Who says it does? It is still a point. This is one of your stumbling blocks.
Deeper than primes
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Who says it does? It is still a point. This is one of your stumbling blocks.
doronshadmi
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And it is still a bended atomic 1-dim element, so?
As soon as you have a 'bend', it is no longer 1-dimensional.
doronshadmi
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jsfisher said:
A little sense of beauty, that is all you need jsfisher (http://www.internationalskeptics.com/forums/showpost.php?p=5703507&postcount=8989):
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Ooh, shiny!
jsfisher
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I have provided a complete statement of the axiom. I'm sorry you don't understand the language in which it was expressed, but that is your problem, not mine.
No, terms you invent don't actually mean anything because you refuse to define them. Still, it is nice to see you admit that you also invent multiple terms all to mean the same thing. It reinforces the notion that your gibberish confuses even you.
You assume far too much. You also didn't comprehend the question I asked. No surprise on either count.
The Man
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“rid of”? So you are simply and deliberately ignoring the “points (localities)” as well as dimensions because you want to be “rid of” them?
Nope, as zooterkin has pointed out to you several times already your ‘bended’ line is no longer one dimensional. You have 'bent' it at some “points (localities)” into at least one other dimension. In fact the fully iterated Koch curve (which is a fractal as noted by jsfisher) has a Hausdorff dimension of log(4)/Log(3) or about 1.2619, same as the Cantor set in 2 dimensions referred to as “Cantor dust”
ETA line: 3 such Koch curves would form the Koch snowflake or anti-snowflake.
http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension
http://en.wikipedia.org/wiki/Cantor_dust#Cantor_dust
What, so now the circle is convergent? Again a circle is one dimensional because of the consistency of its radius, your ‘bended’ line has no such consistent radius (if it did it would be a circle).
Again a set does not have to have its limit (or limits) as a member (or members) of that set. Again if you simply make “open and incomplete” synonymous with “infinite” then your are simply claming “as a result we get a naturally ” infinite “convergent series“.
Again your simple and deliberate ignorance combined with your morbid fantasies do not constitute facts (other than you being deliberate ignorant and enjoying your morbid fantasy).
Again we see that you simply mentioning “DNA” and “the mass of a shrinked star” “clearly summarizes your “deep” understanding of” those subjects. Doron you simply mentioning those topics does not suddenly imbue either you or your OM with any understanding of them (“deep” or otherwise).
Who ever said anything about “stretched points”, other then you?
What? So now the series does not even have a limit? Again you simply making “incomplete” sysnonomus with “infinite” means all you are claiming is that the series “is inherently” infinite.
Your simple and apparently deliberate ignorance of what constitutes a fractal does not infact make them fractals
Um “incomplete” would be a class of collections (even when you do simply make it mean infinite), again since you make “incomplete” synonymous with “infinite” you are again simply stating that “any infinite collection is inherently” infinite.
Again your simple and deliberate ignorance as well as your preference for your morbid fantasy do not refute that proof.
No, it is closed under an operation of succession as clearly stated and affirmed by your own assertion.
Until you stop deliberately choosing to be just a baby about things. Any chance of you growing up any time soon Doron?
It was Head/Hummer that I recommended, if you recall.
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doronshadmi
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The Man said:
Bended line has no impact on its length, and this is exactly the reason of why infinitely many bended levels are inherently incomplete (the 0 length at the limit is not reached, otherwise we get the false equation (X>0)=0).
Standard Math can't deal with this anomaly by using Limits.
The Man said:
1) The invariant length of Koch's fractal is measured under 1-dim (only the length is considered).
2) The length of the 1-dim element , which clearly converges at each additional bended level, is not influenced by the infinitely many additional bended levels.
3) So we get an anomaly of standard analysis, where at the base of 1/1+1/4+1/16+1/64+1/256+… convergent series of bended levels there is an invariant length > 0, which is resulted by an incomplete number of bended levels, because it logically can't reach the limit point, which its length is exactly 0.
4) By including the limit point as a part of the convergent series of bended levels, we actually claim that the invariant length > 0 is also equal to the length of the limit point, which is exactly 0, which is a contradiction notated as (X>0) = 0.
5) Conclusion:
X>0
X+X+X+X+… stands at the basis of a convergent series like 1/1+1/4+1/16+1/64+1/256+… and as a result this series is incomplete exactly because (X>0) = 0 is false.
The limit (which has length 0) or any bended location along the 1-dim element, do not contribute anything the invariant X>0 length of the 1-dim element.The Man said:
The bended locations along X invariant length contributes only the convergence of X upon infinitely many bended levels, which are incomplete, exactly because X length is invariant under infinitely many convergent bended levels ((X>0) = 0 is not a part of the reasoning).
So The Man, after all 1+1+1+… is relevant under a convergent series like 1/1+1/4+1/16+1/64+1/256+…
You are right about that. You used the term "dragged point" in order to define a line.The Man said:
In that case please show us how a dragged 0-dim, which is local by nature, can define a 1-dim, which is non-local by nature.
Good morning The Man, your limit notion is only a part of your false dream.The Man said:
No.The Man said:
Incompleteness is exactly the notion that is not bounded by the Class notion.
Succession it a Trojan horse of any closed notion, exactly as the invariant X>0 is a trojan horse of the convergent series 1/1+1/4+1/16+1/64+1/256+… which is naturally opened (the inconsistency of (X>0)=0 is not a part of the consistent reasoning of the openness of any infinite collection).The Man said:
The Man said:
Any chance that (X>0)=0 will not be a part of your reasoning, The Man?
The "sudden effect" of these topics is the result of your obsolete Limit-oriented knowledge of these topics.The Man said:
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doronshadmi
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Nonsense.jsfisher said:
Real universal notions are not limited to any particular language or form of expression.
So this time please translate the universal notion to plain English and do not hide behind your particular expression of it.
jsfisher said:
Wake up jsfisher it is already done at http://www.internationalskeptics.com/forums/showpost.php?p=5704824&postcount=9004 (both by a diagram and a string of symbols) but you can't get it because your reasoning is closed under the expression of a sting of linear representation of symbols (which is nothing but a particular expression of a notion, and if a notion is limited to some particular representation, its universality is lost).
This is the whole idea of a universal notion, it is not limited to any particular expression of it.jsfisher said:
Again your linear-only step-by-step local-only reasoning rising its limited head.
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doronshadmi
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The Man said:
Again generalization problems The Man?
The general thing here is Length.
By providing the proof without words (http://en.wikipedia.org/wiki/Proof_without_words) below, I clearly expose an anomaly at the Limit-oriented reasoning, where a convergent length is linked with an invariant length, over infinitely many convergent scale levels, and as a result the convergent series of that convergent length can't have 0 as a part of that series.
As a result we get infinitely many and incomplete convergent scale levels, that approaches but can't get length 0.
The Man said:
1) 1.2619… is not an accurate value, so you have no accurate sum of Koch's fractal dimension, and your Limit-oriented approach fails also in this case.
2) 1.2619… is some (and non-accurate) result of a particular logs's base, so also in this case 1.2619… does not provide the dimension of Koch's fractal.
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doronshadmi
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The Man said:
EDIT:
So they are least upper bounds or greatest lower bounds, which are known also as the limits of a given set, which are not necessearly members of a given set.
It does not change the fact that the limit element is not the final element of an infinite collection, whether it is a member of a given set or not.
We are dealing here with a limit of a convergent series of added length, and I provided a proof without words in http://www.internationalskeptics.com/forums/showpost.php?p=5704824&postcount=9004 which proves that an infinite convergent series has no limit.
This proof is an anomaly of standard math of this subject, and therefore cannot be comprehended by using the standard knowledge of this subject.
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The Man
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The point wasn’t about length, but dimensions. Are you simply or deliberately unable to distinguish length from dimensions?
Since you bring up length anyway, the Koch curve has an infinite length giving the Koch snowflake an infinite perimeter, but it still encompasses a finite area.
Try actually learning and using what you call “Standard Math”, at least then you might understand the difference between length and dimension.
That “length” still involves more than one dimension so the appropriate term would be perimeter.
In the actual construction of a Koch snowflake the perimeter increases by 1/3 with each iteration so the value of it’s perimeter is divergent not convergent.
Now in limiting that perimeter to a finite value (1 in this case) you wind up with an interesting problem. In that you have to scale down the construction (of an actual Koch snowflake) by 1/3 with each iteration to maintain your finite perimeter requirement. So you are simply scaling down your inscribing circle by 1/3 each time and thus end up with a convergent series with a common ration of 1/3 that starts at a value of 2*p*{[Tan(60)*1/6]-[Tan(30)*1/6]} or about 1.209 (the circumference of your first circle). Making the difference between the 3 times series and your original as 6*p*{[Tan(60)*1/6]-[Tan(30)*1/6]} (3 times circumference of your first circle) and thus the sum of your series as 3*p*{[Tan(60)*1/6]-[Tan(30)*1/6]} or about 1.814 (3/2 times the circumference of your first circle).
So your inclusion of your perimeter limited pseudo-Koch snowflake is entirely superfluous, as jsfisher has already noted.
The “anomaly of standard analysis” simply remains yours, based once again on your simple or deliberate misunderstanding and misrepresentation of what you call “Standard Math”.
Again the limit of a set need not be a member of that set and the perimeter in the construction of an actual Koch snowflake is divergent not convergent. The fractal has an infinite perimeter, but encompasses a finite area.
“1/1+1/4+1/16+1/64+1/256+…” is not “X+X+X+X+…” it is however X+X/4+X/16+X/64+X/256.…. Again “X+X+X+X+…”, having a common ratio equal to 1, would be divergent not convergent. Once again your assertions are easily demonstrated to be simply false.
A limit contributes exactly that, a limitation. Exactly as your perimeter value always equals one is just your own limitation in this instance.
If “X” is “invariant” then a series of infinitely many “X”s is not convergent.
No Doron even after all your nonsensical gibberish “1+1+1+…” is still only divergent and “1/1+1/4+1/16+1/64+1/256+…” only convergent.
It was already given to you before Doron.
http://en.wikipedia.org/wiki/Dimension
http://en.wikipedia.org/wiki/Inductive_dimension
Just another way of considering or defining the dimensions of an object or space in what you like to call “Standard Math”.
Good morning Doron, oh wait, sorry, you still haven’t woken up from your morbid dream of saving our civilization with your OM fantasies. Well, maybe tomorrow then?
Unbounded sets are a class of sets just as bounded sets are.
http://en.wikipedia.org/wiki/Unbounded_set
No the inclusion in the set of the successor of any element in that set is specifically what closes the set under an operation of succession on any element of that set. If you think it is a “Trojan horse” that attacks your notions that’s just because you brought it in yourself.
It never has been Doron, it is simply part of your deliberately failed “reasoning” that you like to ascribe to others.
“sudden effect”? So you do think that simply mentioning some topic out of hand has a "sudden effect" that you hope will confuse people into thinking you actually know something about that topic?
Again Doron “generalization” does not mean simply claiming whatever you think suits your notions.
Again the appropriate term would be perimeter since more than one dimension is involved.
Again a limit need not be a member of the set. For some reason you seem to think that the set not including its limit or limits as members somehow makes it incomplete. Of course since you simply make “incomplete” synonymous with “infinite” your assertion of “As a result we get infinitely many and incomplete convergent scale levels” simply means “As a result we get infinitely many and” infinite “convergent scale levels”.
“sum of Koch's fractal dimension”? Who said anything about a “sum of Koch's fractal dimension”, other than you. So now you are just going to deliberately confuse the Hausdorff dimension of a fractal with the sum of a convergent series? Yes “1.2619… is not an accurate value” that is why I said “or about 1.2619” the exact value is log(4)/Log(3) also as clearly given before.
It provides the Hausdorff dimension of that fractal and others. As jsfisher has asked before….
What you call “standard math” is not the dogmatic adherence to previous understanding that you like to pretend and profess it to be.
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I think this should be noted as a red-letter day. Doron has added something interesting to the thread.
The Man
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Not all sets are bounded.
If it is a member (and least upper bound) then it is the finail element of that collection.
No you didn’t, you simply imposed your own limit of the perimeter value for your superfluous pseudo Koch snowflake must be one and that still didn’t remove the limit of 0 for your scaled down inscribing circles or the sum of that series, which I have given you in my previous post.
The “anomaly” is just in your brain Doron that has you preferring your own misinterpretation and misrepresentations and therefore you simply can not comprehend “the standard knowledge of this subject”.
The Man
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Its about time.
Manopolus
Metaphorical Anomaly
The Man
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Does it count if the only one Doron actually intimidates into believing his notions or “proof” is himself?
jsfisher
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Since "real universal notions are not limited to any particular language or form of expression" you should have no trouble dealing with the form I provided.
In other words, you deal with the translation.
Was there something you found lacking in my formulation of the Axiom of Infinity? If so, let's discuss that rather than your lack of fluency in formal languages.
No, it wasn't already done back in that or any URL. You don't define your terms, ever.
It can be a universal notion only if it is, um, what's the word, oh yeah, universal. Yours are not. They are just nonsense. What to prove me wrong? Then define something.
jsfisher
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Setting aside for a moment your bogus attempt at using AutoCAD as an automated theorem generator, what is it you think you actually proved? Can you give a concise statement of your theorem?
doronshadmi
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The Man said:
No, it has an incomplete area based on infinite interpolation that has no accurate sum.
You still do not get that any infinite collection is inherently incomplete, whether it is expressed as infinite interpolation or infinite extrapolation.
All you did is to show that an infinite interpolation has no accurate sum (in your language it is about 1.814…), which is exactly the same result of my infinite converges series, which has an invariant length of Koch's fractal > 0 that can't reach the limit value, which is exactly 0.The Man said:
And I also showed it without using any circle, but simply show how the convergent length between the opposite edges of the Koch's fractal can't be 0, as long as these edges are in common with the invariant length of the Koch's fractal, upon infinitely many bended levels, here it is again (no circles are used):
You simply have no real notion of the inherent incompleteness of infinite collection (and in this case, infinite collection of bended levels).
A finite value has an accurate sum, an infinite value does not have an accurate sum, but you simply can't get it because you do not understand the real nature of infinite interpolation\extrapolation.
The Man said:
The Man said:
Again, the convergent length between the opposite edges of the Koch's fractal can't be 0 (where 0 is the value of the limit), as long as these edges are in common with the invariant length of the Koch's fractal, upon infinitely many bended levels, as shown above, but you prefer to ignore this proof without words, because it does not fit your Limit-oriented notion, which is obsolete.
Exactly because the Koch's fractal has an invariant length > 0 , there are infinitely many bended levels that can't reach the value of the limit, which is exactly 0.The Man said:
The limitation is entirely the result of your Limit-oriented approach, that prevents the notion of infinite interpolation\extrapolation, which is inherently non-limited.
You do not get that in my model there is no dichotomy between invariant AND convergent length, as clearly shown and explained above, but you can't get this anomaly because you are using a model that is based on dichotomy.The Man said:
Both Wiki sources are not based on the qualitative difference between the local and non-local atomic aspects that send at the basis of any complex like Set (for example).The Man said:
Again an obsolete knowledge is used by you The Man, which is irrelevant to OM's novel notions, of this subject.
No, the incompleteness of a collection is not closed under Class, where a set is a particular case of a collection that is closed under Class.The Man said:
Since any infinite collection (where a set is a particular case of a collection that is closed under Class) is inherently incomplete (it has a “Trojan horse”), it does not have "closed gates".The Man said:
You simply ignore the inherent incompleteness of any collection, whether it is closed under Classes or not.
Again, the "“sudden effect” is the result of your obsolete Limit-oriented notion of this subject.The Man said:
No, it is about an anomaly of the standard model, which shows how a length can be both invariant AND variant (converges, in this case) in a one model.The Man said:
This is another example of your inability to understand the generalization of this subject.The Man said:
Any infinite collection is inherently incomplete, or in other words, any given element of that collection is not its final element, and order has no impact on that fact.The Man said:
On the contrary, your Limit-oriented notation, can't get the model where both invariant AND variant (converges, in this case) length are found.The Man said:
Your built-in dichotomy of your notions simply can't get this anomaly of Standard Math model of this subject.
A typical reply of a person that uses built-in dichotomy and Limit-oriented notions of this subject.The Man said:
How boring.
doronshadmi
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zooterkin 
doronshadmi
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The Man said:
Not at all.
Two sizes of the same incompleteness have result 0 if they are subtracted from each other.
The real problem here is 1 – (1/2+1/4+1/8+…) and Archimedes did prove that it = 0.
The self similarity over scales clearly shown also by the following diagram, where the values 1,2,4,8,16,32,… etc. are not reached, ad infinituum:
In other words:
1 – (1/2+1/4+1/8+…) > 0
2 - (1/1+1/2+1/4+...) > 0
4 - (2/1+1/1+1/2+...) > 0
...
etc. ad infinituum/
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The Man
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Since it is the 2 times series (the series added to itself) minus the series, that just leaves the series as the difference between the 2 times series and the series, which in this case is 1.
What so now 1 has “the same incompleteness” as “(1/2+1/4+1/8+…)”? Again what Archimedes proved is that an infinite convergent series has a finite sum and in this case it is 1
Well that goes against your statement above.
Seems you do have a “real problem here”, but it is just with yourself.
Further assumptions based on your simple assumption that the “(1/2+1/4+1/8+…)” has no sum are just as invalid as your initial assumption, which again was proven wrong some 2,300 years ago.
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The Man
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Oh, and happy birthday zooterkin.
jsfisher
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No, you got a big fail on this for multiple reasons.
First, you still continue to refer to the generations of Koch's curve as a fractal. This is pure ignorance on your part; only the generation limit is a fractal.
Second, you have not actually proven the curve generations under your length invariant constraint fit your "lute of doron" shape. It is trivial to do, but you seem unable to actually do it.
Third, you claim (in effect) the distance between the end points of any Koch curve generation cannot be zero in your construction. While the statement is true (but completely beyond your ability to prove, I suspect), it does not let you draw your bogus conclusion about the limit.
Fourth, you make a baseless assumption relating end-point distance and overall curve length for the limiting case in your Koch curve construction.
Fifth, you still insist on using the bogus word "bended".
For your original construction of Koch's snowflake, your argument was equally deficient, but the focus then was the relationships of area and perimeter.
jsfisher
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Uh-oh. Not just any birthday, either. Happy Mid-century Day.
Be very careful, though. Body parts no longer just atrophy; some actually fall off.
doronshadmi
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The Man said:
The Man, 1 is an accurate value where (1/2+1/4+1/8+…) does not have an accurate value.
As a result 1 – (1/2+1/4+1/8+…) = 0.000…1[base 2]
X = (1/2+1/4+1/8+…)
If you think that X+X = accurate value, you simply wrong, because 2X, 4X, 8X etc … do not have accurate values, and Archimedes did not prove that any of 1X, 2X, 4X, 8X ,16X , 32X … etc. have accurate values, and the following diagrams are a proof without words that Archimedes initial assumption was wrong:
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doronshadmi
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jsfisher said:
Exeactly the opposite, only the incomplete generation is an infinite fractal.
Again, 1 is not a fractal and (1/2+1/4+1/8+1/16...) is a single path along a fractal exactly because 1-(1/2+1/4+1/8+1/16...)=0.000...1[base 2], exactly as shown in:
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jsfisher
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It continues to be a great disappointment that you were unable to receive a dictionary for Hanukkah. Have you considered just buying one on your own?
What are you on about now? Nobody has even suggested that 1 be a fractal. That would be idiotic.
The Man
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Again just your baseless assumption that has already been proven wrong some 2,300 years ago.
X = (1/2+1/4+1/8+…)
Just what do you think “Archimedes initial assumption was”? Unlike you he did not simply assume something then draw some images representing that assumption and claim it’s “a proof without words”. Again the basis of Archimedes proof are self similarity, that X=X and X+X-X=X. To refute the proof your have to refute one or all of those aspects the proof is actually based on not simply repeating your assumed and imaginary “accurate value” nonsense. If think you can refute one or all of those aspects to refute that proof you are going to end up just digging a hole for yourself as even your OM depends upon those aspects being valid.
doronshadmi
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You still do not get it do you?
So let us improve the proof without words, by using Koch's fractal.
1) Take a straight 1-dim with length X.
2) Bend it and get 4 equal sides along it.
3) Since the length between the opposite edges is changed to the sum of only 3 sides, and since the number of the sides after the first bending is 4 sides, we have to multiply the bended 1-dim element by 1/(the number of the bended sides), in order to get back length X.
As a result the bended 1-dim element has length X, but the length between its opposite edges becomes smaller (it converges).
In general, this convergent series of 1/(the number of the bended sides) is resulted by 1/1+1/4+1/16+1/64+1/256+... , where X is subtracted by (2a+2b+2c+2d+…)
Here is the result:
4) By Standard Math X – (2a+2b+2c+2d+…) = 0
5) (4) is false because (2a+2b+2c+2d+…) can be found as long as X is found.
6) Since X is found upon infinitely many scale levels then (2a+2b+2c+2d+…) must be < X , and as a result X - (2a+2b+2c+2d+…) > 0.
7) Conclusion: (2a+2b+2c+2d+…) does not have sum X.
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doronshadmi
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The Man
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Why does the area encompassed by the Koch snowflake need to be a sum? Or based on some imaginary reference of your “interpolation that has no accurate sum”?
The area is complete and finite.
You still don’t get assumptions as well as imaginary reference like “infinite interpolation or infinite extrapolation” do not constitute facts or proofs, Even "proof without words" which none of your so called "proofs" are actualy without (the words that is, they are certianly without and proof)
Again the exact value of that sum of your infinite convergent series was give as “3*p*{[Tan(60)*1/6]-[Tan(30)*1/6]}” and “3/2 times the circumference of your first circle”, 1.814 is just an approximate decimal rounded off representation of that value, which again is why I specifically said “or about 1.814”.
Who has claimed it would be 0 other then you and your deliberately erroneous “reasoning” that you just like to ascribe to others? Again the Koch curve increase in length by 1/3 with each iteration. So you still have to scale down each iteration to keep your constant length. Thus you still end up with a common ratio for the series of 1/3. Making the difference between the original series and the 3 times series still equal to twice the sum of the original series and 3 times your original series starting value. So the sum of your original series is still 3/2 times your starting value. If that starting value is 1 then the sum of the series is just 1.5.
You simply have no real notion of the easily demonstrable invalidity of you assumptions, even some 2,300 years ago.
Again simply your assumption and the fact that an infinite convergent series has a finite sum was proven some 2,300 years ago.
Again
Who has claimed it would be 0 other then you and your deliberately erroneous “reasoning” that you just like to ascribe to others? Again since the Koch curve increase in length by 1/3 with each iteration. So you still have to scale down each iteration to keep your constant length. Thus you still end up with a common ratio for the series of 1/3. Making the difference between the original series and the 3 times series still equal to twice the sum of the original series and 3 times your original series starting value. So the sum of your original series is still 3/2 times your starting value. If that starting value is 1 then the sum of the series is just 1.5.
Oh so now it has a limit again?
No Doron the limitation is simply yours since you can’t seem to make up you mind what you think you what to claim you prove “without words”. The series has no sum, the series has no limit or the sum simply does not equal the limit. The real reason you can’t make up you mind it that you simply do not know what you are talking about and you do prove that with words.
A significant problem for your “model”, but hey it’s your model and your problem.
So they are not based on your unsupported and often proven wrong assumptions, I’m sure everyone will be so dismayed.
Again Doron your simple reliance on your fantasies, misunderstanding and misrepresentation are not “novel notions”, you just happen to think they are because they are yours.
Unbounded sets are still a class of sets just as bounded sets are.
The inclusion in the set of the successor of any element in that set is still specifically what closes the set under an operation of succession on any element of that set. If you think it is a “Trojan horse” that attacks your notions that’s just because you brought it in yourself.
You simply assume that “inherent incompleteness of any collection” and think since it is your assumption it should be significant.
Nope just your imagination since you’re the only one who thinks they experience your “sudden effect”.
Again the anomaly is just in your brain, you required the “length” of your pseudo-Koch snowflake to be invariant (1 in this case). So your imaginary “anomaly of the standard model” of it being both “invariant AND variant” is just your simple or deliberate confusion of the “length” you required to be invariant with an actual, well, variable.
This is another example of you thinking “generalization of this subject” means just claiming whatever nonsense suits you.
Again, If it is a member (and least upper bound) then it is the finail element of that collection.
Your simple assumptions, misinterpretations and misrepresentations have “no impact on that fact”
Again your anomaly is only in your brain and results from you simply or deliberately confusing some invariant value (one that you required in this case) with an actual, well, variable.
A typical reply of some one who can not see that they have deliberaly constructed some imaginary “anomaly” to attribute to others since they can not acctualy address what they to call “Standard Math”
How sad.
doronshadmi
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jsfisher
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Project much?
You mean a line segment of length X? You really, really need that dictionary.
Sloppy, sloppy, sloppy. Koch was never so sloppy as this in describing his procedure for generating each next iteration. You need to accurately describe what the result of this bending needs to be, yet you didn't.
By the way, line segments, even bent ones, don't have sides.
That presupposes many things not stated in Step 2. So, this is another fail for doron.
How about we just set aside your gibberish and assume you meant for Steps 2 and 3 that we applied Koch's procedure and then shrunk it by 3/4 to hold the overall length of the result constant.
Under my description of the steps, sure; under yours, not so much. In other news, "bended" is still not the right word to use here.
Another doron failure. So far, your steps take you from a line segment to line segment with a triangular bump in the middle. Perhaps you meant to reapply Steps 2 and 3 to the individual line segments in the current result to get the next result?
No wonder you get so much wrong. You just keep jumping from assumption to wrong conclusion without the least consideration for any gap between the two.
So, why not go back to my post and actually address my points rather than wasting our time with this failed tangent.
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Congratulations, you now have a square.
doronshadmi
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As I said, you simply can't get that X-(2a+2b+2c+2d+...) > 0 as proved in http://www.internationalskeptics.com/forums/showpost.php?p=5715516&postcount=9032 by using a proof without words (http://en.wikipedia.org/wiki/Proof_without_words).
Your rambling will not help you here, jsfisher.
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doronshadmi
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1. should be "square"
2. is this the AutoCAD program? if so - your AutoCAD probably uses "direct perception" as well....
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