3 or 5 is equally inaccurate. Engineers usually round it up from however accurate they need it. Scientists usually try to use it to as many digits of significance as they can.
3 or 5 is equally inaccurate, it doesn’t matter which you use if you think that’s accurate. Most people, engineers and scientists and mathematicians, use computers, but you’ll find they can get inaccurate pretty quickly too.
Again, 3 or 5 is a meaningless distinction to round an irrational number to. 3 is not an accurate value of pi in any sense and neither even is 3.14.
I would draw your attention to the difference between mathematics and reality. Although mathematics is extremely useful in modeling reality, it’s important to remember that while all models are wrong, some are nonetheless useful.
Thus, a household gardener or storage tank owner or a builder of small boats can choose the appropriate diameter of hose, tank, or pontoon very effectively by rounding PI to 3 but cannot do so when “rounding” to 1 or 5. In these cases, it literally doesn’t matter how many decimal points you use, because the difference between 3 and any arbitrary decimal expansion of PI will be too small to have concrete meaning in actual use.
Under the philosophy you are promoting, it would be impossible to act in the physical world whenever it throws an irrational number at us.
I don’t know, but I suspect that there is a whole branch of mathematics, engineering, or philosophy that describes what kinds of simplifications and rounding are acceptable when choosing to act in the physical world.
The real world in which we act has a fuzziness about it. I think it’s better to embrace it and find ways to work with that than to argue problems that literally have no numerical solution, at least when those arguments would have the effect of making it impossible to act.
Lol, my philosophy is exactly yours. Allow simplification as necessary, because to do otherwise is a pointless uphill battle. Only use as much accuracy as you really need.
In this case, it doesn’t matter if pi is 3 or 5 or 30. It’s just for teaching purposes. You would need critical thinking to determine how much simplification you can do, which is much better taught by simplifying things differently as you need, rather than just keeping pi as 3 and saying that works everywhere.
I get it now. I was taking exception to your characterization of 3 and 5 being equally inaccurate in the sense of how close they are to the actual true value, which, of course, can never be known, except in every more accurate approximations.
In that case, I guess we still have a difference of opinion. I think that using approximations that are closer to their true value are more useful in teaching, despite (and maybe because of) the greater difficulty. If the student is not yet ready for that level of difficulty, then perhaps a different problem should be presented.
To that end, I actually think that there are several things to teach. That PI is not 3 or 3.14 or any other decimal expansion. That 3 is close enough for most casual encounters outside school. That 3.14 is close enough for most engineering work. That 3.1416 is close enough for most scientific work. That 15 decimal places is close enough for rocket scientists. That 37 decimal places are enough to calculate the circumference of the universe to within the diameter of a hydrogen atom. (https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/ is my reference for the last two items. The others are just wild-ass guesses.)
What I mean is, if you’re using 3, you’re approximating, heavily. If you do anything critical using that value, it’s as bad as using 5 really, imo. Is it really the case that 3 can be used casually? Like in what, workmanship, crafting or something else?
Personally, I would say that pi should be presented as 3.14 and calculators should be used, there’s no reason to fear less than elegant numbers xD. And no, that’s not close enough for most engineering work, as an engineer we don’t usually approximate that much despite the memes, since you have to reduce the margin of error as much as practical. You generally don’t even approximate, just leave it as pi the symbol for the most part since in the end you won’t calculate it manually. The errors stack up the more you use the value. Eg, multiply an inaccurate value of pi by pi and the error you get is exponential.
That aside, I think 5 is more elegant than 3 so if youre approximating to avoid the cumbersome numbers why not go for elegance instead of accuracy? xD
When I’m figuring the buoyancy of a 20 litre pail or, alternatively, how much it’ll weigh when filled with sand, 3 is easier to work in my head for off-the-cuff estimates so I know about how many pails I need.
That said, I do typically use the π button on my calculator when it comes time to actually execute on the project. :)
Of course. They already use it like it’s some kind of hack. Make it official. Teach them the ins and outs of Wolfram. Better than memorising and regurgitating information, no?
So? You think you’ll get the correct result by using 3? Or 3.14? Not quite. You can only get infinitesimally close to the correct result by increasing digits of pi.
And of course, if you really need that circumference for something critical, guess what? You use the things people developed for this very problem, software packages, and so on. And of course, you get it double checked, triple checked.
If it’s assume pi is 5, it’s not misinformation. If they point guns at kids and say it’s 5 for real, then yes.
Or you could just use 3.14 which is infinitesimally more correct than 5, not lie about the number and aim for correctness and accuracy so people learn how to do things right the first time.
If you can’t handle a few decimal points then you aren’t ready for pi, go back to third grade.
I don’t think you understand what infinitesimally means! It means the opposite- you want to use ‘infinitely’ there. Because you’re kinda agreeing with me otherwise xD
Now, not being a condescending asshole, I really take issue with you calling an approximation a ‘lie’. And honestly, who’s multiplying decimal points mentally? That’s difficult. Use a calculator. Want to avoid calculators for an exam? Simplify! That’s why they use 5 and not 3.14.
I was typing in a rush and mistyped, but you understand what I meant.
Simplify! That’s why they use 5 and not 3.14.
That’s a bullshit excuse. 3 could be argued but 5 is straight disinformation. And I do multiplication of decimals in my head because I was taught how to in school, that’s how far behind the US system is.
It’s to make the numbers simple because they aren’t important, the methodology is
I get that, it’s like rounding gravitational acceleration (on earth) to 10…
But why don’t they just use 3, preceded by a “pi is a little more than 3, but for now we’ll round down to 3.”
Especially given that using π=3 is accurate enough for most daily use by ordinary people for ordinary things.
3 or 5 is equally inaccurate. Engineers usually round it up from however accurate they need it. Scientists usually try to use it to as many digits of significance as they can.
3 or 5 is equally inaccurate, it doesn’t matter which you use if you think that’s accurate. Most people, engineers and scientists and mathematicians, use computers, but you’ll find they can get inaccurate pretty quickly too.
Again, 3 or 5 is a meaningless distinction to round an irrational number to. 3 is not an accurate value of pi in any sense and neither even is 3.14.
I would draw your attention to the difference between mathematics and reality. Although mathematics is extremely useful in modeling reality, it’s important to remember that while all models are wrong, some are nonetheless useful.
Thus, a household gardener or storage tank owner or a builder of small boats can choose the appropriate diameter of hose, tank, or pontoon very effectively by rounding PI to 3 but cannot do so when “rounding” to 1 or 5. In these cases, it literally doesn’t matter how many decimal points you use, because the difference between 3 and any arbitrary decimal expansion of PI will be too small to have concrete meaning in actual use.
Under the philosophy you are promoting, it would be impossible to act in the physical world whenever it throws an irrational number at us.
I don’t know, but I suspect that there is a whole branch of mathematics, engineering, or philosophy that describes what kinds of simplifications and rounding are acceptable when choosing to act in the physical world.
The real world in which we act has a fuzziness about it. I think it’s better to embrace it and find ways to work with that than to argue problems that literally have no numerical solution, at least when those arguments would have the effect of making it impossible to act.
Lol, my philosophy is exactly yours. Allow simplification as necessary, because to do otherwise is a pointless uphill battle. Only use as much accuracy as you really need.
In this case, it doesn’t matter if pi is 3 or 5 or 30. It’s just for teaching purposes. You would need critical thinking to determine how much simplification you can do, which is much better taught by simplifying things differently as you need, rather than just keeping pi as 3 and saying that works everywhere.
I get it now. I was taking exception to your characterization of 3 and 5 being equally inaccurate in the sense of how close they are to the actual true value, which, of course, can never be known, except in every more accurate approximations.
In that case, I guess we still have a difference of opinion. I think that using approximations that are closer to their true value are more useful in teaching, despite (and maybe because of) the greater difficulty. If the student is not yet ready for that level of difficulty, then perhaps a different problem should be presented.
To that end, I actually think that there are several things to teach. That PI is not 3 or 3.14 or any other decimal expansion. That 3 is close enough for most casual encounters outside school. That 3.14 is close enough for most engineering work. That 3.1416 is close enough for most scientific work. That 15 decimal places is close enough for rocket scientists. That 37 decimal places are enough to calculate the circumference of the universe to within the diameter of a hydrogen atom. (https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/ is my reference for the last two items. The others are just wild-ass guesses.)
What I mean is, if you’re using 3, you’re approximating, heavily. If you do anything critical using that value, it’s as bad as using 5 really, imo. Is it really the case that 3 can be used casually? Like in what, workmanship, crafting or something else?
Personally, I would say that pi should be presented as 3.14 and calculators should be used, there’s no reason to fear less than elegant numbers xD. And no, that’s not close enough for most engineering work, as an engineer we don’t usually approximate that much despite the memes, since you have to reduce the margin of error as much as practical. You generally don’t even approximate, just leave it as pi the symbol for the most part since in the end you won’t calculate it manually. The errors stack up the more you use the value. Eg, multiply an inaccurate value of pi by pi and the error you get is exponential.
That aside, I think 5 is more elegant than 3 so if youre approximating to avoid the cumbersome numbers why not go for elegance instead of accuracy? xD
When I’m figuring the buoyancy of a 20 litre pail or, alternatively, how much it’ll weigh when filled with sand, 3 is easier to work in my head for off-the-cuff estimates so I know about how many pails I need.
That said, I do typically use the π button on my calculator when it comes time to actually execute on the project. :)
Then let’s teach kids to use Wolfram Alpha.
Of course. They already use it like it’s some kind of hack. Make it official. Teach them the ins and outs of Wolfram. Better than memorising and regurgitating information, no?
Sure, until you actually need the correct result of the circumference of a circle and think pi is 5.
Misinformation is education. Welcome to the future.
So? You think you’ll get the correct result by using 3? Or 3.14? Not quite. You can only get infinitesimally close to the correct result by increasing digits of pi.
And of course, if you really need that circumference for something critical, guess what? You use the things people developed for this very problem, software packages, and so on. And of course, you get it double checked, triple checked.
If it’s assume pi is 5, it’s not misinformation. If they point guns at kids and say it’s 5 for real, then yes.
Or you could just use 3.14 which is infinitesimally more correct than 5, not lie about the number and aim for correctness and accuracy so people learn how to do things right the first time.
If you can’t handle a few decimal points then you aren’t ready for pi, go back to third grade.
I don’t think you understand what infinitesimally means! It means the opposite- you want to use ‘infinitely’ there. Because you’re kinda agreeing with me otherwise xD
Now, not being a condescending asshole, I really take issue with you calling an approximation a ‘lie’. And honestly, who’s multiplying decimal points mentally? That’s difficult. Use a calculator. Want to avoid calculators for an exam? Simplify! That’s why they use 5 and not 3.14.
I was typing in a rush and mistyped, but you understand what I meant.
That’s a bullshit excuse. 3 could be argued but 5 is straight disinformation. And I do multiplication of decimals in my head because I was taught how to in school, that’s how far behind the US system is.
That’s impressive. Mental math isn’t one of my talents to be honest. And let’s agree to disagree about the disinformation.
It’s a skill like any other, you have to be taught it to learn it, and you need practice to get better.
Lots of skills in the world, some more useful than others.