Comments URL: https://news.ycombinator.com/item?id=47897447

Points: 4

# Comments: 1

I just learnt that fact from Wikipedia's article on Mordel's conjecture (now Faltings' theorem), was curious whether the theorem could be strengthened to obtain a full proof of Fermat’s Last Theorem (FLT) that is genuinely different from the Taylor–Wiles proof (or its later variants) and so asked an AI (in this case Grok via Twitter).

Grok correctly told me "no it's not possible", but then surfaced (as an aside) a nice expository article on the Taylor–Wiles proof by Faltings from AMS notices in July 1995, which I thought I'd share here:

https://www.ams.org/notices/199507/faltings.pdf

https://www.boost.org/library/latest/graph/

https://www.boost.org/doc/libs/latest/libs/graph/doc/biconne...

Am I correct to suppose both are C++ implementations of Tarjan's algorithm?

Can you say how the it's similar and how it's different to superficially similar sounding work?

(1) https://github.com/linebender/vello , dual Apache/MIT, by Raph Levien et al

(2) https://sluglibrary.com/ , proprietary, by Eric Lengyel (Terathon)

Are you able to say what the relevant settings are? (I would like to be able to do that too ...)

There isn't a "solution" - you're looking at a life-long mitigation and management strategy that will not be "brief".

The time commitment typically goes up as one ages. I could spend 40 hours a week on nutrition, exercise and relaxation if I was trying to optimize for chronic pain reduction.

But then nothing else would get done.

Become a select customer of Shapr3D and their CEO István Csanády might send you one.

https://twitter.com/istvan_csanady/status/188829861216722566...

Edit: Unigraphics X SDRC became the system we know today as Siemens NX

It came out at the end of 2024 - these guys must all be around 80 by now.

https://news.ycombinator.com/item?id=43169194

The article came out at the end of 2024 ... these guys must all be around 80 by now.

Edit: Unigraphics X SDRC became the system we know today as Siemens NX

Comments URL: https://news.ycombinator.com/item?id=43169194

Points: 10

# Comments: 2

DCM then chooses one valid solution that it believes is "close" to initial supplied positions/directions/radii etc for the geometry.

Does the current add-in use AI at all?

What is your plan when, in the event of you getting some traction, Autodesk etc. copy you innovations into the main product?

As per my other comments [1][2], I worked on this area at D-Cubed and Solidworks from 1995 to 2002. Feel free to connect with me via twitter DM @delhanty [3].

[1] https://news.ycombinator.com/item?id=41440016

[2] https://news.ycombinator.com/item?id=41440150

[3] https://twitter.com/delhanty

Well those systems and pretty much all of the mechanical CAD industry is built upon D-Cubed's DCM, so I'd expect the behaviour to be the same.

If I was creating a new 3D CAD system from scratch now I'd probably license Parasolid eventually, but I'd pass on DCM.

I don't want to dump on D-Cubed and John Owen though. I have huge respect for him and the company he created. This is technical criticism with the benefit of hindsight.

This is always the problem with add-ins like this as a business - you're essentially doing free market research for the application vendor.

In my experience of building a sketcher at D-Cubed for a consultancy client (1995-2000) on top of D-Cubed's DCM, this is because DCM's curves (which are unbounded BTW) are not directed so that there are lots of erroneous solutions to attempting to constrain G1 chains of tangent bounded curves. For example the Apollonius Problem [1][2] of 3 tangent circles/lines has 2^3 = 8 solutions. IMO if John Owen had chosen directed curves for DCM then dragging configurations of tangent circles would be more stable.

I'll end with a quote from the Preface of Julian Lowell Coolidge's 1916 "A Treatise on the Circle and the Sphere" [3]:

> Among the cartesian theorems there is a sharp sub-division between those where the radius is looked upon as essentially signless and those where a positive or negative radius is allowed.

[1] https://mathworld.wolfram.com/ApolloniusProblem.html

[2] https://observablehq.com/@d3/apollonius-problem#

[3] https://en.wikipedia.org/wiki/A_Treatise_on_the_Circle_and_t...

True - I implemented the first Solidworks Autodimension sketch as a contractor around 2002 based upon earlier work that I'd done for a consultancy client at D-Cubed in the late 1990s. I'm sure it could be improved with AI and a large data set of sketches though.

> Solidworks tries to help with this in the form of cycling through what it thinks are the most likely constraints to remove and then re-solving the sketch. It's OK, but that sort of tool could be better.

I agree it could be better. The behavior with under-constrained sketches depends on D-Cubed's DCM, and I seem to recall they were rather floppy. It seems kind of ridiculous to make users jump through the hoops of making sketches fully constrained once they've added the constraints they care about.