MT thoughts ;7)

[Georg Künstler]

Hi Fletcher,

as I have pointed out,

the rolling weights are acting as a 2 stage pendulum.

an example of an 2 stage oscillator you can find under

http://pendulum-lever.com/two-stage-oscillator.html

When the carrier frame is rolling over the dowels, we have 80 of this in Besslers wheel, the complete frame is used as first pendulum, the rolling weights are the second lever.

In the mechanical books and equations this is also known as a parasitic oscillation.


Here you have Besslers 'Herde die herumgeht' in your words 'Herd that walks around'.

as you can also see, the supporing frame is not fastend on the middle axle, it can freely move.

Still we haven't broken the symmetry. Because our oscillation is still in the sine shape.

Please have a deep think about it.

But we can change that now easily.

[ME]

I guess it doesn't hurt and perhaps of interest to explore the variety of selections one can make no matter if it's a code or just an arbitrary selection.

3 x 4 (12) + 3 x 5 (15) + 4 x 5 (20) = 47

When the equation-result (that 47) needs to be a number pointing to a valid MT-drawing then this is the only possible solution for an integer-length right-sided triangle.
The first three for [a²+b²=c²] and [T=a·b+b·c+a·c] are:

a= 3, b= 4, c=5, T= 47 ---[3-4-5 triangle]
a= 6, b= 8, c=10, T=188 ---[3-4-5 triangle] *
a= 5, b=12, c=13, T=281 ---[5-12-13 triangle]

* note: This second is also the only other where the factors of T are all within the range of MT: a·b=48, b·c=90, a·c=60

When only a,b and c needs to be valid MT-numbers (max 143) then surprisingly (or not) the amount is 47
The last three:

a=75, b=100, c=125, T=29375 ---[3-4-5 triangle]
a=78, b=104, c=130, T=31772---[3-4-5 triangle]
a=55, b=132, c=143, T=34001 ---[5-12-13 triangle]

There are only 15 where a,b,c forms a 3-4-5 triangle.

[daxwc]

Hi Fletcher I came across Oystein’s website a long time ago by accident searching an image. Some of his claims are a bit of a stretch. By that I mean not that they aren’t true but it lacks meat to get your teeth into. Most of this knowledge was for people in the know already, not needing any proof with presentism problems.

I am going to post something which will I hope bolster one of his claims and another will cement one both have. In the end it help all of us. It will take me some time to get it ready and I will post it under my thread.

[daxwc]

That is interesting Me ... just something I can't put my finger on.

[eccentrically1]

I think he means 47 is the only result that falls within the numbered (1-143) drawings; 3-4-5 being the smallest whole numbers for that triangle. I forgot why that equation (ab+bc+ac) is relevant.

[daxwc]

eccentrically1: I think he means 47 is the only result that falls within the numbered (1-143) drawings; 3-4-5 being the smallest whole numbers for that triangle. I forgot why that equation (ab+bc+ac) is relevant.

No what I meant was it seems like an equation (ab+bc+ac) but not.
Is there an equation that fits A + B + C^2 + D^2 +E = 47
and involves 3-4-5 triple and primitive sequence?

[Fletcher]

I think you are referencing back to your possible ToyPage equation dax.

[Fletcher]

If that didn't hurt ME then you are positively gonna like looking into this ..

This is my matrix and summary for deciphering JB's name change. He used a 26 letter alphabet substitution type code. His purpose was to establish a sort of provenance for his mech, an important part of his machines near to the heart of the matter. It also highlights, by cross-referencing, important MT notations thru the first 25 of MT IMO.

N.B. unlike writing computer code (which I don't) which must detail every single step taken, I have assumed people will be able to follow along.

09 - connectedness principle
10 - correct handle-construction
15 - Prime Mover
20 - harness horse in front (Prime Mover)
24 - something one must first learn
25 - more to it than one supposes

Anyways .. it reveals an innocuous little horizontal SB mech. Not much at all. Just < x > ( <x> ).

Hmmm .. he did say in MT41 that ..

.. the present horizontal application of the stork's bills is always better than the machine with the vertical application .. I can assure the reader that there is something special behind the stork's bills ..

The behind the SB comment wasn't about a SB breaking the Law of Levers or having super-powers. It was its very basic action of being a double ended linear lever. The ability to contract (pull) and expand (push) on both sides (being centrally pivoted) at once. With the correct handle-construction of course. And that is what the ToyPage shows. Levers falling and horizontal push and pull by a SB, IMO.

And the other interesting thing to me is that two bookends (IMO) come out of the analysis. MT35 and MT42 (Kassel lock & key). MT35 being the first MT to show the double horizontal cam wheel lifters operating in the Zed. And MT42 being the last of the 3 that show that point of difference to ordinary OOB systems.

[daxwc]

If we use the first two Pythagorean Triple numbers 3-4-5 and 6-8-10 and the toypage A+B+C+C+D+D+E = 47
3=A 4=B 5=C then the second triple as 6=D 8=E F=10
If we assume the is a hidden F on the toypage then it adds up to 47
3+4+5+5+6+6+8+10 = 47
I don’t see no hidden F

Strangely I am looking for a missing letter for during a compass construction also on the toypage.

[daxwc]

Wasn't it a F we lost on MT 41 ?

[daxwc]

Yep, MT 41 folded; we lost an A , B , F leaving no F's in the fold


it left A, B, C, C, D, D, E with a missing F

[ME]

... And I have no idea why (ab+bc+ac) is relevant at all. Perhaps Fletcher could elaborate.
(In case there's a need for that list with 47 triangles, just ask)

Fletcher, here are my previously published MT head-lines: http://www.besslerwheel.com/forum/viewtopic.php?t=6282
We can combine your MT's into a story:
MT009 + MT010: The connectedness principle is a good principle, although without the right handle construction it hops from here to there.
MT015 + MT020: Then things become useless pretty fast as the prime mover wasn't properly harnessed.
MT024 + MT025: Basically, perhaps counter-intuitively, because shorter poles simply outperforms longer poles as they fall inwards.


Both MT041 as MT047 have an F.

[daxwc]

If we add up all the letters on the original MT41 with first two Pythagorean Triple numbers 3-4-5 and 6-8-10 we get:

A + A + B + B + C + C + D + D + E + F

3 + 3 + 4 + 4 + 5 + 5 + 6 + 6 + 8 + 10 = 54

Right where the comments stop.

[ME]

Why do we need to add the sides of a triangle?
Wasnt' Pythagoras's proof about squares and areas?

The choice seems arbitrary, I like this one:
The area of triangle[3-4-5] equals 6
The area of triangle[6-8-10] equals 24
6 x 24 equals 144, which point to the missing MT

[daxwc]

ME:

Why do we need to add the sides of a triangle?
Wasnt' Pythagoras's proof about squares and areas?

I don't know why but R+C put a lot of priority Pythagorean Triple numbers and 3-4-5 triangle.