For the mathematicians PI doesn't exist??

[sjastro]

Here is an example of pure drivel.
http://milesmathis.com/pi3.html

I know of 3 rebuttals to this nonsense.

I'll leave as an exercise for any budding mathematicians to refute.

Regards

Steven

[leon]

Bugger, gee you lost me Steven, I will just stick to what I was taught so many years ago, it worked for me then, and I expect it will still work for me now.

Leon

[Robh (Rob)]

Nice fudge!
It is, of course, this statement that is incorrect ...
"If we take this process to its limit, we take our path to the path of the arc AC."
As the number of sub-triangles approaches infinity, it is the sum of the hypotenuses of each sub-triangle that approaches the length of the arc AC.
The hypotenuse of a right-triangle is always less than the sum of the other two sides. Therefore, taking the limit, the arc AC < AD + CD
or arc AC < r, the radius of the circle.

Regards, Rob.

[sjastro]

Originally Posted by Robh

Nice fudge!
It is, of course, this statement that is incorrect ...
"If we take this process to its limit, we take our path to the path of the arc AC."
As the number of sub-triangles approaches infinity, it is the sum of the hypotenuses of each sub-triangle that approaches the length of the arc AC.
The hypotenuse of a right-triangle is always less than the sum of the other two sides. Therefore, taking the limit, the arc AC < AD + CD
or arc AC < r, the radius of the circle.

Regards, Rob.

Thanks for your comments Rob.

If you use Mathis' geometrical step construction you will in fact find the sum of the lengths of the hypotenuses of the sub triangles is a constant value irrespective of the number of sub triangles used. You will never approach the length of the arc as the number of subtriangles approaches infinity.

http://mathisdermaler.wordpress.com/...sion%E2%80%9D/

The second disproof of Mathis' ideas is particularly elegant.

Regards

Steven

[Robh (Rob)]

Originally Posted by sjastro

If you use Mathis' geometrical step construction you will in fact find the sum of the lengths of the hypotenuses of the sub triangles is a constant value irrespective of the number of sub triangles used.

I didn't find any reference to this constancy, which is patently ridiculous as sqr(x1^2+y1^2)+sqr(x2^2+y2^2)<>sqr( (x1+x2)^2+(y1+y2)^2). The fact is that the length of any curve can be obtained by integrating ds where ds^2=dx^2+dy^2.
dx and dy can be considered the horizontal and vertical components of an infinitesimally small right triangle drawn on the section of curve. His assumption that ds=dx+dy is a clear contradiction of Pythagoras' Theorem. As I mentioned before ds<dx+dy for all right-triangles on the curve. His assumptions are unjustifiable.

Regards, Rob

[CraigS]

Aha .. the violation of Pythagoras' Theorem !!

That was going to be my contribution, also !

But I don't think Miles cares about Pythagoras, either !!


But how does he sneak this in ?? At the very beginning, he declares the angle to be 45 degrees and the sides DB and DC to be equal (this is pythagoras' theorem in action). Then he completely refutes it in:

"In other words, it is the hypotenuses of the little triangles that converges upon the curve, not the sums of the other legs of the triangles."

Its kind of like starting off with certain assumptions to prove something and then disprove the assumptions because of some other assumption !

Having made this point ...

Ahhh look, guys … Miles is right !! .. he's a genius and Newton … and everyone since … was just plain wrong !


Cheers
PS: (As he carefully avoids the maths required to disprove Miles) !!

[sjastro]

Originally Posted by Robh

I didn't find any reference to this constancy, which is patently ridiculous as sqr(x1^2+y1^2)+sqr(x2^2+y2^2)<>sqr( (x1+x2)^2+(y1+y2)^2). The fact is that the length of any curve can be obtained by integrating ds where ds^2=dx^2+dy^2.
dx and dy can be considered the horizontal and vertical components of an infinitesimally small right triangle drawn on the section of curve. His assumption that ds=dx+dy is a clear contradiction of Pythagoras' Theorem. As I mentioned before ds<dx+dy for all right-triangles on the curve. His assumptions are unjustifiable.

Regards, Rob

The flaw with Mathis is that he is calculating the length of the chord AC, not the arc AC.
This is clear from his geometrical construction.

For example the chord AC= (AD^2+DC^2)^0.5 is for the triangle ADC.
The chord AC is an approximation of the arc length using a single triangle.
For simplicity lets subdivide into equal subtriangles.
A subtriangle can be constructed with sides AD/n, DC/n where n is the number of subtriangles used. In this case 1/n is a scale factor.

The hypotenuse for a subtriangle is y= ((AD/n)^2 + (DC/n)^2)^0.5.
The total length is the sum of the hypotenuses = n*[((AD/n)^2 + (DC/n)^2)^0.5].

But n*[((AD/n)^2 + (DC/n)^2)^0.5] = (AD^2+DC^2)^0.5 which is the length of the chord AC not the length of the arc AC.
Hence for any value n the result is the same.

Mathis doesn't know his chords from his arcs.

Regards

Steven

[sjastro]

Originally Posted by CraigS

Aha .. the violation of Pythagoras' Theorem !!

That was going to be my contribution, also !

But I don't think Miles cares about Pythagoras, either !!


But how does he sneak this in ?? At the very beginning, he declares the angle to be 45 degrees and the sides DB and DC to be equal (this is pythagoras' theorem in action). Then he completely refutes it in:

"In other words, it is the hypotenuses of the little triangles that converges upon the curve, not the sums of the other legs of the triangles."

Its kind of start off with certain assumptions to prove something and then disprove the assumptions because of some other assumption !

Having made this point ...

Ahhh look, guys … Miles is right !! .. he's a genius and Newton … and everyone since … was just plain wrong !


Cheers
PS: (As he carefully avoids the maths required to disprove Miles) !!

Maybe we should have a "spot the number of errors" competition.

Regards

Steven

[adman (Adam)]

the equation he derives that relates the circumference to the radius of the circle is C = 8r....

bugger the mathematics - you could refute that with a piece of string!

[CraigS]

Not that we're finished with this guy Mathis, yet but here's another beauty …

Bill Gaede's Double Slit debunk.

This one's actually a good laugh …mainly cause of Bill's performance (and of course .. the sheer attention to detail in setting up his experiment) !

Bill was a real life Cold War industrial spy who stole semiconductor industry secrets whilst working for Intel and sold 'em to the Cuban Govt. A wonderful character reference ! His main hobby is Physics … I think he got into it whilst he was in prison.

Still, one of our beloved members, publically recommends his Double Slit refutation !

To be perfectly honest, I think you'd need a Quantum Mechanical background to refute Bill's debunk of it all (??).

Have fun & get a bowl of popcorn for this one (it runs for about 10 mins - sorry, Steven).

Cheers

[Robh (Rob)]

Originally Posted by sjastro

The hypotenuse for a subtriangle is y= ((AD/n)^2 + (DC/n)^2)^0.5.
The total length is the sum of the hypotenuses = n*[((AD/n)^2 + (DC/n)^2)^0.5].

Mathis doesn't know his chords from his arcs.

Regards

Steven

Steven, I agree with your last statement. He doesn't know his chords from his arcs.
However, no matter what way you look at it, the sum of the minor hypotenuses (or chords) will still not equal the larger hypotenuse AC. The triangles are just not similar. You cannot divide AD equally into n parts and result in each sub-triangle having a height of CD/n.

Rob

[Jarvamundo (Alex)]

Steve, might be better if you start with his papers on orbital dynamics prior to moving into this one... then also go for the 'long' version of the paper.

http://milesmathis.com/pi2.html
Abstract: I show that in kinematic situations, π is 4. For all those going ballistic over my title, I repeat and stress that this paper applies to kinematic situations, not to static situations. I am analyzing an orbit, which is caused by motion and includes the time variable. In that situation, π becomes 4. When measuring your waistline, you are not creating an orbit, and you can keep π for that. So quit writing me nasty, uninformed letters.

2-dim pi is the circular ratio of circumference to diameter, C/D = 3.1415926...
3-dim pi is the spherical ratio of surface area to cross-sectional area, 4(pi)R2/(pi)R2 = 4

Strongly recommend reading his other papers... i started with this one first, it threw me off for a while. Having now read his book (but i still struggle with some parts of it), it leads you through the *ideas* in more depth before you hit this stuff, then you understand the domains for applying the *math*.

But yes, quite correct in 2dim pi = 3.14etc.... acknowledged by Mathis.... you need to switch to kinematics.

He's got a fascinating, confronting and challenging book, seems to be getting a bit of traction call the "Un-unified field", gets pretty big wrap from some at NASA, not that that should weigh your own mind examining the material, i'm sure this will be debated for a while yet. I'd love to have your take on it, if you ever find the time.

By the way, turns out associated hydroxyls are expected... still getting some more info on the chemistry, but thanks for the query and IR stuff, it helped my understanding... will write it up in a post when i have the detail in full, or near enough.

[Robh (Rob)]

Originally Posted by CraigS

Not that we're finished with this guy Mathis, yet but here's another beauty …

Bill Gaede's Double Slit debunk.

This one's actually a good laugh …mainly cause of Bill's performance (and of course .. the sheer attention to detail in setting up his experiment) !

Bill was a real life Cold War industrial spy who stole semiconductor industry secrets whilst working for Intel and sold 'em to the Cuban Govt. A wonderful character reference ! His main hobby is Physics … I think he got into it whilst he was in prison.

Still, one of our beloved members, publically recommends his Double Slit refutation !

To be perfectly honest, I think you'd need a Quantum Mechanical background to refute Bill's debunk of it all (??).

Have fun & get a bowl of popcorn for this one (it runs for about 10 mins - sorry, Steven).

Cheers

Unfortunately, I didn't have any popcorn but Bill's performance was rather humorous. Electromagnetic ropes - sounds like a stronger version of some string theory ... ropes and strings.
Instantaneous action at a distance. Smacks a little of our holographic theory again - everything is connected to everything else.

Regards, Rob

[CraigS]

Rob;

Yes .. loved the bit with the cork and the pin !

Sounds a bit like quantum entanglement to me !

Putting all the humour aside though, it did make me think about it all.

Cheers

[CraigS]

Originally Posted by Jarvamundo

Steve, might be better if you start with his papers on orbital dynamics prior to moving into this one... then also go for the 'long' version of the paper.

2-dim pi is the circular ratio of circumference to diameter, C/D = 3.1415926...
3-dim pi is the spherical ratio of surface area to cross-sectional area, 4(pi)R2/(pi)R2 = 4

Strongly recommend reading his other papers... i started with this one first, it threw me off for a while. Having now read his book (but i still struggle with some parts of it), it leads you through the *ideas* in more depth before you hit this stuff, then you understand the domains for applying the *math*.

But yes, quite correct in 2dim pi = 3.14etc.... acknowledged by Mathis.... you need to switch to kinematics.

He's got a fascinating, confronting and challenging book, seems to be getting a bit of traction call the "Un-unified field", gets pretty big wrap from some at NASA, not that that should weigh your own mind examining the material, i'm sure this will be debated for a while yet. I'd love to have your take on it, if you ever find the time.

By the way, turns out associated hydroxyls are expected... still getting some more info on the chemistry, but thanks for the query and IR stuff, it helped my understanding... will write it up in a post when i have the detail in full, or near enough.

Man Alex;

Beats me how you do it mate !!
It takes me ages before I can synch up with this bizarre world to the extent where I can understand where these guys are coming from .. let alone snoop out all the holes in their logic !!

Mind you, I've been thinking a bit about you & all this stuff lately ..

I think I'm prepared to make a concession ..

I really do think that unless you go looking for a specific phenomenon in the Universe, it is arguably, not probable that you'll stumble across it.

This much I do concede.

Such as intergalactic magnetic & electric fields (of notable magnitudes), or significant amounts of predominately non-ionised plasma.

This is not to say that mainstream does not go looking for them. They clearly do.

Just thought I'd say that.

Cheers

[The_Cat (Jeremy)]

Originally Posted by sjastro

Here is an example of pure drivel.

http://milesmathis.com/pi3.html

...

Pure drivel ? Yes! definitely.

Quote from the article (above link):

"The tangent is a component of the arc ... "

and

" ...arc is composed of the tangent. ... "

I know the moderator will kill this sentence, but before one publishes statements like the ones above one really needs to establish the relative positions of the elbow and backside.

Jerry.

[Jarvamundo (Alex)]

Man Alex;

Beats me how you do it mate !!

Instead of dismissing, just apply some sincere attention to the material in full, or simply why even bother in the first place?

The guys preface was written by a current NASA Astrophysicist, whilst not an indication of correctness, it just illustrates there are some, well schooled, who might turn more than one page. It becomes fairly obvious, when studied, Mathis' has a very deep understanding of Newton's & Columb's original works, from original sources. His logic is always presented from first principles.

PS: I'm glad Gaede makes you think.... now try (add) this... http://milesmathis.com/double.html Miles work is very mechanical in nature, and so it uses the simplest of math, it is the ideas that are challenging for those with entrenched schooling, I am still working through and challenged by some of it.... other parts of it have resolved many paradoxes for me. Again i'm more than interested to discuss with anyone who studies the material, especially if some of the brighter sparks around here do so! There are many benefits in challenging ones ideas, if it's done with sincerity.

PPS: I suggest the book Isac Watts - improvement of the mind... written in 1830's it's what sparked Faradays endeavors. Tesla was not a savant obsessively dividing everything he saw by 3, because he was a nutter.... he was performing mind sharpening exercises, it seems modern man is not usually capable of bothering beyond the lazy quick-fire "does it match my textbook" effort, that these giants saw as necessary.

[sjastro]

Abstract: I show that in kinematic situations, π is 4. For all those going ballistic over my title, I repeat and stress that this paper applies to kinematic situations, not to static situations. I am analyzing an orbit, which is caused by motion and includes the time variable. In that situation, π becomes 4. When measuring your waistline, you are not creating an orbit, and you can keep π for that. So quit writing me nasty, uninformed letters.

Alex,

Take Kepler's Third Law. The third law relates the period of a planet's orbit, T, to the length of its semimajor axis, a. It states that the square of the period of the orbit (T2) is proportional to the cube of the semimajor axis (a3), and further that the constant of proportionality is independent of the individual planets; in other words, each and every planet has the same constant of proportionality.

Guess what the constant of proportionality contains? It contains π=3.1416... , and yes this is a "kinematic" example. The law is based on empirical data.

It is absolutely ludricious to consider a static π and a kinematic π, let alone they should have different values. It reflects Mathis' nonsensical mathematics in this case.

Regards

Steven

[Jarvamundo (Alex)]

Yup, this is what's covered.... and why it's best familiarize yourself with all of the celestial mechanics papers.

Or yes get the book, it's easier this way since Miles has ordered the thesis in a more digestible manner. I wish i'd done this earlier.

I could back n fro here on IIS, but it'll just be pointless. The ideas need to be layed out from first principles, i do not have time to do this, and Miles has already done so.

Tickle your interest: http://milesmathis.com/cm.html http://milesmathis.com/ellip.html

I'll loan you my book when i'm done with it, or yeah i think it's 9 bucks for the e-copy.

[CraigS]

So let me get this straight, Alex;

Although you haven't stated it outright, I suspect that you don't necessarily accept Miles Mathis' 'Proofs' as being correct, am I right ?

What you're pointing to is that his stuff gets one thinking and causes you to go back to when you first learnt this stuff in High School Physics ?

In my case, I simply can't remember all the ins and outs of Keplarian physics, first principles of geometry and then calculus. I simply accepted it, (perhaps naively at the time) but, as what I learnt all those years ago turns out to be scientifically and mathematically still valid, I don't have to revise some guy's incorrect version of it.

So, the real benefit of this rather painful exercise for me, has been to simply reinforce what I accepted all those years ago … is this any real benefit at all ?

Has it furthered my knowledge of anything ?

Sometimes relying on foundation concepts actually does lead to progress. In my case, I have made a career out of moving forwards in this way. (What we learn at school is not all myth !!)

It seems that Miles' 'proofs' are certainly not good foundations and thus can be safely discarded, now.

Please let me know your thoughts as I'm finding your support of this guy very difficult to fathom.

Cheers
PS: The same goes for Gaede's work … right ??