Just put two π ohm resistors in series duh
Whats wrong with your 3!
Ugh, 3 factorial is most definitely not equal to π. It’s something more like, idk, 9? Honestly I don’t even know how I got here; I majored in Latin and barely past
Barely passed your English classes as well I assume. /s
They barely passed me.
Math is a liquid. Or a language.
My high school English teacher still has night terrors about me starting sentences with conjunctions. And that was the least of their problems.
Edit: kind of unrelated, but that song about conjunctions is now stuck in my head. 🎶Conjunction junction, what’s your function? 🎶
Have you been chillin with the phunkadelic crew sober?
In case anyone wondering factorial is
n! = n * n-1 * n-2 * … * 3 * 2 * 1
Erm. In what world do you live that the precedent in your expression is right?
In all languages and countries I know multiplication binds more strongly than addition. So what you wrote would be
n^2 - n - 2n - 3n…
I wrote it correctly. It is the definition of a factorial.
No, correctly it would be n * (n-1) * (n-2) * … * 3 * 2* 1
Or the actual recursive definition
1! = 1
n! = (n-1)! * n
Well…
g1/2 = e = 3 = pi
e = π = σ = ε = µ = Avogadro’s Number = k = g = G = α = i = j = 3
(at least that’s how they all look when viewed from ∞)
I was not ready for this truth bomb
Shouldn’t have i in there, or j if you’re using that to represent the imaginary number. The complex plane is separate.
Let epsilon be substantially greater than zero…
The list of things I shouldn’t do, but do regardless, stretches past infinity.
Imaginary numbers are best understood as symbolizing rotation. If we’re imagining a number line here, “looking back from infinity” - at a scale where Grahams number looks like the mass of an atom expressed in kilograms, i would not be in that infinite set of numbers, it would be a point above that line and creating a perpendicular plane to it.
I hate the term “imaginary” because it’s misleading. Most high school algebra teachers don’t understand what they are either, so people learn about these things called “imaginary” numbers, never learn any applications with them, hopefully graph them at best, and then move on understanding nothing new about math.
Students also tend to get really confused about it as possibly a variable, (it’s really annoying with in second year algebra courses, where e and logs also show up). We say “ah yeah, if you get a negative sign, just pull it out as an i and don’t worry about it. or just say no real solutions.”
3 = 10^(1/2)
π = 1
3! = 10Seriously, if you’re working with analog electronics, 𝛑=√1̅0̅ is close enough. If you need more precision, use active error correction, and in the 21st century that’s easiest to do digitally anyway.
Isn’t 3 factorial equal to 6??
Without using fancy components: Just simply adding a 6.2 and a 2400 Ohm resistor in parallel already gives you 6.18402 Ohm ⚡️
Real world resistors usually have a tolerance of ±5%, so you’ll never get anything that precise.
That’s why I keep a roll of 20 AWG nichrome on hand. Spool off 9.7195853528209 feet and it’ll be bang on.
So 1 inch of your wire would weigh ~0.0987 grams, so to measure down to 8.6350242338508 inches of wire your scale would need to weigh down to ~0.00000000000007 grams. Which is the weight of about a dozen atoms or so.
Yeah which is why you use a Kibble balance. Are you sure you’re cut out for this kind of work?
I’m not a scientist, I’m just in IT haha
I figured there was a way to measure that small of weight but I didn’t know!
Its akin to having an electon microscope in your kitchen
We move onto the next issue. How to precisely measure the length of the wire?
Eyeball it. Gotta squint right tho.
If you trust the gauging, you weigh it.
With a 6 digit voltmeter
With an ohm meter?
I’ve actually found 1% to be a lot more common nowadays.
Grab a box full and test a bunch until you find one that works well for your use case. That way you end up with a resistor that’s much better than the rated tolerance you’d get if you just grabbed one resistor at random.
couldnt you technically fine tune a potentiometer to be this resistance if you were precise enough?
Mathematically yes. Practically, right now? No.
So you need a resistor of this value for your widget.
For that many places of precision you’re looking at a potentiometer with a 10 nano-ohm precision.
I am not aware of any commercially available resistor that can do that but you could create one using microelectronic structures used for ICs and derive a 10 nano-ohm resistor by design and then chain enough of these elements into a resistor network or potentiometer to create the super precise resistance value you want.
Cool, congratulations.
Now how are you going to use this 10 nano-ohm resistor? What voltage will you be applying across it? What current do you expect it to handle? And therefore what are your power requirements? What are your tolerances, how much can the true value deviate from the designed ideal?
Because power generates heat through losses, and that will affect the resistance value so how tightly do you need to manage the power dissipation?
How will you connect to this resistor to other circuit components? Because a super precise resistor on it’s own is nothing but an over-engineered heating element.
If you tried connecting other surface mount devices (SMDs) from the E24 or even E96 series to this super precise resistor then the several orders of magnitude wider tolerances of these other components alone will swallow any of the precision from your super accurate resistor.
So now your entire circuit has to be made to the same precision else all of your design work has been wasted.
Speaking of which, now your heat management solution now needs to be super precise as well and before you know it you’ve built the world’s most accurate widget that probably took billions of dollars/euros/schmeckles and collaboration from the worlds leading engineers and scientists that probably cost more time and money than the Large Hadron Collider.
Yes
True. Would the effort have any beneficial application? Aside from being bad ass.
No
Therefore we should do it anyway.
There should be a badassness scale for decisions like these.
9 significant figures? good luck!
You’ll make do with three and you’ll like it!
The tolerance would be greater than the difference anyway.
Don’t sneeze right next to it with that kind of precision.
Sure, except the resistance will constantly change with time, temperature and other environmental variables.
For starters resistance changes with temperature.
Also even in a multi-turn potentiometer, getting a precision of 1 in 10^9 would require an equal level of precision in the angle you rotate that potentiometer to (for example, a 0.1 degree error in a 10 turn potentiometer - which I believe is more turns than anything that actually can be bought - translates into a 1 in 36,000 error in resistance, so about 3000 larger than 10^9) even if you had a perfect material whose resistance doesn’t change with temperature.
(PS: Just out of curiosity I went and dove down further and to translate a 1/3000 deg movement in a rotating potentiometer into a 1mm movement at the end of a bar attached to it, you would need a 176m long bar - i.e. the radius for 1/(360*3000) of a circumference to be equal to 1mm, is aproximatelly 176 m. This of course has serious mechanical problems even if you remove the bar at the end of the process as the removal process itself would shift the potentiometer by much more than 1/3000 degrees)
The joke here isn’t even specifically about resistances and electronics, it’s that the real world has all sorts of limitations that when you’re doing things wholly in the mathematical world you don’t have to account for, and that’s a hard realisation for Physicists (having gone to study Physics at uni and then half way in my degree changing to Electronics Engineering I can tell you that’s one of the shocks I had to deal with in the transition).
(In a way, it’s really a joke about Theoretical Physicists)
See also the “assuming this chicken is a spherical ovoid” kind of joke.
I had a potentiometer on a circuit board that adjusted a timer, but I found that the timer varied in timing. I ended up replacing with a few resistors and it corrected the variations.
I’m a physicist. If you are an engineer that sounds like a “you” problem.
Not using the correct resistors does cause a U problem every once in a while.
Or an I problem, depending on your perspective
Sounds like a 6 ohm resistor solution.
They’re 5.6 or 6.8 ohms usually
OK, the solution is “how accurate will make the physicist and accountants both only kinda mad”
I’m not an engineer
This is also a “you” problem. Fix that at your earliest convenience.
Too true, and my problem is about to be your problem and the cycle continues comrade.
Numbers like that are why I quit majoring in mechanical engineering. Physics took the beauty of math and made it ugly.
You knew something was wrong in calculus when you got a fucked up coefficient that wasn’t a nice number.
Numbers like that should have been why you kept going in mech E.
Once you get past the educational stage, every one of those calculations becomes “OK now round to the closest whole number that gives you the larger factor of safety and move on”
Using π = 4 is only a 27% safety margin, better go for π = 10 just to be safe.
Pi r square, square have 4 sides. No problem found.
Pi r not square. Pi r round. Cornbread r square
Behold, pies r square
Saw midwest.social, was not disappointed
Truly an ugly pizza. You can even see how dry and tough the crust is. And crust is like 90% of that thing.
Rounding up seems very stupid here. I’d go with π = 0
The difficult part of engineering is figuring out what number you have to round then multiply by 1.2 or 0.8
Eh, it’s just fundamentally ugly to me and that really turned me off. Rounding doesn’t help, that’s like turning the lights off for sex to make it better. I still know the ugliness exists, even if I don’t see it.
Engineering is still very cool to me, and I have huge respect for those who do it, but I’d never have made it. It’s physics but even further perverted by reality. Math was beautiful to me because of how “pure” it was. Just straight logic, divorced from the messy world we live in. Tidy coefficients and elegant derivations.
I have to hard disagree with you there. The beauty of the math equations they test you with in school is completely artificially selected. The vast majority of math does not have nice neat solutions. There is a lot of it that doesn’t have any solution at all. The beauty of engineering is figuring out how much of things you actually need. You might calculate that some quantity should be an irrational number for some design optimum, but the amount of precision you actually need will be some range around that. When you do that and see your design in the real world actually functioning, that’s the greatest feeling in the world by far.
Not knocking people’s choices, it just wasn’t for me. If math in reality isn’t math in education, it’s even better that I left.
I’ll still contend math is much more elegant than physics or engineering, though. There’s no e^I*pi + 1 = 0 equivalent for either.
I actually really like physics, and it’s 100% because I’m fucked up and evil
Respect. Physics is way up there in terms of hard science nerd cred.
the philosopher floating on a cloud: So how do you guys really know what’s real?
“no you see, its better to just isolate yourself in a mountain. thats how you like, find out who you truly are, man”
The trick is to round everything. Pi? Basically 3.
I’ve heard a story (so like 4th hand at this point) where an astrophysicist was talking about galaxy rotations or something. “And for this model, we can simplify pi to 10.”
My thermodynamics professor made so approximations in his derivations that all of his equations had an “O” term to represent the inaccuracy. Every time he made another approximation he’d say “and, of course, the O sucks up the error”.
After calculus though, they just expect you to cope with fucked up coefficients. In Diff Eq, sometimes you do just get something like 3/111 cos (6/111 x). It gets harder to come up with examples that work out with nice integers.
Physics can also have some really beautiful math, look at Lissajous figures. Once you understand the connections between e, the imaginary plane, and sine/cosine, you get some profound understandings about how electric and magnetic fields work.
That level of precision in a resistor would literally be thrown off if you breathed on it. If you actually needed that, then you need to build an extremely controlled environment around it. Even then, the heat from the electricity itself would throw it off. Maybe in a liquid nitrogen bath?
Its funny the first thing I thought of was, at what temperature.
First, assume a spherical resistor in a vacuum, that can also dissipate heat with 100% efficiency.
Now that we’re in physics land, anything is possible.
Only if it isn’t applied physics.
A big aspect of good design is being able to solve an issue as succinctly as possible, with as wide an operating range as possible. Lower tolerance requirements = better.
If you need that level of precision, you might want to reconsider your career in circuit design.
You can’t tell me that there isn’t a good reason that 0.001% resistors exist. Otherwise why sell them?
4 Sig figs vs 9 Sig figs is a big gap. If you need your resistors in a circuit to be precise to 9 Sig figs, seek a new career.
It is almost always possible to take a system and make it more precise by using more precise parts (just gotta make sure you know what part you are changing to improve what tolerance). You do get diminishing returns with that, but it beats inventing a new system if the tolerances you need are just alittle ways away.
i miss old school radioshack. i did not know what all those bins of tiny electronic hobby parts were for, but I desperately wanted to learn. I did eventually but you have to get all your stuff from some shady oligarch.
Yeah we’re living in the ruins of the old America already and have been for like 25 years.
It’s dirty they just use the same business names they did in the 20th century. While making smoke and mirrors versions of the old products.
i did not know what all those bins of tiny electronic hobby parts were for, but I desperately wanted to learn.
From what I understand, prior to the personal computer boom of the 1980’s, HAM radio was kind of a big deal with nerds. The parts were there for all manner of electronics tinkering, but a big mainstay was building and modifying radios. Yeah, you had people tinkering with computers in the 1970’s too, but it was more niche (until it wasn’t).
I’m fond of the gentle expert dudes who are so old they heard about the mad Max signal intrusion that day
Ah yes, the old “send the new guy out to buy an isotropic antenna and an electron trap” on their first day
Can we do a fraction of an electron boss? The economy is kind of rough. Guy on the phone says he can do a time share too.
Sorry, we need two electrons with identical spin and orbitals. Better check the place across town.
maybe there should be?!
The only application I can think of off the top of my head that would require that precision is a R2R DAC.
Just sort through a bin until you find one.
Rheostat, my dudes
Trimmable precision resistor.
Even better
I just came up with the absolute dumb simple solution :D
“just stick a pot on the board bro, it’ll stay at 1.49284762340598 ohms for 9 or 10 nanoseconds after leaving the factory.”
Until finding out about finite measurement resolution
This guy looks like the dude from Programmers Are Human Too
I can assure you they are not.
Quantum Ampere Standard
https://www.nist.gov/noac/technology/current-and-voltage/quantum-ampere-standard
.
there also been research for defining a quantum volt and quantumly stable resistorshttps://www.nist.gov/noac/technology/current-and-voltage
Quantum-based measurements for voltage and current are moving toward greater miniaturizationP.S. :
https://en.m.wikipedia.org/wiki/Quantum_Hall_effect
Quantum Hall effect →
Applications →
Electrical resistance standards :(…) Later, the 2019 revision of the SI fixed exact values of h and e, resulting in an exact
RK = h/e2 = 25812.80745… Ω.(this is precise to at least 10 significant digits)
Wait until they connect something to a battery.
best they can usually do is three fiddy, and thats usually enough.
