The Fuzzle

[MichaelT_123]

Hi Fusionates,

As I encountered some inaccuracies in one of the projects, I devised a simple test of the sketch solver. In particular, I was interested in solver inaccuracies in a case of chained tangential relations.

The picture below (and the respective file) represents the idea of the test. In verbose terms:

Calculate radiuses of a series of tangential circles inscribed on two vectors of angle α.

The results for L=100 and α=30 deg are as follows:

i = 0 r_t = 33.3333333333333 r_m = 33.33333333 δr = 3.33332650370721e-9 Σ2*r_m = 66.6666666666667

i = 1 r_t = 11.1111111111111 r_m = 11.11111111 δr = 1.11111475575854e-9 Σ2*r_m = 88.8888888888889

i = 2 r_t = 3.70370370370370 r_m = 3.7037037 δr = 3.70370445423873e-9 Σ2*r_m = 96.2962962962963

i = 3 r_t = 1.23456790123457 r_m = 1.2345679 δr = 1.23456822542778e-9 Σ2*r_m = 98.7654320987654

i = 4 r_t = 0.411522633744856 r_m = 0.41152263 δr = 3.74485614740294e-9 Σ2*r_m = 99.5884773662551

i = 5 r_t = 0.137174211248285 r_m = 0.13717421 δr = 1.24828539171951e-9 Σ2*r_m = 99.8628257887517

i = 6 r_t = 0.0457247370827618 r_m = 0.04572474 δr = -2.91723818712786e-9 Σ2*r_m = 99.9542752629172

where:

r_m – measured value

r_t  – theoretical (calculated) value

δr   – absolute error r_m - r_t

The test results are generally satisfactory, although it also says the Fusion sketch solver does not meet the standards required in more dimension-sensitive environments.

The exercise also delivered a bonus outcome … the fuzzle … for the weekend.

It should be easy for young & bright to sharpen their geometrical skills and, for more mature but still lusty …, stir some of the sediments in the abyss of distant memories.

The fuzzle is:

What is a formula, an equation of variables (i, L, α) defining the radius of i circle?

Rᵢ = 𝓕(i, L, α) = ????

Regards

MichaelT

[TrippyLighting]

Tagging @rohit.bapat 

[jeff_strater]

Remember, Fusion is designed for manufacturing things in the real world.  As such, it defines specific tolerances within which an answer is considered acceptable.  For the Fusion sketch environment, the point-point tolerance is (I think I recall correctly) 1.0E-06 CM.  So yes, the answers will not be exact to atomic tolerances.  I do not see any answers here that I would consider to be incorrect within that tolerance.  I apologize if I have missed any of those, if so, please indicate which values are incorrect.

[Drewpan]

Hi,

Have you been watching those "If you can solve this "simple" problem you can get into MIT" type of videos on

YouTube?

Again! 😎

Cheers

Andrew

[MichaelT_123]

It is not that difficult ... Mr Drewpan 🙂

[MichaelT_123]

Hi Fusionates,

This is a buzz, buzz, buuuzzzz ... for The Fuzzle.

Unless requested otherwise, ... I will post the solution tomorrow.

Regards

MichaelT

[MichaelT_123]

Hi Fellows,

… here is the solution to The Fuzzle A.

It is presented graphically, as I could not find a way to draw advanced mathematical expressions in the input dialogue applet. Look at the solution formula … it is like a crystal ball … showing how the equation is devised.

With a little spark of wizardry or witchery spirit … even a foggy picture will be crystal clear.

Remember, … abracadabra, a powdered frog with snake oil and dragon tooth, … or other your favourite implements might help also.

If necessary, … I will follow up with additional explanations.

The result of the first ten radii. (all digits but the last are significant)

33.33333333333333
11.11111111111111
3.703703703703704
1.234567901234568
0.411522633744856
0.137174211248285
0.045724737082761
0.015241579027587
0.005080526342529
0.001693508780843

Attached files:

Fuzzle_A_guestion.png   (0.2MB)  https://a360.co/4dqXHAa

Fuzzle_A_answer.png     (0.2MB)  https://a360.co/44umdw8

Fuzzle_A_extra.png        (0.2MB)  https://a360.co/4b32iqs

The Fuzzle and the related files can be used as they are for didactic purposes without restriction.

Postface:

This Fuzzle has been assessed as a worthy hurdle for entry to MIT … by Mr. Drewpan,

thus, I am tempted to present another related one at a much higher level of difficulty. I reckon it could open doors even to Yale, … and not only for you but also for your close cousins.

Regards

MichaelT

PS. The files and pictures has been reapplied/corrected (11:08 ET, 3.05.2024)

[MichaelT_123]

Hi Fellows,

Unfortunately, a couple of rouge pixels … made The Fuzzle_A answer picture worthless and also misleading. In the end, it is/was not the fault of your monitor … but solely mine. Please accept my apologies. The erroneous post correction will be performed in situ soon, and previous relevant links will be invalidated. As compensation … I will send an enhancement to the Fuzzle_A in the new post titled “The Fuzzle B”. It will be much more challenging, so …. consider reviewing the prices of Yale dormitories, … but relax, … only after you have solved it!

I would not spot the error … unless the ‘wizardry’ of Mr. CADacombs. He claims he is not a Wizard, but I don’t believe him. Bellow, with his permission, I am attaching our PM conversation about the matter.

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 CADacombs 

The solution for 

"What is a formula, an equation of variables (i, L, α) defining the radius of i circle?"

doesn't include a product sequence. Instead,

L * Φ* (1 - 2*Φ)^i

Where Φ= sin(α) / (1 + sin(α))

Hi Mr CADacombs,

You are absolutely right. You are a Wizard

The Fuzzle, … was the outshoot of my exercise of developing platonic polyhedra inscribed spheres fractal. The first level of them … is child play, but quickly, things become pretty complicated.

The formula presented was related to the distance stack of spheres covered. Sort of distance to a nose in Socrates? Polemic.

There were a lot of formulas.

At first instance, I planned to include (in The Fuzzle) both Rt(I,lφ) and Lt(I,lφ).

It was a point … where hurdles started.

When possible, I synthesize formulas in LaTeX. It in itself has different flavours.

Placing the formulas in the Fusion input applet was another challenge. LateX (which is HTML itself) is not supported. Hence, I decided to take the SVG path.

I have tried to encapsulate SVG in HTML brackets … to no avail.

Then, I had a Yahoo idea. Insert SVG in Fusion design.

The cost of it was the most significant part of the whole exercise. Look at my post ‘SVG multiline’

I was switching, going back and forth, changing syntaxes in the whole chain … and in the end, I picked the wrong/misformed SVG, which resulted from a miss-edited LaTex.

And, yes, in the end, despite the ‘misery’ and ‘hurdles’ … it was my fault!

Thank you for correcting it. I repeat, “You are a Wizard”.

I will correct the original post. Perhaps I will postpone it for a day or two … to see if other Wizards are out there.

If you do not object, I would like to include our conversation in its entirety.

Well, …. Perhaps I will add some colours. 😊

With Regards

MichaelT

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Regards

MichaelT

[MichaelT_123]

FYI, 

... more challenging - The Fuzzle B.

https://forums.autodesk.com/t5/fusion-design-validate-document/the-fuzzle-b/td-p/12764131

Regards

MichaelT