Good thing I don’t need to do math at work. Saw a video the other day where someone said “10x400” and was shocked that they couldn’t instantly multiply by a power of ten. And then I walked into this.
For the purpose of teaching young school kids how to substitute real values for constants/variables, does it matter? π is a constant, but the value you use for it in exams and real life will not be the same, or the actual correct value. Getting students used to the idea that even constants can have varying values in exams or software is useful.
In my exams π had values ranging from 3, 3.1 to whatever the calculator had. g also ranged from 9.8 to 10, although in fairness g is not a constant.
At least setting it to 5 can spark debate around what a more reasonable approximation should be.
It’s just assuming that π is 5 in this specific scenario, just like it’s reasonable to assume the existence of a spherical cow in a frictionless environment. Yeah, if you use the results of this problem to develop a real cylinder you’re going to have a bad time but nobody is doing that all what’s the problem?
Nobody is saying that from this point in time and going forward π = 5 and now math is broken forever. People need to chill
If it’s teaching grade school kids, I would argue it is problematic, only as to not draw confusion on reassigning π away from it’s widely accepted consistent value of ~3.14 for most applications. Once you start getting into theoretical physics and the like, that’s a different story. Math is already a tough subject for many kids and this would just throw another wrench into the learning curve. I’d argue to only start debating the fundamentals and theory after a firm grasp of the fundamentals has been established and practiced repeatedly, preferably in upper level courses.
More or less that age, yeah. I’m guessing you’re outside the US, typically grade school here refers to Kindergarten to 12th grade (basically 5y to 17/18).
Perhaps this is an American methodology, but we were always taught that π is intended to represent the constant of 3.14 as it applies to circles in geometry and trigonometry, while various variables of x/y/z/etc were values to either be input or solved for. It wasn’t until Calculus that it was suggest that π could be variable dependent on other factors in a certain context, but that was usually pretty rare.
And yeah I enjoy math as well, but I also helped tutor my peers who didn’t grasp it, so I can understand why it was taught that way (that and our education system is interesting, for lack of a better term).
Yup, Australian, and thats primary+secondary school here. Im only harping on the test/exam thing because i vaguely recall having some tests were π was set to a specific value like 3.1, and that if you used the calculator π, all your answers ended slightly off. It wasnt anything to do with π being a variable, just the you had better read the exam question carefully and that blindly typing the equation into the calculator would not always be the answer.
I think i have typed π more times today than the last 15 years since I left highschool :D
Ah gotcha. It’s been a while but as I recall, on tests without calculators we were usually told to use 3.14 and round our answers to the nearest hundredth, though some teachers were more flexible if you were pretty close but slightly off in the decimals, while tests with calculators were pretty stringent on being precise. And yeah, I remember pretty early to ensure the decimal lengths because I tended to use the calculator’s length of π instead of hundredths or thousandths or whatever and it botched my answers after rounding off.
I feel ya there, though I’m starting up school again in the fall so this is getting me somewhat excited for math classes again.
minor nitpick but the value of π is technically a parameter of the space you are operating in . which means it can have any arbitrary value as long as you are willing to operate in non euclidean spaces (and the space we live in is not euclidean though not to a measurable extent unless you are near a black hole)
but yeah in this context saying π is a constant is as correct as saying you cant take a square root out of a negative number .
edit : possibly better example is that a triangle’s angles sum to 180°
As a dyscalculic, I can’t solve this but I don’t see a problem here… I see all you people freaking out that the little symbol thing equals five but it’s a little symbol thing haha it doesn’t have to be pie haha it could be a little symbol thing.
Nobody knows how to think like a dyscalculic at all haha… it’s just a little symbol thingy… it doesn’t have to be pi. Just like X is a little symbol thingy… the x is now just kind of a table right now… it’s just a little symbol thingy and it means five it’s not that difficult. Lmao
Yes it does have to be pi because that’s the formula for the volume of a cylinder. If you take a simple, cylindrical glass or container and measure it and apply the formula with pi, you’ll see that you’ll get the correct volume of the container. If you just want your kids to calculate a random x that’s 5* 10 *10 *10 just tell them to do that, don’t give them a made up formula, it’s not that difficult.
Mathematically, no, it does not. We make up the definitions. If you wanted to see what the consequences of a, I don’t know, 5-dimensional universe with Pi set to 5.65 were, you can do that. These are scribbles on pages, there is literally nothing stopping you.
Academically, what’s stopping you is whether these calculations are useful. The only problem I see here is that it’s kind of misleading to imply to someone that Pi is something it conventionally isn’t. But even then, I think I’d respect the mathematician who could recognize Pi as a symbolic name for, usually, one particular transcendental constant a little bit more than one who refused to even entertain the idea. Like, imagination is important to mathematics, too.
And to be clear, “let Pi = 3.14” is also incorrect. It is closer than 5, but it is still infinitely wrong.
[edit] And also, I was imagining this question was for a younger audience. Reading it again, I’m not going to pretend I know what’s going on up there.
To be Devil’s Advocate:
Given that the rest written in Comic Sans, it may be an early elementary school exercise, aimed at teaching kids to do multiplications. In this case, it’s tolerable and/or defensible to find a simplification for pi.
That said, making pi equal to 3 would have been more accurate for that…
Depends on the level of precision you need. If I want the volume in a 500 foot long, 3 inch pipe to roughly estimate how much supply I need to order, I wouldn’t need a calculator. It would very roughly be 90-95 ft3. (Divide 500 by 4 two times and multiple by 3)
Then I would spend 5 minutes double checking myself haha.
In astronomy, pi=1 or 10, depending on whether you’re trying to over or under estimate something. Because when you’re trying to estimate distances measured in millions of light years, the difference between 3 and 10 is just one or two orders of magnitude on a small number. It’s pretty common for astronomers to do napkin math by rounding every single number to the nearest zero. 91k becomes 100k for instance. Because the napkin math estimations are just trying to gauge whether some celestial event or object is a thousand light years away, ten thousand, a hundred thousand, etc… And pi becomes 10, because that’s the nearest round number.
…if they’re above average, I think they’ll figure out the explicitly defined variable. I think the instructor is trying to make sure this problem doesn’t require a calculator and figured defining pi as 5 makes it clear that you can treat it as a whole number. 3 would be more accurate and just as easy, but meh idk that this is that great of a blunder.
You can be a smart kid and not realize that adults are lying.
I remember the Peas and the Punnett Square. Sure, mendelian genetics explains pea plant colors, but doesn’t explain dog fur colors. Just providing a footnote that more completed genetics exists would have been nice.
Or it’s from an ME. They seldom can remember the rounded value of Pi, but they’re pretty sure it’s somewhere between 3 and 4. But you probably should use 5 just to be safe…
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