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One is not prime
- Thread starter Doctor Q
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Sun Baked said:
Brilliant example!
So just is what is wrong with teaching that pi = 22/7? It's close enough (3.1429 vs 3.141592......) so that everybody who has been exposed to it can remember a 'working' approximation to pi. Is there anyone reading these posts who both knows and understands the actual derivation of pi, the reason/s why it should be known to n decimal points or even cares? That there is a number of people out there who really care passionately about pi in detail is one thing, but if everybody can think pi=22/7 ... terrrific!
The trouble with that "I divided by zero" T-shirt is the infinite price!
The post above by UKnjb has been the most interesting so far. Perhaps every teacher passes along knowledge that is understood at their level, to those whose knowledge is at a lower level, so teachers should not be expected to teach absolute correctness, just closer-to-correctness, and we all learn a series of approximations of the truth.
Examples: The rule "0 divided by anything is 0" might be a fine guideline in elementary school, because it works almost all of the time, and in particular for any practical cases kids might encounter (like how much pizza does each member of the family get if you have no pizza). Thinking a meter is exactly 3 feet may be good enough for rough measurements. And you can almost always use Newton's laws, without considering relativity, when solving practical kinetics problems.
The post above by UKnjb has been the most interesting so far. Perhaps every teacher passes along knowledge that is understood at their level, to those whose knowledge is at a lower level, so teachers should not be expected to teach absolute correctness, just closer-to-correctness, and we all learn a series of approximations of the truth.
Examples: The rule "0 divided by anything is 0" might be a fine guideline in elementary school, because it works almost all of the time, and in particular for any practical cases kids might encounter (like how much pizza does each member of the family get if you have no pizza). Thinking a meter is exactly 3 feet may be good enough for rough measurements. And you can almost always use Newton's laws, without considering relativity, when solving practical kinetics problems.
UKnjb said:
Okay...gotcha. Missed the "only" in your statement.
Nevertheless, the "or" argument fails because it would destroy Euclid's Fundamental Theorem of Arithmetic, which states that every integer greater than one can be written as a unique product of prime numbers. Because you could keep multiplying by one (thus destroying the uniqueness of the solution), one can not be prime number.
It's not that you've got it wrong, it's just sloppy wording. Any number is divisible by itself and one. Primes are special because they are ONLY divisible by themselves and one.UKnjb said:
It's sloppy because it is not possible to have a number be divisible by itself but not one, or by one and not itself. That 'or' really should be an 'and'.
I've always used 355/113 if I neeed a fractional version. It's much more accurate than 22/7.Sun Baked said:
22/7 is off by about 0.0012645 (about one tenth of one percent), while 355/113 is off by only about 0.00000026676 (a few hundred-thousandths of one percent).
Doctor Q said:
I found this an interesting read: Arguments for and against the primality of 1. And learned that until 1899, professional mathematicians considered 1 a prime number.
In my AP Chemistry class a looooong time back I had a question that was supposed to have a... I don't even remember the name for the symbol... but it looked like an equals sign = with a hump on the top line. I think it had something to do with molarity... anyway instead of using that symbol the chem teacher drew this other symbol ≈... a wavy equals sign which also made the question valid, just different. So we all got the question right with the wavy equals sign but she marked us all wrong (there were only 4 of us in the class... ). When we asked her about it she told us that the symbol she used was the = with the hump. It clearly wasn't though and she exclaimed, "Well I'm a chemistry teacher not an artist!" and was very upset. None of us ever did get that question right... ah well.
My "pet peeve" is parents telling their kids false things to get them to stop doing something. I know I know... have kids and I'll understand... but my face didn't stay that way, I doubt the electric bill will go up much from me flicking the lights on and off, and Santa will bring me stuff if I'm bad anyway...
). When we asked her about it she told us that the symbol she used was the = with the hump. It clearly wasn't though and she exclaimed, "Well I'm a chemistry teacher not an artist!" and was very upset. None of us ever did get that question right... ah well.My "pet peeve" is parents telling their kids false things to get them to stop doing something. I know I know... have kids and I'll understand... but my face didn't stay that way, I doubt the electric bill will go up much from me flicking the lights on and off, and Santa will bring me stuff if I'm bad anyway...
mactastic said:
Me, from my position here in the UK, say you are so so wrong. But I cannot be bothered to argue. The interesting thing here is that we now enter into the realms of semantics and 'accurate' grammar. I have my own working knowledge of English (and accept that I am entirely ignorant) and maintain that my original construct is correct. Your criticism is valid if, and only if, you have formally-accepted superior knowledge of English grammar. My working knowledge of English may differ from yours and give different meaning and emphasis to what I communicate. Which may reinforce the point that was raised by the OP.
An 'or' condition means that only one item need be true for the whole item to be considered logically true. As an example, 'if A or B then C' is true if either A or B is true. On the other hand, 'if A and B then C' is only true if both A and B are true. Since it is not possible (as I noted previously) for a number to be divisible by itself but not one, the 'or' condition is not accurate.UKnjb said:
Like I said, it's not that you're wrong per se. I'm sure you've got the concept correct in your head, it's just not technically correct to put an 'or' where you did. But hey, some people worry about whether math is wrong -- I worry about language. I deal with a lot of contracts, and a misplaced 'or' (or other sloppy wording) can have serious monetary consequences.
I've been correcting my teachers since fifth grade when Mrs. Wilson thought "Einstein" was spelt "Einstine."
Teachers don't like being corrected by kids who are younger and generally less-educated, but in high-school it seems to be okay. The teachers usually thank the students who correct them, at least in my school.
Teachers don't like being corrected by kids who are younger and generally less-educated, but in high-school it seems to be okay. The teachers usually thank the students who correct them, at least in my school.
as an avid hockey fan, i love that statementiNeedtoSwitch said:One time I was at a hockey game, when a lady walked up to me and said "Excuse me, can you tell me when the ref is going to blow the whistle, I need to go to the washroom"
Doctor Q said:
Factor prime numbers? Is that really the kind of busy-work they give kids today?
This is why our country has terrible math/science scores.
On that topic, if anybody wants a tutor in northern virginia...
Except for one problem - the original comment said something to the effect of "divisible only by itself or 1." That would mean that an exclusive or is being used in this context - thus stating that the number would have to be either divisible by itself or divisible by 1 (and no other number). I suppose there is some issue with a number not being divisible by 1, but that is less of an issue than what you proposed. I guess trade usage clarity make all the difference...got to avoid Peerless problems...mactastic said:
My teacher told us that 22/7 is more accurate to use than just 3.14, but that it's still not truly pi. That's why she almost always has us leave stuff in terms of pi.Sun Baked said:
Oh yeah... almost forgot one of my favorite quotes from the movie "Little Man Tate"...
*teacher writes some odd and even numbers on the chalkboard*
Teacher: Who can tell me how many of these numbers are divisible by two? Anybody? Fred! Hm? I know that you can tell me how many of these numbers are divisible by two.
Fred: Um... All of 'em.
(It's only kinda funny because she means only evenly divisible by 2)
*teacher writes some odd and even numbers on the chalkboard*
Teacher: Who can tell me how many of these numbers are divisible by two? Anybody? Fred! Hm? I know that you can tell me how many of these numbers are divisible by two.
Fred: Um... All of 'em.
(It's only kinda funny because she means only evenly divisible by 2)
I guess you're right: http://en.wikipedia.org/wiki/Prime_numberDoctor Q said:
Strange to think that my studies in engineering never taught me that bit of numeric trivia
Throughout my schooling this happened occasionally I suppose, but usually a student would pick up on a mistake and correct the teacher. Same thing if there was a student teacher in the class. Everyone was quite happy to point out any mistakes on their part because the teachers didn't mind.
I suppose in Primary/Elementary school things are a little different and students may not have the knowledge/confidence to be able to correct the teacher so such problems occur. Though I think that even if kids have learnt something that is incorrect, most will be able to relearn it later on without too many hassles.
I suppose in Primary/Elementary school things are a little different and students may not have the knowledge/confidence to be able to correct the teacher so such problems occur. Though I think that even if kids have learnt something that is incorrect, most will be able to relearn it later on without too many hassles.
I remember in ninth grade i had the greatest history teacher ever, and by far the best teacher at Yorktown high school. When the time came for a test on the American revolution, the first question was something about a battle during the revolution, and the hint was "it's the name of the school you go to." He said if anyone got it wrong, they would fail the course. I have always wondered if anybody ever got that question wrong...
I once got into an argument with my first grade teacher about gravity on the moon. She insisted that there was none... probably an easier concept for first graders than explaining less gravity but man that irked me....
I also had issues with one of my boss's daughter's geometry teachers. He sent home a problem (which my boss brought to work) which consisted of a parallelogram with various measurements and the object was to find the area of the parallelogram. The only problem was that the vertical height was greater than the length of the parallel sides. The answer he was looking for was a simple trick but I still maintain that the shape could not exist in real space and thus had no answer....
I also had issues with one of my boss's daughter's geometry teachers. He sent home a problem (which my boss brought to work) which consisted of a parallelogram with various measurements and the object was to find the area of the parallelogram. The only problem was that the vertical height was greater than the length of the parallel sides. The answer he was looking for was a simple trick but I still maintain that the shape could not exist in real space and thus had no answer....