What is the definition of an arbitrary angle? wonder!

[bassam king karzeddin]

So, it is a very naive simple question, but it seems that there are so many confusions amongst professional mathematicians in understanding the real meaning of the word (arbitrary) in mathematics, for sure

To illustrate this little concept in angle measurements, it is very simple to understand arbitrary as an existing angle (that is all)

But how do they understand it?

A simple example that constructing an angle of say (Pi/9) was proven impossible construction in mathematics by Wantels for sure

But still, they might understand it as an existing arbitrary angle, and also challenge you to construct it exactly, wonder!

Then the innocent Question by a child comes as this,

If mathematics proved it as impossible construction by all the means given, then what is the probability that you draw randomly an arbitrary angle that exactly equals to (Pi/9)?

Of course, it is zero probability for sure

But the professional's mathematicians say NO, wonder!

Do you have any explanations to this incurable dilemma? really wonder!

But frankly, I personally have those published explanations, for sure

Regards
Bassam King Karzeddin
May 22, 2017

[burs...@gmail.com]

Stevie Wonder, again?

Am Montag, 22. Mai 2017 16:30:15 UTC+2 schrieb bassam king karzeddin:
> So, ... for sure
>
> To (that is all)
>
> But ?
>
> A simple ... for sure
>
> But still, ... wonder!
>
> Then ,
>
> If ?
>
> Of ... for sure
>
> But ... wonder!
>
> Do ... really wonder!
>
> But .. for sure

[Dan Christensen]

On Monday, May 22, 2017 at 10:30:15 AM UTC-4, bassam king karzeddin wrote:
> So, it is a very naive simple question...

See the definition of angle given at https://en.wikipedia.org/wiki/Angle ? By "arbitrary angle," we just mean an angle of unspecified measure in a proof.

I hope this helps.


Dan

[burs...@gmail.com]

Yes! A placeholder without a domain restriction.

An arbitrary angle: a
An angle between 0 and pi/2: a such that 0 =< a =< pi/2.

http://wordnetweb.princeton.edu/perl/webwn?s=arbitrarily

[bassam king karzeddin]

> On Monday, May 22, 2017 at 10:30:15 AM UTC-4, bassam
> king karzeddin wrote:
> > So, it is a very naive simple question...
>

> See the definition of given at

> https://en.wikipedia.org/wiki/Angle ? By "arbitrary

> angle," we just mean an angle of unspecified measure.

>
>
> I hope this helps.
>
>
> Dan

Yes, I looked into those pages at Wikipedia, but it seems that they have so many confusions about the angle concept, from being the intersection of straight lines, planes, curves, ... etc

But, so, unfortunately, I cannot write there professionally to correct them about mixing up so many other issues together

but truly they have not understood the real meaning of an arbitrary angle, which is always an existing angle provided in any arbitrary constructible triangle

So, yes they are useless untruthful sources for sure

BKK

[burs...@gmail.com]

There is no reason that an arbitrary angle can mean a constructible
angle. It depends on the context you are working in.

For example in the context of natural numbers:
An arbitrary natural number means: n in N
A natural number between 10 and 15 means: n in {10,11,12,13,14,15}

The word arbirtrary is neither antonym nor otherwise in
any relationship to the word constructible.

It only indicates that in the current domain you are working,
you pick any element from the domain.

If your domain is some constructible angles A, then arbitrary
means from this domain A.

The word arbitary also indicates somehow that the placeholder
is an input, and not an output dependent on some input.

Since an output cannot be arbitrary anymore, it depends on
the input. So if we for example have as input:

Input:
n : an arbitrary natural number

And as output the succeessor:

Output:
m = S(n) : The successor of n

The m cannot be arbitrary (in German beliebig) anymore,
if both n and m were arbitrary we could choose:

n m
1 1
2 1
1 2
2 2
etc..

But since m=S(n) we can only have:

n m
1 2
2 3
3 4
etc..

Thats also why you don't understand angle trisection,
or any other math here, in angle trisection:

Input:
a : An arbitrary angle

Output:
b = a/3 : The trisected angle

Angain a and b cannot be both arbitrary anymore, since
this would allow:

a b
360 360
360 120
120 360
120 120
etc..

But for trisection we need:

a b
360 120
etc..


Get some skills Stevie Wonder. Skills is everything.
The word arbitrary is pretty standard in math. Its the
most easy way to say in passing that something is input

in a construction. You find it in dozen texts, here are
some samples:

"It concerns construction of an angle (=output) equal to
one third of a given arbitrary (=input) angle"
https://en.wikipedia.org/wiki/Angle_trisection

"it's suppose to be impossible to trisect (=ouput) an
arbitrary (=input) angle with just a compass and
straight-edge"
https://math.stackexchange.com/a/2181844/4414

The word arbitrary has of course a further connotation,
here, since some angles are indeed trisectible, it highlights
that we are asking for a general solution.

It asks whether trisection works always, so for each
input can we get an output?

[burs...@gmail.com]

Corr.:
There is no reason that an arbitrary angle cannot mean a constructible

angle. It depends on the context you are working in.

[Dan Christensen]

On Monday, May 22, 2017 at 1:50:12 PM UTC-4, bassam king karzeddin wrote:
> > On Monday, May 22, 2017 at 10:30:15 AM UTC-4, bassam
> > king karzeddin wrote:
> > > So, it is a very naive simple question...
> >
> > See the definition of given at
> > https://en.wikipedia.org/wiki/Angle ? By "arbitrary
> > angle," we just mean an angle of unspecified measure.
> >
> >
> > I hope this helps.
> >
> >
> > Dan
>
> Yes, I looked into those pages at Wikipedia, but it seems that they have so many confusions about the angle concept, from being the intersection of straight lines, planes, curves, ... etc
>

"In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.[1] Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.

"Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation."

Which part did you not understand?

> But, so, unfortunately, I cannot write there professionally to correct them about mixing up so many other issues together
>
> but truly they have not understood the real meaning of an arbitrary angle, which is always an existing angle provided in any arbitrary constructible triangle
>

They do understand. It is you who seem to be mixed up, as on so many issues.


Dan

[bassam king karzeddin]

On Monday, May 22, 2017 at 10:21:14 PM UTC+3, burs...@gmail.com wrote:
> Corr.:
> There is no reason that an arbitrary angle cannot mean a constructible
> angle. It depends on the context you are working in.

Good that you had corrected yourself immediately, and a chosen arbitrary angle is simply a constructible angle (by common sense only)

Exactly, similar to the case when you take an arbitrary distance or length, that must be represented by a constructible number, no wonder!

Didn't you just construct it arbitrarily? so this the common sense that mathematics stay behind, it is a more powerful tool than what they called rigorous proof, it is indeed the common sense that had been forgotten or deliberately ignored for so many centuries for not being considered as the golden hen,

So, this is what we have been trying to convey to the mathematicians for long, it is mainly the common sense which is essential to mathematicians before anything else, for sure

BKK

[burs...@gmail.com]

No, not by any fixed common sense. Math explores spaces.
You have the choice:
- you can study real numbers
- you can study algebraic numbers
- etc..

Go home, you are drunk. Learn some math Queeny
the Unicorn sodomizer.

[Dan Christensen]

On Monday, May 22, 2017 at 12:34:26 PM UTC-4, burs...@gmail.com wrote:
> Yes! A placeholder without a domain restriction.
>

As geometric figure in a plane, an angle is determined by three points (some restrictions apply). The measure of an angle can be any real number. The units are usually given as degrees or radians.

Dan

[bassam king karzeddin]

On Tuesday, May 23, 2017 at 3:07:39 PM UTC+3, burs...@gmail.com wrote:
> No, not by any fixed common sense. Math explores spaces.

which spaces that maths can explore, wonder!

The negative coordinate (3D) space, they so foolishly adopt? wonder!

Or that imaginary space in your dreams you mean?

Or maybe that multi-dimensional fictitious spaces they claim? wonder

The bitter fact is that even the only real existing (3D) space around your so tiny head couldn't be understood by the giant dinosaur size genius mathematicians on earth and so shamefully up to this date, wonder!

> You have the choice:

Believe it, there is no choice in true mathematics but only force

> - you can study real numbers

Real existing numbers are only those existing constructible numbers for sure

> - you can study algebraic numbers
> - etc..

Yes, but only those real existing constructible algebraic numbers

>
> Go home, you are drunk. Learn some math Queeny
> the Unicorn sodomizer.

You must drop the largest portion of your junk fake maths in order to be normal person, for sure

And an arbitrary angle means exactly constructible angle

And an arbitrary length means a constructible length that is constructible number

And if it is proven beyond any little doubt that some angles or some lengths are of impossible to construct exactly, then how the hell would be that possible by arbitrary construction, wonder!

But yes, this is the modern so advanced mathematics where Monkeys can state theorems, but which theorems? wonder!

BKK

[bassam king karzeddin]

No, this is false conclusion for sure

A geometric figure in a plane defined by three arbitrary points not colinear determine a triangle, with three constructible sides and three constructible angles, for sure

And if mathematics itself had proven that exact construction of the alleged real number 2^{1/3} is impossible and the exact construction of the angle (40) degrees is also impossible, then how the hell is that exactly possible by random arbitrary construction? wonder!

So, The claim that says the measure of an angle can be any real number is definitely false, for sure, based mainly on common sense

And the funniest part in angle measurements, that they used units angles that never existing angles, such as one rad. angle, or one-degree angle, wonder!

So much ignorance in mathematics, for sure

BKK

[Dan Christensen]

On Tuesday, May 23, 2017 at 10:50:23 AM UTC-4, bassam king karzeddin wrote:
> On Tuesday, May 23, 2017 at 3:44:07 PM UTC+3, Dan Christensen wrote:
> > On Monday, May 22, 2017 at 12:34:26 PM UTC-4, burs...@gmail.com wrote:
> > > Yes! A placeholder without a domain restriction.
> > >
> >
> > As geometric figure in a plane, an angle is determined by three points (some restrictions apply). The measure of an angle can be any real number. The units are usually given as degrees or radians.
> >
> > Dan
>
> No, this is false conclusion for sure
>

Only in silly little math fantasy world, BKK.

> A geometric figure in a plane defined by three arbitrary points not colinear determine a triangle, with three constructible sides and three constructible angles, for sure
>

There is no requirement that a triangle be "constructible" with your antiquated drafting tools.

> And if mathematics itself had proven that exact construction of the alleged real number 2^{1/3} is impossible and the exact construction of the angle (40) degrees is also impossible, then how the hell is that exactly possible by random arbitrary construction? wonder!
>

Wrong again on both counts, BKK. 2^(1/3) is constructible with a Cauchy sequence or a Dedekind cut. See https://en.wikipedia.org/wiki/Construction_of_the_real_numbers

And a 40 degree angle is constructible with an ordinary protractor. Think of it as 1/9 of a revolution. There is nothing "unreal" about it. I wonder what you must do in your silly little math fantasy world when you come across a triangle that has angles 90 and 50 degrees. Can you not calculate the other angle? You are an idiot if you think such triangles do not exist.


Dan

Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

[bassam king karzeddin]

On Tuesday, May 23, 2017 at 10:48:49 PM UTC+3, Dan Christensen wrote:
> On Tuesday, May 23, 2017 at 10:50:23 AM UTC-4, bassam king karzeddin wrote:
> > On Tuesday, May 23, 2017 at 3:44:07 PM UTC+3, Dan Christensen wrote:
> > > On Monday, May 22, 2017 at 12:34:26 PM UTC-4, burs...@gmail.com wrote:
> > > > Yes! A placeholder without a domain restriction.
> > > >
> > >
> > > As geometric figure in a plane, an angle is determined by three points (some restrictions apply). The measure of an angle can be any real number. The units are usually given as degrees or radians.
> > >
> > > Dan
> >
> > No, this is false conclusion for sure
> >
>
> Only in silly little math fantasy world, BKK.
>
>
> > A geometric figure in a plane defined by three arbitrary points not colinear determine a triangle, with three constructible sides and three constructible angles, for sure
> >
>
Dan wrote:

> There is no requirement that a triangle be "constructible" with your antiquated drafting tools.

Of course, this was not anyone else requirements but only my theorem:

So, for any arbitrary angle on a plane formed by intersection of two straight lines, take any two known distances from the intersection point (say in constructible numbers since you have no other choice to avoid any confusions), then you have three points on your Euclidean plane where they must form a triangle, where also the third side must be constructible number, so for the arbitrary angle that must be constructible,

Hey, did not you construct it arbitrarily, wonder!

I know these types of theorems are too difficult to prove in the current wrong concepts of modern mathematics since they need basically the tool called the common sense, where this is a missing element in maths for sure

>
> > And if mathematics itself had proven that exact construction of the alleged real number 2^{1/3} is impossible and the exact construction of the angle (40) degrees is also impossible, then how the hell is that exactly possible by random arbitrary construction? wonder!
> >
>
> Wrong again on both counts, BKK. 2^(1/3) is constructible with a Cauchy sequence or a Dedekind cut. See https://en.wikipedia.org/wiki/Construction_of_the_real_numbers

That is like many alleged wrong proofs, but so foolish and too naive conclusions as proved many times in my posts and not better than any trial and error endless approximations even before BC

> And a 40-degreeS angle is constructible with an ordinary protractor. Think of it as 1/9 of a revolution. There is nothing "unreal" about it. I wonder what you must do in your silly little math fantasy world when you come across a triangle that has angles 90 and 50 degrees. Can you not calculate the other angle? You are an idiot if you think such triangles do not exist.

>
>
> Dan
>
> Download my DC Proof 2.0 software at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

OK, the triangle with given sides (2, 3, 4) has all of its angles simply constructed and EXACTLY, so provide us only with any constructible sides triangle that has one of its angles (40) or (50) degrees, then I must believe you for sure

I am afraid that you may require that perfect circle that doesn't exist for sure

Good luck

BKK

[bassam king karzeddin]

I am quite sure that you would never come back with that constructible sides triangle that has one of its angles (40) or (50) degrees angles since, in reality, the whole existing universe is insufficient to include that triangle exactly

But see how funny is that so easily possible in mathematics, just press on sin function in degrees for sin (40) and within a second it would immediately display you around 10 decimal digits answer and you would be more than happy with such alleged accuracy, wonder

So, the machine is also dumber than the programmer or the theorists who betrayed also every stone chess in this big game of mind illusions for sure

That is to say as once described by me many years ago, that the science of trig functions (sin (theta), cos, tan, sec, ...etc) is totally flawed and bad translation to the mainly greatest theorem in mathematics (Pythagorean theorem)

So, they had betrayed Pythagoras for sure, and he is really very, very angry

So, Dan is clueless as always as usual for sure

BKK

[Markus Klyver]

You can define the angle θ between two vectors u and v in a linear vector space as the smallest real number θ such that <u, v> = ||u|| ||v|| cos θ. From this, we see that θ = arccos( <u, v>/(||u|| ||v||) ).

If we consider the vector space of all polynomials, with <p, q> := int_{-1}^1 p(t) * q(t) dt as the inner product, we see that the angle between the polynomials p(t) = 1 + t and q(t) = t^2 is θ = arccos( <u, v>/(||u|| ||v||) ) = arrcos( (2/3) / sqrt(8/3) sqrt(2/9) ) = arccos( 1/(3 sqrt(3) ), which is approximately 78.9 degrees.

[John Gabriel]

How old are you sonny? The guy you responded to is an engineer. He knows all this crap. You are not understanding his question/comment.

You should ask when you don't understand and stop pretending.

[Markus Klyver]

Well, the usage of "abitary" means every angle can be picked.

[John Gabriel]

Nope. Arbitrary means you have a number that describes every angle. Not possible. There are no irrational numbers.

[Dan Christensen]

Of course it does, but BKK is an idiot. If I understand correctly, in his mathematical fantasy world, angles of 40 degrees cannot exist because he doesn't know how to construct them using ancient drafting tools (some kind of ruler and compass). On this basis, 45 degree angles are somehow sacred, while 40 degree angles are unholy, the work of the devil or some such nonsense.

Welcome to sci.math, Markus. Yes, the inmates seem to have taken over the asylum here. But there is still some worthwhile discussions going on in the corners.

[Markus Klyver]

Well, you could restrict yourself to rational numbers if you wish so. But I don't know what an "irrational angle" would be, as you can choose your unit angle in a way such that you can make any angle "rational".

[bassam king karzeddin]

Markus Klyver

> Well, the usage of "abitary" means every angle can be picked.

Good enough, you are on the right way and about to get it completely & so intuitively and very away of any well-established mathematical concepts as hallucinations.
however, you must drop that old common conceptual meaning among the common (old and modern) mathematician of understanding the true deep meaning of the word arbitrary, which is related deeply to the probability of an occurred event, and generally (possibility vs impossibility).
or (existence vs non-existence)

So, my modification to your answer would be as this:

"An arbitrary angle is that angle which is an existing angle and also a constructible angle, for sure"

Same for real number definition as this:

"An arbitrary real number is that number which is an existing number and can be constructed exactly relative to any arbitrary existing and constructible unit"

Note here the proof depends solely on common sense, (i.e self-proved statement)

I am also aware that a common sense principle is not accepted in (old and modern mathematics) wonder!

Which constitutes the main objection barrier of blocking the human minds

Regards
Bassam King Karzeddin
May 27, 2017

[Markus Klyver]

What's a "constructable angle"? Is this just very naive constructivism?

[bassam king karzeddin]

On Saturday, May 27, 2017 at 12:00:25 PM UTC+3, Markus Klyver wrote:
> What's a "constructable angle"? Is this just very naive constructivism?

Well, based on above illustration, you can say the constructible angle is simply the arbitrary angle created in any triangle with constructible sides or arbitrary sides

It seems that the word (arbitrarily) is exactly equivalent to (constructible) in maths, for both numbers or lengths, and angles to wonder!

It seems for the first while confusing, but it is true for sure

Take any arbitrary length on the real number line, don't you just construct it exactly? wonder

Take any arbitrary angle on the unit circle line, (angle Pi) don't you just construct it exactly? wonder

Constructible numbers are also in Wikipedia, check it

BKK

[Markus Klyver]

Oh, so it is just naive constructivism. You believe no other lines, points and numbers exist except those that can constructed with unruled straightedge and compass.

[konyberg]

Since I was the guy who triggered you I should tell you what I mean by arbitrary angle.

An arbitrary angle is an angle that is undetermined; not assigned a specific value.

KON

[bassam king karzeddin]

Indeed, it is exhausting to explain to everyone separately, but you can so simply see my challenges in my recent posts

Just consider that given to Dan. get us any triangle with exact sides that has at least one of its angles is exactly (40) degrees

Good luck

BKK

[burs...@gmail.com]

Queeny, they are not called unexisting angles, they
are called Mothra numbers. When will you learn?

For lengths we use Unicorn numbers.

For angles we use Mothra numbers.

Mothra VS Godzilla
https://www.youtube.com/watch?v=4bhoWfC1L9k

[Markus Klyver]

Well, I would suggest you grow up and widen your narrow-minded view that mathematics is all geometry. It isn't.

[bassam king karzeddin]

On Saturday, May 27, 2017 at 2:28:55 PM UTC+3, Markus Klyver wrote:
> Den lördag 27 maj 2017 kl. 12:40:37 UTC+2 skrev bassam king karzeddin:
> > On Saturday, May 27, 2017 at 12:00:25 PM UTC+3, Markus Klyver wrote:
> > > What's a "constructable angle"? Is this just very naive constructivism?
> >
> > Well, based on above illustration, you can say the constructible angle is simply the arbitrary angle created in any triangle with constructible sides or arbitrary sides
> >
> > It seems that the word (arbitrarily) is exactly equivalent to (constructible) in maths, for both numbers or lengths, and angles to wonder!
> >
> > It seems for the first while confusing, but it is true for sure
> >
> > Take any arbitrary length on the real number line, don't you just construct it exactly? wonder
> >
> > Take any arbitrary angle on the unit circle line, (angle Pi) don't you just construct it exactly? wonder
> >
> > Constructible numbers are also in Wikipedia, check it
> >
> > BKK
>

Markus wrote:
> Oh, so it is just naive constructivism. You believe no other lines, points and numbers exist except those that can constructed with unruled straightedge and compass.

there is nothing called naive, or any naive constructivism is not yet defined in mathematics but soon you might find it in Wikipedia, wonder!

Arbitrary construction means construction for sure

BKK

[Markus Klyver]

Yeah, you're taking a position of extreme constructivism.

[bassam king karzeddin]

I thought that I was the guy who intrigued you about the true meaning of the (arbitrary angle) since it is still there in my old posts from 2004

And misunderstanding this true meaning would certainly make it as perpetual puzzle, or unsolvable problem or impossible construction,...etc, for sure

But I think, I had already solved the whole puzzle, for sure

Please think slowly about it, it is no more a puzzle

And there isn't any puzzle of denying my solution to this old solved puzzle, for more many puzzling reasons that are not of any puzzling mathematics, wonder!

BKK

[bassam king karzeddin]

On Sunday, May 28, 2017 at 12:47:48 PM UTC+3, Markus Klyver wrote:
> Yeah, you're taking a position of extreme constructivism.

So, again with another new undefined concept, wonder!

And what do you mean by extreme constructivism?

BKK

[bassam king karzeddin]

Certainly, the current modern maths is not only geometry or number theory but also with so many fiction sections that had been built up over many centuries with baseless foundations such as, real numbers, complex numbers, negative space coordinates, polynomial roots, ....etc

You would certainly grow up if you really widen your mind and tell me which angle that you construct and can not trisect exactly in this published method of angle trisection

to trisect any existing angle or any arbitrary angle just consider the following circle with arbitrary radius and center at point (C)

then chose any arbitrary two points at the circumference as (A & B)

So, you have a triangle (ABC), say CLOCKWISE

Bisect the angle (ABC), and let the bisector intersects the radius (CA) at point (D)

And let your assumed arbitrary angle be simply (CDB) clockwise, then the angle (DBC) is the exact trisection angle of your assumed arbitrary angle for sure

But, you will get completely confused whenever you assume (but cannot construct) in mind a fiction and nonexisting angle for angle CAB, that explained well enough in my posts

Even the Greeks who posed this OLDEST problem did not understand it the way I expose it here for you, and for sure

(c)

Regards
Bassam King Karzeddin
May 28, 2017

[burs...@gmail.com]

Repaste alarm, same shit again and again:
https://groups.google.com/d/msg/sci.math/X1RsSI7xx6I/L7EFKA8bAgAJ

[Markus Klyver]

You say that a mathematical object can't exist if it can't be constructed with compass and straightedge in a finite number of steps. That is a very naive and extreme form of constructivism to take. Do you reject the concept of proof by contradiction as well?

[bassam king karzeddin]

On Monday, May 22, 2017 at 5:30:15 PM UTC+3, bassam king karzeddin wrote:
> So, it is a very naive simple question, but it seems that there are so many confusions amongst professional mathematicians in understanding the real meaning of the word (arbitrary) in mathematics, for sure
>
> To illustrate this little concept in angle measurements, it is very simple to understand arbitrary as an existing angle (that is all)
>
> But how do they understand it?
>
> A simple example that constructing an angle of say (Pi/9) was proven impossible construction in mathematics by Wantels for sure
>
> But still, they might understand it as an existing arbitrary angle, and also challenge you to construct it exactly, wonder!
>
> Then the innocent Question by a child comes as this,
>
> If mathematics proved it as impossible construction by all the means given, then what is the probability that you draw randomly an arbitrary angle that exactly equals to (Pi/9)?
>
> Of course, it is zero probability for sure
>
> But the professional's mathematicians say NO, wonder!
>
> Do you have any explanations to this incurable dilemma? really wonder!
>
> But frankly, I personally have those published explanations, for sure
>

> Regards
> Bassam King Karzeddin
> May 22, 2017

And the word arbitrary in mathematics means exactly constructible for sure

And this seeming so little misunderstanding is actually a huge factor in realising many important issues, that vast majority of Top Professional mathematicians do not comprehend yet, sure

Otherwise try

BKK

[bassam king karzeddin]

On Monday, May 22, 2017 at 5:30:15 PM UTC+3, bassam king karzeddin wrote:
> So, it is a very naive simple question, but it seems that there are so many confusions amongst professional mathematicians in understanding the real meaning of the word (arbitrary) in mathematics, for sure
>
> To illustrate this little concept in angle measurements, it is very simple to understand arbitrary as an existing angle (that is all)
>
> But how do they understand it?
>
> A simple example that constructing an angle of say (Pi/9) was proven impossible construction in mathematics by Wantels for sure
>
> But still, they might understand it as an existing arbitrary angle, and also challenge you to construct it exactly, wonder!
>
> Then the innocent Question by a child comes as this,
>
> If mathematics proved it as impossible construction by all the means given, then what is the probability that you draw randomly an arbitrary angle that exactly equals to (Pi/9)?
>
> Of course, it is zero probability for sure
>
> But the professional's mathematicians say NO, wonder!
>
> Do you have any explanations to this incurable dilemma? really wonder!
>
> But frankly, I personally have those published explanations, for sure
>
> Regards
> Bassam King Karzeddin
> May 22, 2017

And after all those many demonstrations heading the topics, the arbitrary choice of a real length must represent a constructible number only, for sure

And according to the general definition, I PUBLISHED

BKK

[bassam king karzeddin]

On Monday, May 22, 2017 at 5:30:15 PM UTC+3, bassam king karzeddin wrote:
> So, it is a very naive simple question, but it seems that there are so many confusions amongst professional mathematicians in understanding the real meaning of the word (arbitrary) in mathematics, for sure
>
> To illustrate this little concept in angle measurements, it is very simple to understand arbitrary as an existing angle (that is all)
>
> But how do they understand it?
>
> A simple example that constructing an angle of say (Pi/9) was proven impossible construction in mathematics by Wantels for sure
>
> But still, they might understand it as an existing arbitrary angle, and also challenge you to construct it exactly, wonder!
>
> Then the innocent Question by a child comes as this,
>
> If mathematics proved it as impossible construction by all the means given, then what is the probability that you draw randomly an arbitrary angle that exactly equals to (Pi/9)?
>
> Of course, it is zero probability for sure
>
> But the professional's mathematicians say NO, wonder!
>
> Do you have any explanations to this incurable dilemma? really wonder!
>
> But frankly, I personally have those published explanations, for sure
>
> Regards
> Bassam King Karzeddin
> May 22, 2017

***

[Zelos Malum]

An arbitrary angle is a real number between 0 and 2pi, easy peasy

[bassam king karzeddin]

On Friday, February 9, 2018 at 9:48:54 AM UTC+3, Zelos Malum wrote:
> An arbitrary angle is a real number between 0 and 2pi, easy peasy

So, what is the probability that you choose randomly say a real non-constructible (algebraic or transcendental) number? wonder!

Hint: Zero, (proved earlier in my posts), sure

BKK

[Zelos Malum]

Actually its 1 in naive statistics you moron.

[bassam king karzeddin]

Now and after so many lessons, you should be smart enough to answer this question for sure
BKK