're opinion is as useless as your arguments.

But, I'll just take your argument at face value with no evidence, mathematics, no opinion, no theory, no evidence, and no hypothesis and assume that you're a self made expert in this brand new "scientific field of sky spirals."

Oh, by the way...here's my prediction for your next post. You'll avoid the inquiry on your ability to translate the math, because this is where you are weakest (get back with me later on that one...right???). You'll attempt to discredit the source and make a general statement like; "There are flaws in the link that EM provided" but, of course, you won't be able to provide a reason as to why, and then try to create a diversionary tactic such as an insult to deflect your blatant ignorance of the content that is being discussed in this thread.

You're a hoot!!! I wish I could sit in a corner all day saying...la la la I can't hear you...la la la. That works in grade school, but not the real world.

Nighty night...just stay asleep, you're still dreaming.


[edit on 8-2-2010 by EvolvedMinistry]

Originally posted by davesidious
reply to post by tauristercus

 

Crap, sorry - I should have been more clear in my request. I wanted to know how you turned frames from the video into locations in GE. Your technique of plotting the spiral in GE from photos showing landmarks is well-documented (and still awesome).

Again, sorry for making you write all that out. It'll help others, though, I'm sure. These threads will be referred to for aeons to come, I'm sure.

Sorry for taking so long to respond ... the real world has a habit of intruding and requesting my attention !

No apologies, necessary ... I'll give the explanation another shot in a min.
Though I'm starting to get a sneaking suspicion that you enjoy having me slave over a hot keyboard, typing away

Ok, I think we're both on the same page finally ... you specifically want to know the method I employed to extract specific spiral location info from that jerky and unstable video clip that was taken in the Tromso area.

Initially I was quite prepared to reject the clip for the simple reason that unlike the other still images that had distinctive backgrounds (basically mountainous areas) that were reasonably clear and sharp due to being silhouetted by the approaching dawn, the Tromso video was completely lacking in such a detailed background. As you know, my methodology to identify the various locations had been to use GE, after setting the time and date to 7:50am on 9 December 2009, which put GE into a similar silhouetted appearance. Then I laboriously adjusted the approximate GE location until I was absolutely positive that the silhouette background from the pics could be perfectly (as far as GE would allow) overlayed using Photoshop with that of the silhouette from GE. If they matched, I therefore had my equivalent GE location that matched the observers location when they took the pic.

But again, with the Tromso vid, I didn't have that luxury.
However, after repeated viewing of the vid, it suddenly occured to me that the opening seconds of the vid showed a very distinctively shaped building ... and it didn't take much Googling to determine that this building was the famous (in Norway, anyway) Arctic Cathedral.
So a screen capture from the vid gave me the image on the left as seen here.

[atsimg]http://files.abovetopsecret.com/images/member/b45cb1f52cd9.jpg[/atsimg]

Now to the right of the Cathedral appears to be a fairly large building (not sure what it is but no matter) which indirectly gave me a 2nd reference point that I could use. So if you look at the left image, you can see that the spiral in the sky is positioned in such a way that its to the right of the Cathedral and directly over this large building. Essentially I've isolated the spiral using these two buildings as a reference points. Now the original observer appears to have been standing in such a way that like the spiral, he was positioned roughly facing the Cathedral with the large building to his right.

[atsimg]http://files.abovetopsecret.com/images/member/120281712f4e.jpg[/atsimg]

So dragging GE out and bringing up Tromso as it looked that morning, it didn't prove hard at all to reproduce this view and get a reasonably good idea of where the observer stood. Even if he wasn't in that EXACT spot, that makes no difference as long as the line of sight drawn in GE matched the line of sight in the captured screen print.

[atsimg]http://files.abovetopsecret.com/images/member/333d0f115e0c.jpg[/atsimg]

And the most satisfying part of this is that after I had established the observers line of sight, I then extended the line all the way to the White Sea, to find that it intersected perfectly with multiple other lines drawn to that particular spiral location from other observers ... so was I pleased with myself ? you betcha !

Originally posted by amari
reply to post by tauristercus

 

tauristercus, I will pose this question to you again maybe you have an answer.

If this spiral was not caused by a sonic blast then could this be electron plasma oscillations called Langmuir waves created by magnetic plasma Flux in space?

Unfortunately I hadn't heard of Langmuir waves until you mentioned them and so had to quickly Google some info to redress my ignorance

From what I've read, a key constituent of Langmuir waves is that they require a plasma in which to manifest themselves.

Again, due to my complete ignorance, I have no idea if the missile even had such a capability and if assuming it did, whether it directly or indirectly could produced such a plasma ... whether by creating an artificial plasma around itself or making use of naturally occurring plasma at the altitude that I have determined the spiral to have existed at.
I have no idea whether such technology was even part of its design, payload or testing mode so please don't anyone think I personally am considering that it did.

Originally posted by Point of No Return
reply to post by PhotonEffect

 

Interesting? It proves that it wasn't a Bulava missile.

If you found it interesting, why make no further attempt to discuss these findings, wich are the topic of this thread, and only focus on EM's posts?

He focuses on my posts because of a different thread where his demigod "you know who" was destroyed by some of my information where the mods gave me an applause over the allmighty, "you know who." (so petty). Since then, "You know who" and company has made it a personal mission to discredit anything that I say, but, its always groundless and without any evidence to back their opinions. Its actually an honor for me to consistently make them look silly because they obviously consider me to be a "viable threat" to their stability on ATS. The only true threat is the one that is consistently addressed, and attacked. And as you can see, they've spent a great deal of effort consistently addressing my posts. I welcome it.

Nonetheless, I have posted one link that seems to really get under their skin on top of the mounds of evidence that I've provided before. They consistently attack it, but, have absolutely no foundations for their rejection of its analysis. Usually its just rhetoric spewed over opinions, and talking around the facts as opposed to addressing them. As you can see...I've asked for Photon numerous times to mathematically debunk my link's claims, but, there's never a response.

So, I'm like an infected sore to them. They keep scratching at it in a vain attempt to gain relief, but, ultimately the infection just keeps spreading.

Anyway, this missile theory has been destroyed twice. And, as far as I'm concerned, the OP was a genius for the way he baited these guys in the last thread (although I'm sure it was unintentional) and then disproved that very theory in this one. Absolutely brilliant. I love a great puppet master even if he wasn't aware that he did it.



[edit on 9-2-2010 by EvolvedMinistry]

Originally posted by PhotonEffect
reply to post by Point of No Return

 

Exactly, I still maintain an open mind where need be...

I'm not sure if the OP had provided how he came up with that 108km distance using GE. I know davesidious had asked him about that but not sure if the OP responded yet...

PhotonEffect ... I'm not sure how you missed it in my opening post of this thread but I show clearly how I arrived at the 108 km distance.

Here's the relevant image again ...

[atsimg]http://files.abovetopsecret.com/images/member/41e998f5029d.jpg[/atsimg]

Those 3 inset images were taken from the Tromso video immediately before the spiral began dissipating, through to almost final dissipation. There was no difficulty in matching those images with their respective locations along the trajectory line running through the White Sea area.
Bear in mind that the White Sea trajectory was obtained by "triangulation" using multiple observer data points and consequently I have high confidence in it's accuracy.

So, if the vid spiral immediately prior to start of dissipation maps to Spiral2 position along the trajectory line and the almost complete collapse from the vid maps to Dissipated spiral position along the trajectory line ... then GE gives us a distance value of 108 kms between the starting and ending points.

We therefore have to conclude (unless someone can disprove the accuracy and location of my trajectory line) that during it's dissipation/collapse phase, that the spiral phenomena traveled a distance of 108 kms in approx 10 seconds ... which implies a speed of 38,800 km per hour.

I'm more than open to anyone wishing to reanalyze my entire work, calculations and results. If the 108 kms is grossly inaccurate, then please speak up and say why !

[edit on 8/2/10 by tauristercus]

reply to post by tauristercus


It is not likely to be a plasma because plasma requires certain temperature ranges. Langmuir waves are specific oscillations of plasma. I highly doubt that any type of plasma spread through multiple atmospheric layers would have the same sustained temperatures. Also, I believe the oscillations in Langmuir waves refer to microscopic oscillations, not massive uniform waves.

"Langmuir waves" sound like a buzzword that amari picked up somewhere.

I believe it is simply the missile trail, but if I didn't, I would vote for some other type of pressure wave, not related to plasma.

[edit on 8-2-2010 by Protector]

Originally posted by EvolvedMinistry
And ultimately... you'll actually get pissed (like you already are) that I haven't relented my position on the face value of your self professed "expertise" in this field.

But hey, that's not my problem. Its yours.

And again he displays his lacking skills of reading by totally ignoring the fact he could have read one of the other dozen topics where Phage and others blew their little fantasy right out of the water

And what's this, you're admitting to be a troll now EvolvedMinistry? You realy give yourself too much credit at being able to get me "pissed". Laughing at your fantasy does not equate to being "pissed". Nice try though

Don't get mad because you can't prove your theory, get mad because Phage and others made you look very small, and you're trying to desperately to wriggle out of it on this thread. I'm gonna grab me a beer and watch the rest of the grilling.

[edit on 9-2-2010 by secretbear]

Originally posted by secretbear

Originally posted by EvolvedMinistry
And ultimately... you'll actually get pissed (like you already are) that I haven't relented my position on the face value of your self professed "expertise" in this field.

But hey, that's not my problem. Its yours.

And again he displays his lacking skills of reading by totally ignoring the fact he could have read one of the other dozen topics where Phage and others blew their little fantasy right out of the water

And what's this, you're admitting to be a troll now EvolvedMinistry? You realy give yourself too much credit at being able to get me "pissed". Laughing at your fantasty does not equate to being "pissed". Nice try though

[edit on 9-2-2010 by secretbear]

Look at all of the heat coming off of this post. My goodness someone needs an afternoon nap.

It would be good to stay on topic regarding the thread. Nonetheless, until you've posted some information that is relevant, I don't think that I can really take you seriously...now can I???

reply to post by tauristercus


It would be nice to have the timestamps for the images from Skjervoy to get an accurate timespan . I think the video you used only captured the end of the incident. Various descriptions indicate that it lasted quite a bit longer than 10 seconds.

I saw the spiral for about 2 minutes. I think I caught it at its begining, couse it was really small when I first saw it.

www.abovetopsecret.com...

I stared at it for about two minutes, so I drove on. But then I had to stop again, and when I saw the light on for about a minute, "he says

Lødding says he saw the phenomenon in a couple of minutes, until light in the middle extinguished.

nrk.no...

The phenomenon lasted for the several minutes and looked like a bright spin the bass high in the sky.

www.tv2nyhetene.no...

There is some variation in the reports but two minutes seems to be pretty common, it certainly lasted longer than ten seconds. Lets say the witness are talking about the entire portion of the flight which you propose in Part 1 (launch to dissipation). That track is about 275km long.

Using a two minute duration we get a speed of 8,250kph. Even if the estimates were double the actual time (we know eyewitness reports are not entirely reliable) the speed would have been 16,500kph. So we're still well within the proposed speed range of the Bulava.

Of course we don't really know how much of the flight the witnesses are reporting but it doesn't sound like anyone saw the actual ascent. Anything less than that 275km will yield a lower speed than above. I don't think the Bulava has been ruled out.

[edit on 2/9/2010 by Phage]

Originally posted by Phage
reply to post by tauristercus

 

It would be nice to have the timestamps for the images from Skjervoy to get an accurate timespan . I think the video you used only captured the end of the incident. Various descriptions indicate that it lasted quite a bit longer than 10 seconds.

I completely agree with you regarding the Skjervoy images and a timestamp as they were by far the most detailed of all the pics available. Just too bad the photographer hadn't bothered to turn on that particular function within his camera

Yes, I'm aware that there are varied reports on the total event time and I've come across a wide range ... from a few minutes all the way up to 12 mins or so. So unfortunately we don't have, and probably wont get, an accurate TOTAL event timing.

However, we are fortunate that we have the Tromso video clip that DOES give us a very good timing for a certain segment of the event that happened towards the end of the sighting ... namely from the point at which the spiral begins it's dissipation process from that of a stable spiral shape to what eventually looks like a complete void.

As much as I wish we could accurately time the entire event, I'm still more than happy to settle for a speed estimation across that smaller segment of the event towards the end of the sighting.

Considering that we apparently have an accurate trajectory path (unless someone can show/prove otherwise); and we have an accurate timing from spiral collapse to completion, thereby giving us a speed estimate (no matter how incredibly large) ... I'm not really sure whats remaining to debate except for the mechanism powering such an incredible speed over such a short distance.

Hmmmm ... it just occurred to me that perhaps there are many ATS'ers reading this thread who may be under the misunderstanding that the speed I calculated applied to the entire event, from the very beginning of the event until the final dissipation, quite some time later.
Just making it absolutely clear that the speed I calculated only applied to perhaps the last 10 seconds or so until the spiral was virtually completed dissipated.
Speed estimates over the earlier sections of the event are currently unknown.

[edit on 9/2/10 by tauristercus]

reply to post by Phage

I don't think the Bulava has been ruled out.

I'm hoping that in this and the preceding thread, that I haven't given the mistaken impression that I do not believe a Russian missile was involved at the time of the Norway Spiral event ... far from it.

I find the evidence of a launch at that particular time to be virtually unassailable.
What I am trying to get across is that apart from the confirmation of a Bulava launch - after all there is an obvious exhaust plume rising from below the horizon - I'm essentially saying that my observations based on available photographic/video evidence, analysis of said evidence and eventual personal deductions derived from said analysis, strongly indicate that the observed effects were completely inconsistent with something as simple as a leaking 3rd stage.
Do I have an alternative and confirmable alternative ? Unfortunately, no.
But I do have a PERSONAL opinion based on the research that I've presented and that rather than a REPORTED failed missile test, the Bulava MAY have been conducting tests of new technology ... and from the spectacle in the sky that morning, the Bulava test flight may have indeed been a SUCCESSFUL one ...

... but that's merely MY opinion only ... and not to be taken to the bank !

reply to post by tauristercus


Thanks, Taur! That's a great methodology, which is indeed paying dividends.

My follow-up question is how do you then continue to measure the position of the centre of the spiral through the video, which would be necessary to measure the speed of the missile causing it? I've seen the image with the three frames overlaid on Google Earth, but I don't know how you managed to position them where you did, coming to your distance of 108 km.

And no, you slaving over the keyboard doesn't make me happy. Getting to the bottom of this phenomenon does, though

Originally posted by davesidious
reply to post by tauristercus

 

Thanks, Taur! That's a great methodology, which is indeed paying dividends.

My follow-up question is how do you then continue to measure the position of the centre of the spiral through the video, which would be necessary to measure the speed of the missile causing it? I've seen the image with the three frames overlaid on Google Earth, but I don't know how you managed to position them where you did, coming to your distance of 108 km.

And no, you slaving over the keyboard doesn't make me happy. Getting to the bottom of this phenomenon does, though

Ahhhhh .... I see where I'd lost you in my previous explanations

The Tromso vid clip was of use because it gave us 3 very important data points.
The 1st being the ability to find a corresponding location for the spirals direction on GE by using a clear screenshot of the Arctic Cathedral visible in the opening scenes of the vid. This was then used to match the observers line of sight and extend it to the White Sea area and happily, intersect in the exact same location with other observer viewpoints (as described a few posts earlier).
The above operation has now given us the ability to locate this spiral position on the trajectory line (Spiral2), which now becomes the start point for our distance measuring.

[fingers hurting]

The 2nd useful data point we obtained from the Tromso vid was an estimate of the time elapsed from beginning of spiral dissipation to almost complete dissipation.

The 3rd useful data point obtained was a clear visual confirmation of the dissipation phase ... from start to almost complete dissipation.

Armed with these 3 data points, we could care less about the remainder of that shaky vid clip and don't need to watch it any further.

Now, the 3rd data point from the vid clearly shows a spiral that has virtually dissipated. By itself, not much use. However, lets now jump to the series of pics taken at Skjervoy which (hallelujah) contain an image not only of the spiral in terminal dissipation mode, but more importantly, another pic of the spiral virtually completely dissipated.
Earlier in my derivation of the missile trajectory, I had used this very image and successfully managed to allocate a corresponding position for it on the trajectory line (Dissipated spiral).

[fingers really hurting]

So finally, here we are .... we now have the following:

- the location on the GE trajectory path of the spiral a split second before it enters the dissipation phase
- the location on the GE trajectory path of the spiral as it completes dissipation
- the elapsed time from start dissipation to end dissipation

So there you have it ... I then used GE's distance measuring tool which produced that magic value of 108 kms between start and end of dissipation.

I've gone over my methods of deriving this distance value many times and find nothing screwy ... and so we end up with a calculated speed value to raise the eyebrows !

reply to post by tauristercus


I understand. Thanks, again, for taking the time to explain that to me.

You know this is coming, but I still don't see how we can be that accurate to get 108 km from these sums. There are estimations, albeit somewhat mathematically accurate one, stacked on top of each other, multiplying the margins of error as it goes.

We need some further correlating evidence to remove this doubt before I believe it's fair to say there was something amiss with the missile's speed. I'm sure you agree that one measurement is not enough to make the leap from "Bulava" to "Exotic new ICBM".

Again, thanks for the hard work. If you feel like taking EM down a peg or two with his crazy ideas, that would be much appreciated

Originally posted by davesidious
reply to post by tauristercus

 

I understand. Thanks, again, for taking the time to explain that to me.

You know this is coming, but I still don't see how we can be that accurate to get 108 km from these sums. There are estimations, albeit somewhat mathematically accurate one, stacked on top of each other, multiplying the margins of error as it goes.

We need some further correlating evidence to remove this doubt before I believe it's fair to say there was something amiss with the missile's speed. I'm sure you agree that one measurement is not enough to make the leap from "Bulava" to "Exotic new ICBM".

Again, thanks for the hard work. If you feel like taking EM down a peg or two with his crazy ideas, that would be much appreciated

You won't get any arguments from me that additional "confirmations" would be very much appreciated.

I've mentioned the following before but it's worth reiterating as from MY personal point of view, I feel that I DO have such additional confirmation ... two of them, in fact. They may not be strictly "scientific" in nature but I'll tell you what, I just about did cartwheels when I noticed these confirmations ... so do I feel that I've achieved high enough accuracy in my derivation of the missile trajectory whilst crossing the White Sea ? Most certainly ...

Ok, I originally spent a considerable amount of time in trying to locate sufficient numbers of quality pics and then matching them to the corresponding GE locations ... for no other reason than to give me the best chance to construct a very accurate triangulation of the missiles location over the White Sea area.
So eventually, there I had it ... 5 intersecting locations over the White Sea area based on multiple data points for additional accuracy.

It didn't take more than a few mins after that for me to notice that the 5 location points looked as if they were aligned in a straight line.
So out once again with GE's line drawing tool ... click the 1st location, drag the mouse to the 5th location and WTF !!! ... ALL 5 location points fell EXACTLY onto that line ... not near or close ... but spot on the line ! Immediately I realised I was on to something with that line and observation.
So what did I do next ?
I grabbed the end of the line at the 5th location, and making sure that all 5 locations remained on the line, I then dragged and extended the end of the line across the top end of Russia and found that I could drop it smack in the middle of the down range Kamchatka Peninsula missile test area.

I guess it was a combination of the 5 locations EXACTLY on the trajectory line combined with the end of the line terminating just where Russia likes its test missiles to end up - in the middle of Kamchatka.

Honestly, if you or any one had given me 6 random locations in Norway and then expected me to arrive at similar results, you could pay me all the money you want and I couldn't do it unintentionally or by accident.

So, do we have a 2nd "scientific" confirmation ? No
Do I PERSONALLY think I need it ? No
Do I consider that 108 km distance value to be accurate ? Yes

p.s. I'll have to read EM's work again ... then we'll see

[edit on 9/2/10 by tauristercus]

reply to post by tauristercus


I think your work on determining the bearing of the missile to be fantastically accurate. I don't dispute that for a second! I doubt anyone can pick any holes in it what-so-ever.

I don't say this lightly, but determining the bearing doesn't imply proof that any measurements made along it are by themselves accurate, which is the crux of my issue with the magic 108 km measurement

Hat off to you, though, you're a great example of how brilliant ATS used to be, before the "woo-woo" crowd descended.

reply to post by Point of No Return

How could a spiraling missile, launched from point A flying towards point B, produce an image of a head on spiral, when looked at from the side, from sites laying parrallel to the line AB?

Yeah, I wondered about that too. i thought that maybe if the missile were tumbling end over end & the exhaust gas continued to follow at the same speed, it would be possible. Then again, if exhaust gas is so visible, shouldn't somebody see huge arcs of it every time something gets launched into orbit? Its always dawn somewhere, eh?
Anyhoo, I've just read 3 pages of mainly dog barking & wish that I hadn't. I really hope it doesn't put the OP off coming back to this thread, as it seems that tauristicus has a better understanding of the maths of 3D geometry than most of us & a better ability to explain it than many teachers. I also like the OP's approach of analysing the evidence themselves & being willing to adjust a hypothesis based on the findings. Tauristicus should get applause for the effort gone into these 2 threads, imo.