It is simply an obvious fault line in the nature of the problem statement: you can crack the problem in 2 parts: the x^4+y^4=z^4 part, and the part that claims x^p+y^p=z^p with p a prime.
Suppose Fermat solved the proof by using this natural fault line -its just how this cookie crumbles- solved the n=4 case, and then smashed his head a thousand times against the problem and finally found the prime n proof.
He challenges the community, and since they don't take up the challenge, "encourages" them in a manner that may be described as trollish, by showing how to do the n=4 case. (knowing full well the prime power case proof looks totally different)
That's an interesting take but I think it's unlikely for two reasons:
1. In any case you view it, it's not trivial, which was the statement in the note. If it were, the effort to publish just for n=4 would be silly, because it would take equal effort to just publish for general case. That he withheld the proof just to mess with people is highly unlikely.
2. I definitely do not make private notes in my books just so that maybe somebody later on would pick up that book and wonder whether I had indeed discovered the secrets of the universe. I definitely do not write "challenges to the community" there.
The readme shows support for dumping dex files. Edit: missed that it has a comment that stays "unsupport for now" but at least it looks like something planned
Heh, was looking up the wiki on the Baader Meinhoff phenomenon only to find out it sends you to your link. Guess that's an easier name to know it as :)
I maintain a joke domain which I've found sadly applicable through the years. https://adventofrealizingicantread.com. I try to keep it updated pointing to the current day throughout the month
I've found especially as the month progresses it's just as much Advent of Reading Comprehension as it is coding :)
I struggled with this through highschool. Pencil and gel pens were the worst. I never learned to write with my paper tilted like some lefties. I write just like a mirror image of a right hander, which lead to a lot of smudging and having to rewrite papers etc
This change my sophomore year in English class when my teacher told me a trick! Place a sticky note on the side of your hand that rests on the paper. No more smudging!
Looking at pricing, its $15 per 1M input tokens, and $60 per 1M output tokens. I assume the CoT tokens count as output (or input even)? If so and it directly affects billing, I'm not sure how I feel about them hiding the CoT prompts. Nothing to stop them from saying "trust me bro, that used 10,000 tokens ok?". Also no way to gauge expected costs if there's a black box you are being charged for.
This is correct the last I read about it, but there was a project called ArcWelder that would post-process your gcode and convert the motions to true arcs. The printers today support the arc gcode, but the slicers don't generate them.
arc support may exist but be poor. For example, I recently read prusa's documentation, which states "[G2 and G3 controlled arc move] commands don't propperly work with MBL enabled. The compensation only happens at the end of the move, so avoid long arcs." MBL is mesh bed leveling, an important technology that helps compensate for imperfections in the flatness of the print surface.
Bambu Lab does this. The accel values they print with are so high without arcs it would get quite violent. X1C is most impressive piece of hardware I’ve bought recently, just bought another today. Prints 4X faster than ultimaker
This doesn't sound right, plenty of printers print as fast as Bambus and faster, yet arcs are not a go-to for them (Voron, RatRig, Annex communities all seem totally indifferent to that feature). The value of arcs is in reducing gcode size and thus allowing weaker processors to handle particularly curve heavy prints. Since other fast printers have until very recently been mainly DIY and Klipper based, they've had more than enough processing power to handle unwelded gcode without special handling for arcs due to typically doing all the processing on an RPi.
If the slicer can't generate arcs, it has to do what the firmware does in the case of arc gcode, that is generate a large number of small moves to represent the arc with sufficient resolution, this doesn't affect jerkiness because as long as the firmware is keeping up in processing the gcode, the steppers move the same as they would with the equivalent arc gcode. The 'pulses' the page mentions would only occur if the processor can't keep up with the movement of the toolhead.
With multiple smaller movements the printer doesn't have to come to a full stop between moves. It can simply compare the movement vector of the current segment to that of the next one, and adjust the direction it is moving in accordingly. Use enough segments, and you get some pretty smooth movement.
As dotnet00 already mentioned, this is exactly how printers currently implement arcs: the software interpolates the arc into a bunch of tiny line segments. If anything, I'd expect an arc gcode to generate more small movements than whatever the slicer is outputting.
Yes, the controller does (stop between moves), it doesn't have a way of knowing.
Also, with the larger motion commands like arc, some controllers do what's called read ahead and they change what they're doing now based on what they're doing next. If what they're doing now and next are just tiny little vectors that doesn't help, but if they're big moves then it helps a ton.
It's like the difference between a .iges or parasolid file and a .stl file.
Maybe with CNC firmware the controller doesn't have a way of knowing, but Klipper (one of the more popular 3d printer firmwares on printers comparable to Bambus) always looks ahead. Eg if you had two commands to move in a straight line at the same velocity, Klipper will not do the first move, slow down to a stop, then start to do the second move, it'll look ahead and see that it can keep accelerating in the same direction until it reaches the point where it'll have to start slowing down to arrive at the final point while staying within the configured jerk and deceleration limits.
It always has the ability to lookahead and adjust the commands to the steppers. As a result it does not matter if you specify whole arcs or specify them as small lines, because either way it computes the same X and Y stepper positions and velocities.
The 3d printing community is full of tons of enthusiasts who put in a large amount of time, money and effort into devising methods for maximizing the speed and quality of their printers. Despite all the scrutiny, arcs are seen as optional with inconclusive benefits in terms of print quality/printer noise (since, again, most of those enthusiasts are running Klipper).
Any non-arc generates instantaneous acceleration changes at the line inflection points, these are impossible for a mechanical system to perfectly implement. Huge amount of jerk results the closer/faster one tries to achieve instantaneous acceleration. Why wouldn’t a system try to use arcs and splines to minimize these effects?
The CNC controller world has been trying to solve this problem for decades. Turning everything into line segments seems to go in opposite direction of this progress.
Why now? They're expected to announce a successor printer in the next few months and they've said the X1C, as their oldest printer, will stop getting firmware updates next year.
I could see this. Like obviously I live first person, and when I want to look up I pull my head back, to look down I push my head forward. Similarly I expect pushing my mouse forward (up) to look down and pulling my mouse back (down) to look up.
```Top-level members are interpreted as members of the unnamed class, so we can also write the program as:
String greeting() { return "Hello, World!"; }
void main() { System.out.println(greeting()); }```