By the fact that the geometric proof in the link wants to proof the formula, but only does so for a small subset of all a,b for which the formula is correct. This makes it a partial proof, at best.
Ok nvm I can't resist wasting my time and typing stuff on the internet again, probably gonna regret it later.
How is it not obvious to the dullest of the dull that this visual proof is not supposed to work for goddamn commutative rings lmao
It's probably not even supposed to work for negative reals, 0 or the case b>a. It's supposed to demonstrate the central idea of the visual proof. Also yes, by choosing suitable ways to interpret the lengths shown in the diagrams it's absolutely possible to extend the proof to all reals but I'm not convinced it's meant to be interpreted like that.
But bringing commutative rings into this... man you're funny
> One man, watching me while I cut 8-foot lengths of tubing for him, told me that I could simply hook my tape measure over the saw blade and subtract ⅛-inch to find the correct length. Piqued after I explained why his method wouldn’t work for a precise measurement, he responded by quizzing me on something I wasn’t likely to know: the purpose of the black diamonds on my tape measure.
Perhaps I'm picturing the situation wrong, but why wouldn't it work on the precision levels of a tape measure?
The most obvious reason is if your blade isn't 1/8 inch (3.17mm) thick.
If you're cutting with a bandsaw - the blade is a lot thinner than that.
And if cutting with a circular saw, the cutting teeth are wider than the main disk of the saw, which complicates matters - and I can't imagine it'd be easy to keep the tape measure hooked on either.
And of course - subtract 1/8 inch? Are you sure you don't mean add 1/8 inch? If you're learning a clever new technique, better to practice on some scrap, not do it on a customer's material while they're watching :)
At the higher level, saws have no undo function. Cut an expensive bit of metal too short? Someone has to pay $$$ for new material. Buddy on another machine did a load of work on the part before you cut it too short? He's going to have to redo it all. Who'll pay for his time? The stock you cut too short was on a long lead-time or urgent project? You just fucked up the schedule.
So if a machinist is doing some work for you and they want to measure twice and cut once - they're doing you a favour :)
> So if a machinist is doing some work for you and they want to measure twice and cut once - they're doing you a favour :)
This is the real key. Emphasis on (professional) machinist.
I have, however, needed to intervene in the thought process of a Home Depot saw operator's idea of how to cut an 8' sheet into three equal pieces of approximately 32" each. :)
The request may have been to take a 24 foot segment and cut it into equal nearly 8 foot segments. Measuring all at once lets you avoid the last piece being notably shorter.
I don’t know specifically, but If your saw has a stop or something that’s going to be better than repeated tape measure measurements. Also assumes that the saw blade is actually 1/8 of an inch.
she may be implying a lack of precision from the floating tip on a well used/worn measuring tape. i wouldn't rely on that for anything i considered "precise". framing a house? sure.
Fun fact: the floating tip on a measuring tape is loose by design. It's to account for the width of the tip itself when you're measuring by pushing the tip into a corner, versus measuring by hooking the tip around the edge of your material.
So a "loose" tip on a measuring tape is actually more accurate than a fixed rigid tip that does not move. (though I don't think I've ever seen a tape measure that is lacking this feature)
HN's policy is to highlight non-current stories, not current stories of non-current events.
There's an active discusssion of improved titles which would make clearer both current actions and the historicity of the previous retreat of regulators.
