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#76 Re: Dark Discussions at Cafe Infinity » Why is it that teachers keep insisting that 1 is a prime number? » 2008-12-05 13:27:40
Twice a week volunteer my time in a 6th grade math class. The teacher is a seasoned teacher who is pretty decent teacher (as far a the teaching part goes) who isn't very good at math. Every once in a while she'll make a mistake in class but I mostly bite my tongue, it's not my place to correct her, it would be disrespectful.
The other day the class was discussing equivalent fractions and she told the class that anything over zero was equal to zero. She even wrote some examples on the board including 1/0=0, 2/0=0, 3/0=0. At one point one of the students said, "What about 0/1?" and she said , "No"!!!! I was horrified. First chance I got in private (I didn't want to call her out in front of her students) I told her how wrong she was, and all she said was, "Oh, we go over dividing by zero tomorrow" as if it was really no big deal.
I feel your pain...
#77 Re: Dark Discussions at Cafe Infinity » Understanding axioms. » 2008-12-02 08:45:43
A really interesting book that I read that deals with this subject (and a whole bunch of others) is "Godel, Escher, Bach" (http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567).
My understanding is a axiom is like a brick, and a theorem is like a house (does that make a lemma like a wall?). Only these bricks don't come from anywhere, they just ARE. Another book that touches on this subject (but only briefly) is Flatterland (http://www.amazon.com/Flatterland-Like-Flatland-Only-More/dp/0738204420) It's a pretty quick read that explores that idea.
I'd like to expand on that question: What's the differance between:
theorem, lemma, postulate, hypothesis, axiom, rule (like Cramer's Rule), law and anything else you can think to add to this list.
Can someone smarter than me (mostly everyone here) break this down and help explore this?
#78 Re: Dark Discussions at Cafe Infinity » Pen Competition » 2008-11-14 14:25:05
My friend found this: http://usb.brando.com.hk/prod_detail.php?prod_id=00110&dept_id=015&cat_id=041
It's in the mail. I'm afraid that once I get it, me competitor will top it, so more suggestions are certainly welcome.
I can't find evidence anywhere that Math is Fun's LED pen is actually a pen, so I haven't ordered it yet.
And I'm sorry Ricky, while pencils are certainly preferable in math (and they can write upside down) in sales pens are supreme. Any super awesome pencil suggestions are of course welcome though.
#79 Re: Dark Discussions at Cafe Infinity » Pen Competition » 2008-11-13 08:23:43
Great suggestions.
While I myself am a huge Doctor Who fan, I'm also an American, no one I know would know what a sonic screwdriver is. I would think it's cool, but I couldn't win the competition.
The crayon is kinda neat.
The LightTalk II is THE COOLEST THING EVER! Wow! A little pricey, but totally worth it. My only hesitation is if it's not a pen, it won't count towards my competition. Also, I wonder if it really works that well. Does anyone know?
Great finds, please, anyone else, keep them coming!
#80 Dark Discussions at Cafe Infinity » Pen Competition » 2008-11-13 06:21:01
- bossk171
- Replies: 5
I'm currently in a competition with a guy I work with, who can come up with the coolest pen. He has two pens, one that extends and one that can write upside down and in space and stuff. All I have is a pen that looks fancy, but doesn't do anything cool.
So HELP! It can be homemade or bought. I need some ideas, I can't lose this. This is one of the smartest forums on the web, so I know that you will figure something out. I work in the tool department at a major retailer, so tool themed might be neat, but isn't imperative.
I'm willing to spend a little bit of money to win, but please don't come up with some multi-million dollar pen, that's not really realistic. Also, nothing that will get me fired.
I'm counting on you to help save my pride.
Thanks.
#81 Help Me ! » Probability and Statistics » 2008-10-06 06:14:28
- bossk171
- Replies: 2
My buddy sent me this question in an email. Unfortunately I've never take a formal prob and stats class, so I couldn't answer very well. If you could help (with the method, the answer is kinda irrelevant). Much Thanks:
In some small town 7 people die per year out of a population of 760.......
a, what is the average deaths per day
b, what is the probability that there will be no deaths on a given day
c, what is the prob. that there will be 1 death on a given day
d, what is the prob. that there will be 2 death on a given day
a. 7 deaths per year. 365 days in a year: (7/365): 0.019ish
b. About 92.5%
c. A little under 2%
d. 0.04% or less
I didn't use any formulas or anything, went more on intuition, I may be way off (but I don't think I am). Also, deaths aren't random, time of year, death of a loved one, natural disasters, etc. influence the odds. For example, if a house were to burn down, I'd think the odds of 2 deaths in one day would jump considerably. In general, I'd think deaths in small towns would tend to be grouped together in some way.
Well we were going that problem in stat class...over simplified because we were assuming deaths were random.
So I got part a right and comprehended it, so I didn't help there but I didn't know if you would need that part to do the rest.
then my teacher didn't really go over how to figure out the rest.
The back of the book said it would about 98.1%....I couldn't figure it out....my professors just writes on the board 358/365 which is 98.1%...but with no explanation,
then he moved on and said there is something else he needs to teach us...or I think he said that...he mumbles worse than me.
So you weren't horribly off, but I dunno I just don't see it.. the only thing I could think of was that if there's 7 deaths a year, there are 358 days where no body dies....but like that only works if there is a guaranteed one death a day rule...which there isn't...so that's why I'm all hung up.
#82 Re: Dark Discussions at Cafe Infinity » The why so many registered members but virtualy no one here question » 2008-09-30 16:10:47
I personally check this site at least twice a day to keep up on what's going on, but I don't often contribute anything. This is mostly because some members can be a little abrasive when they are passionate about what they're saying, and I'd really rather not deal with it personally.
But I can say I really love reading this forum and I'm a registered member because sometimes I really just want to chime in or share an idea with someone, even if it's not everyday that I post something.
#83 This is Cool » Make Math Manageable » 2008-09-08 07:51:46
- bossk171
- Replies: 1
http://nhpr.org/taxonomy/term/15001
I heard this on the radio today, I thought it was really good (click the link under the picture, "listen").
Thoughts?
#84 Re: Dark Discussions at Cafe Infinity » Help me with Spanish! » 2008-08-13 13:19:47
Yo quiero hablar español también. Yo sabio español un poco pero estoy muy malo.
#85 Re: Euler Avenue » Repeating or Terminating Decimals » 2008-08-05 07:09:02
I didn't forget about this thread, I just had to let it sink in for a while.
I don't really understand what you're saying, Ricky, but mathsyperson's demonstration was really nice. It makes a lot more sense now.
Infinitebrain: What? I'm guessing you're talking about .99999... which is a reoccurring discussion around here, but .9 = 9/10
A thought: can we consider a terminating decimal repeating if we say it's the "0" that's repeating? ex: 1/6=.16666666... and 1/5 = .200000000000...
#86 Re: Introductions » Hey!! » 2008-07-29 03:17:13
Just a little bit ago, I posted this: http://www.mathisfunforum.com/viewtopic.php?id=9921
I would be real exited to work on some posed cryptograms.
EDIT: is your sig just nonsense, or does it mean something significant? My gut instinct says you're dividing in another base... but I haven't gotten around to figuring out which one.
#87 Re: Euler Avenue » Number Bias » 2008-07-29 03:09:41
10 is arbitrary, I have 24 ribs perhaps base 24 is more appropriate? I have 2 ears, perhaps we should go back to considering binary? I have 4 limbs, maybe base 4? I guess the number 10 isn't so arbitrary as the fingers (or toes) being what we use as to count.
And before you try to explain the difficulties of counting on your ribs (I wouldn't really know where to start) that's not really my initial point, it's just my counterpoint.
But you need to realize that you are committing a logic fallacy called a Straw Man. You are distorting Jane's argument, and then arguing against that distortion. Doing such doesn't mean it was done on purpose, but it was done none the less.
What you posted would be valid if Jane was saying, "We use base 10 because we have 10 fingers." But that isn't her argument. Her argument is, "We use base 10 because we have 10 fingers which are in a rather ideal place for counting things and showing to other people."
Unless you can show me a natural way to show someone how many carrots you need with you limbs, your counterpoint doesn't stand up against the argument.
I didn't realize that was called "Straw Man" very interesting. You are right of course, I didn't mean to do that on purpose, but my understanding of her point was flawed and by extension my response was.
But I feel like the rest of my post holds true. I still maintain that it feels very human... and more importantly: that it shouldn't.
TheDude gets my point exactly. Mathematically 10 is very boring. I'm thinking about those really lame energy beings from classic Star Trek that are super evolved have no physical form (and hence no fingers). I wonder what base they'd use?
#88 Re: Euler Avenue » Number Bias » 2008-07-28 13:24:28
Wow that Alamblak system is crazy, good find Jane.
10 is arbitrary, I have 24 ribs perhaps base 24 is more appropriate? I have 2 ears, perhaps we should go back to considering binary? I have 4 limbs, maybe base 4? I guess the number 10 isn't so arbitrary as the fingers (or toes) being what we use as to count.
And before you try to explain the difficulties of counting on your ribs (I wouldn't really know where to start) that's not really my initial point, it's just my counterpoint.
I feel that 10 is very human. Which is arbitrary. I've always thought that math should transcend humanity and should be an unbiased and perfect system. I feel (perhaps wrongly) that humanizing it cheapens it, subtracts from its overall beauty. As MathIsFun pointed out, a cat would still be a cat if there were no people around to name it, just as mathematics would still exist.
This subject has jumped rather abruptly into the realm of philosophy which is all the more fun.
#89 Re: Euler Avenue » Number Bias » 2008-07-28 11:43:28
John E. F: I very much know the feeling of dreaming about math. Many times I have "solved" a math problem in my sleep only to wake and either not remember the solution or (worse) remember it and realize it makes no kind of sense in the real world. I wonder if your profound realization was in fact profound or not.
Ricky: I had forgotten that 10 was a triangular number. However I don't feel like that enough to make it relevant. 9 is a square, and frankly I think square numbers are much more interesting than triangular numbers. I wonder if your considering 10 to be a "nice compromise" is societal conditioning talking. I'm curious, if you had to pick a new base, what would you choose?
TheDude: Base 16 is really interesting. My choice was going to be Base 8 for many of the same reasons, it's interesting that we both went in the same direction with our thought patterns.
MathIsFun: That's a really interesting direction you're coming in from... discussing symbolism over the actual mathematics. It reminds me of a conversation I was having with my father in which I said that few people visualize addition "correctly" I said most people visualize the number one and the number 1 make the number 2 not 1 object and 1 object make 2 objects... am I being clear here?
This is an interesting discussion, and the "no right answer" aspect makes it approachable for almost everyone.
#90 Euler Avenue » Number Bias » 2008-07-28 06:55:41
- bossk171
- Replies: 15
This has been bothering me for some time. It's a very common conversation amongst mathematicians that terms like "complex" , "irrational" and "imaginary" bias math doers against them. By making them somehow unapproachable or non-existent. That's true, the vocab we use to describe numbers is very biased, but I'd like to speak (complain?, rant?) about another more sinister bias:
The decimal system. 10 is a very uninteresting number mathematically. It seems arbitrary to choose it as the base to our numbers. And we are all guilty of letting it affect us, some examples:
When my mom turned 50 I thought that all of a sudden she was very old (half of a century!) but on further reflection, 50 is a really insignificant number. Who cares? On a side note, 49 seems much more exiting, being a square and all...
My family often teases me for cooking something in the microwave for 27 seconds or 33 seconds instead of an "even 30." But why? what does it really matter? What makes 30 any more relevant than 29?
Yesterday I watched an episode of Psych on TV in which all the characters were attending their 13th reunion. It was an ongoing gag that they were having a 13th and not a 10th or 15th.
I could go on forever, but I won't. You should have the point by now.
I understand the need for a base "something" number system, it would be very unrealistic (and impossible) to have a different symbol for ever number. But I propose 10 is a far too arbitrary number to base a number system on.
Are these just delusional ramblings of a mathematical snob? Has anyone else ever felt this way? Most importantly, what would you choose as your base if you had the ability to reset the number system? And if you would leave it the same, why? Let's assume for this discussion that math could be "reset" without a "transition period" i.e. no one would have to relearn how to count... that way a discussion of a societal reaction doesn't cloud the overall mathematical discussion.
#91 Re: Dark Discussions at Cafe Infinity » Batman The Dark Knight » 2008-07-27 12:53:46
Definitely not a kids movie, 16 seems like kind of a high number, I'm very liberal when it comes to movie ratings though. If you think you can handle a violent (as well as disturbing at times) movie, go for it, great character development, amazing acting.
#92 Re: This is Cool » Zero !!! » 2008-07-23 18:08:50
I get it, I think. Some of the formalities are a little over my head, but I get the gist of what you are saying.
On a note of irony, Ricky, my musing are really a direct result of your (awesome) sig. When I first read it, I chuckled a little, but now I take it very (too?) seriously. Now, every time I encounter a mathematical problem, I think to myself, "where is that not a problem?"
#93 Re: This is Cool » Zero !!! » 2008-07-23 16:26:39
Thanks for the new topic, back to the old one...
Could we just define 1/0? The same way we define the sqrt(-1)? My guess is no, because we haven't, but why? I suspect it has something to do with 0 not being a real number (I mean real in the literal sense not the mathematical).
It just seems to me that many times in the past there were plenty of problems that were "un-defined" and we just added more definitions until we could do the problems. It's my understanding that Irrational, negative and Imaginary numbers we all rejected at one time, and yet no more. Why not do the same thing with 1/0? Create "ostentatious" numbers (my word).
#94 Re: Euler Avenue » Division mod n » 2008-07-23 16:20:12
Wow, thanks for giving this so much attention. I see now why division by zero is still a "no-no" in modular arithmetic. I admit (begrudgingly) that the "wheel" stuff is way over my head, but I'm very appreciative that attention was given to my question. Thanks.
#95 Re: This is Cool » Zero !!! » 2008-07-21 18:31:29
I'm not sure, should I start a new topic?
Ricky, can you be a bit more simplistic? And if it's not "exactly modular arithmetic" than what is it?
#96 Re: This is Cool » Zero !!! » 2008-07-21 17:32:56
You are forgetting the kind of people who think they know a lot... but don't really.
Would this be an appropriate time to discuss dividing by zero in modular arithmetic? Dividing by zero definitely plays an interesting role there. I'm not saying any more until either Ricky or Mathisfun gives me the go ahead, because I'm afraid that going into detail might be confusing and hence a bad idea.
#97 Euler Avenue » Repeating or Terminating Decimals » 2008-07-16 05:57:13
- bossk171
- Replies: 6
Please bare with me, I've never taken a formal number theory class, but this is something I've been thinking about...
Any decimal can be represented by a fraction as long as the number is either repeating or terminating.
Terminating: Suppose you have the number 0.4 and wish to represent it as a fraction, it's quite easy, just take every thing after the decimal, and put it in the numerator. Now in the denominator put 10^k (where k = the number of decimal places after the decimal). In this case, .4 = 4/10 = 2/5. Pretty straight forward.
Repeating: Very similar process, take the number until the point it starts to repeat and put that over [(10^k)-1]. For example: .747474...= 74/99
The opposite can be done as well:
Assume a number:
By multiplying it by
You can easily turn it into a fraction b/(10^k) (where k = mn). I think it's kind of obvious even if I've done a poor job explaining it.
What I don't think it obvious is that any fraction NOT in the form:
can be written in the form:
Can anyone prove that with minimal technical jargon? I'd really like that.
#98 Re: Help Me ! » Graph Theory » 2008-07-09 17:23:36
I think I have it:
My thought process is this: The highest degree vertex there can be is 6 (because there's 8 total and you can't shake two hands {your own and your spouse's}) The minimum is 0, which has to be the 6's wife (because all others have already shook hands once. I can really explain it, but I think that the general rule here is if you shake hands n times, your spouse shakes hands (6-n) times.
Seeing how everyone gives you a different answer, that means that you are the one that repeats (we know that at least one repeats because of the other problem). and the only number that repeats is 3 (because 6-3=3) so both you and your spouse shook three hands. Is that the only answer?
#99 Re: Help Me ! » Graph Theory » 2008-07-09 16:24:26
Oh, right, the second is easy... Assume the first vertex has a degree of (n-1) and the next has a vertex of (n-2) so on until the second to last one has only one vertex which means that the last one has to be a repeat. I'm kind of kicking myself for not seeing that before... Thanks.
I paraphrased the problem (too lazy to type word for word) but it does say: "...suppose you ask each person, including your husband..." does that mean that there's more than one answer?
#100 Help Me ! » Graph Theory » 2008-07-09 14:55:22
- bossk171
- Replies: 5
I bought a copy of "Introductory Graph Theory" bu Gary Chartrand yesterday and I'm going through it (by my self). The problem:
You and your husband go to a party with three other couples. Several Handshakes take place. No one shakes hands with themselves or their spouse. No one shakes hands with the same person more than once. After all the shaking is done, you ask every one how many hands they shook, they all give you a different answer. How many hands did you shake? How many hands did your husband shake?
The second one I'm having trouble with is:
A graph G of order p(≥2) is called "perfect" if no two of its vertices have equal degrees. Prove that "no graph is perfect."
I'm assuming that the two problems are similar in nature. Hints and helps would be better than answers, but answers would be appreciated just the same.
Thanks.