Such an ordinary people thing to say.
Comment on PI is what
jadero@mander.xyz 1 year agoEspecially given that using π=3 is accurate enough for most daily use by ordinary people for ordinary things.
Yawnder@lemmy.zip 1 year ago
jadero@mander.xyz 1 year ago
Just an ordinary person doing ordinary things :)
F4lcon@discuss.tchncs.de 1 year ago
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.
jadero@mander.xyz 1 year ago
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.
F4lcon@discuss.tchncs.de 1 year ago
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.
jadero@mander.xyz 1 year ago
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. (jpl.nasa.gov/…/how-many-decimals-of-pi-do-we-real… is my reference for the last two items. The others are just wild-ass guesses.)