## Search found 555 matches

Sun Apr 03, 2011 2:32 am UTC
Forum: Mathematics
Topic: Little Boy Blue, Mathematical Brainteaser
Replies: 10
Views: 1856

### Re: Little Boy Blue, Mathematical Brainteaser

This is a unique and interesting problem. I simultaneously like it and dislike it. :) There's only so much I feel like doing by hand and in the evening, but in terms of orders of magnitude, your answer for the total number of tickets must be close to correct. Among the 9 tickets 1,...,9, there are 9...
Tue Mar 29, 2011 5:09 am UTC
Forum: Mathematics
Topic: Mathematics and Constants- Inconsistency with the Universe?
Replies: 31
Views: 3138

### Re: Mathematics and Constants- Inconsistency with the Univer

We can create a wheel with radius 1. Then dip the rim of the wheel in ink and roll it along a paper so that it turns one full turn. The length of that line will be equal to pi. You sure about that? More argument for tau! :D I think he just means that the diameter must be 1 for the full length turn ...
Tue Mar 29, 2011 3:57 am UTC
Forum: Mathematics
Topic: Mathematics and Constants- Inconsistency with the Universe?
Replies: 31
Views: 3138

### Re: Mathematics and Constants- Inconsistency with the Univer

Qaanol wrote:
taemyr wrote:We can create a wheel with radius 1. Then dip the rim of the wheel in ink and roll it along a paper so that it turns one full turn. The length of that line will be equal to pi.

More argument for tau!
Sun Mar 27, 2011 7:10 pm UTC
Forum: Mathematics
Replies: 4
Views: 1488

I believe "quadrilateral" can refer to any four-sided figure, so I'd interpret the question to mean: make sure the quadrilateral isn't "degenerate", i.e. that no three points among A,B,C,D lie on a straight line. However, I don't know the most efficient way to do that offhand. I'...
Thu Mar 24, 2011 5:45 pm UTC
Forum: Mathematics
Topic: Math Books
Replies: 379
Views: 283076

### Re: Math Books

In a few weeks, I'm going to attending a math team state competition. One of the tests I'll be taking is on the History of Prime Numbers. Does anyone have any good books, or internet sources, that I could read that covers prime numbers well? The Prime Pages at the University of Tennessee at Martin....
Wed Mar 23, 2011 10:29 pm UTC
Forum: Logic Puzzles
Topic: Pill bottle problem
Replies: 17
Views: 3656

### Re: Pill bottle problem

Because you say "large number of bottles", I take it that we need to come up with a general strategy for n bottles. Since a general strategy can be difficult to (i) discover and (ii) state, let's start with a specific example: Say there are 10 bottles. The original labels fell off, but we ...
Wed Mar 23, 2011 8:41 pm UTC
Forum: Mathematics
Topic: Is there a name for this infinite set of functions?
Replies: 5
Views: 852

### Re: Is there a name for this infinite set of functions?

Probably not. It's good to think about these things, but in this case, the set you're talking about is probably too large and/or too "unstructured" to deserve a name. Note that graphically, you're talking about (more or less) all possible curves that go through the point (3,5). (I guess if...
Wed Mar 23, 2011 7:28 pm UTC
Forum: Mathematics
Topic: Locus Problem [HOMEWORK]
Replies: 21
Views: 1569

### Re: Locus Problem [HOMEWORK]

Note that in the original question, if you first, for convenience, consider the case where A and B have "nice" coordinates, the algebra is simpler. For example, you could let A=(1,0) and let B=(-1,0). This will at least tell you relatively quickly what *type* of shape you get in general. I...
Wed Mar 23, 2011 7:24 pm UTC
Forum: Mathematics
Topic: Linear Functions
Replies: 9
Views: 1078

### Re: Linear Functions

It looks like the word "linear" is used with slightly different meanings in different places. The more "mathematiciany" definition of "linear" is the one gorcee just gave. Perhaps at an earlier stage in one's mathematical education, the word "linear" might be ...
Wed Mar 23, 2011 4:16 pm UTC
Forum: Logic Puzzles
Topic: 10 Letters
Replies: 21
Views: 5750

### Re: 10 Letters

One thing that's interesting is that the answer varies very little as you change the number of envelopes!
Wed Mar 23, 2011 4:01 pm UTC
Forum: Mathematics
Topic: Proving functions are constant
Replies: 3
Views: 665

### Re: Proving functions are constant

I'll start off being a little vague with my hints. We can get more specific later if needed. If you're trying to prove a function is constant, what are you trying to prove exactly? How can you express it in symbols, or using expressions like "for all x"? In general, what are some common pr...
Wed Mar 23, 2011 2:23 am UTC
Forum: Logic Puzzles
Topic: 10 Letters
Replies: 21
Views: 5750

### Re: 10 Letters

I've seen this problem before, but for anyone who hasn't, I encourage you to think about questions such as the following. If you had to guess: --do you think the probability is more than 10 percent? --do you think the probability is more than 50 percent? --how do you think the probability would chan...
Tue Mar 22, 2011 7:31 pm UTC
Forum: Mathematics
Topic: Linear Functions
Replies: 9
Views: 1078

### Re: Linear Functions

For math class, we need to prove that the inverse of f(x)=mx+b is also linear. I've gotten it to f^-1(x)=(x-b)/m. From here I have no idea how to prove it aside from graphing every linear function in existence. If someone could point me in the right direction, that would be great. Notice that your ...
Mon Mar 21, 2011 4:18 pm UTC
Forum: Mathematics
Topic: Combination Problem
Replies: 10
Views: 2821

### Re: Combination Problem

That's basically what I did. My verbal description is different, but same idea. First, I noticed that choosing 6 numbers from 1 to 40 is equivalent to choosing a "word" of length 40 where 6 of the symbols are 1, and the other 34 are 0. (1 in position j means j belongs to the set, 0 in posi...
Mon Mar 21, 2011 2:15 pm UTC
Forum: Mathematics
Topic: Combination Problem
Replies: 10
Views: 2821

### Re: Combination Problem

Because of the word "combination", I interpret 1,2,3,4,5,6 to be the same as 6,5,4,3,2,1. That is, we're talking about subsets. I interpret "no consecutive numbers" to mean that 1,3,5,7,9,10 is not OK but 1,3,5,7,9,11 is allowed (note that under my interpretation, that would be t...
Thu Mar 17, 2011 3:07 am UTC
Forum: Logic Puzzles
Topic: golf ball problem
Replies: 5
Views: 3526

### Re: golf ball problem

Name the 12 balls A, B, C, D, E, F, G, H, I, J, K and L Weight A, H, I and K versus E, F, G and J Weight B, G, I and J versus D, F, H and L Weight C, G, H and L versus D, E, I and K Then just look at the results, finding the answer will be pretty straightforward. I am not going to describe the 24 p...
Tue Mar 15, 2011 10:41 pm UTC
Forum: Mathematics
Topic: Matrix multiplication seems so arbitrary
Replies: 19
Views: 4661

### Re: Matrix multiplication seems so arbitrary

I can somewhat sympathize with the OP. I remember taking an intro linear algebra course in my first semester at university, and being a little worried that it wasn't "intuitive" to me why we multiply matrices the way we do. Why do we take a row of the first matrix and a column of the secon...
Mon Mar 14, 2011 6:54 pm UTC
Forum: Mathematics
Topic: Spherical Coodrinates
Replies: 6
Views: 860

### Re: Spherical Coodrinates

Isn't this problem one that could be done without doing any calculus, or am I imagining the problem incorrectly? As in, couldn't you find the height of the cylinder using a triangle, then find the volume of the whole sphere using the normal high schrool formula, and subtract the volume of the cylin...
Sun Mar 13, 2011 3:12 am UTC
Forum: Mathematics
Topic: Monty Hall and GRE Guessing Strategy
Replies: 14
Views: 4204

### Re: Monty Hall and GRE Guessing Strategy

You have to define what it means to pick “at random”. You also have to make sure your choice of values satisfy the given inequality. Once you have done that, then you are correct. Yes, I phrased my post too hastily. Obviously you have to make sure your x and y satisfy the first inequality. However,...
Sun Mar 13, 2011 1:56 am UTC
Forum: Mathematics
Topic: Monty Hall and GRE Guessing Strategy
Replies: 14
Views: 4204

### Re: Monty Hall and GRE Guessing Strategy

This is interesting, and I do see a similarity to the Monty Hall problem (though of course it's not the same problem). If we assume that in the long run, D is the correct answer 25% of the time, then there is a very simple strategy that results in a 75% success rate. Namely, pick values of x and y a...
Thu Mar 10, 2011 3:36 pm UTC
Forum: Mathematics
Topic: Area of Circle to Volume of Sphere
Replies: 9
Views: 3915

### Re: Area of Circle to Volume of Sphere

The tl;dr version of all the above: In general, when integrating, try to think not only in terms of symbolically finding the antiderivative of a formula, but also think about what the integral means geometrically.
Tue Mar 08, 2011 2:34 am UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 158163

### Re: A very interesting Mathematical Paradox

I suppose one could also create a system where we're simply not allowed to have decimal expansions with infinitely many digits. Some deniers of 0.999... = 1 are also not quite happy with 0.333... = 1/3 or 0.142857142857... = 1/7. This would, of course, be a very weak system. Most rational numbers wo...
Sun Mar 06, 2011 10:49 pm UTC
Forum: Mathematics
Topic: Geometry puzzle with a complicated solution
Replies: 2
Views: 704

### Re: Geometry puzzle with a complicated solution

Cool, thanks. I suppose it's not a surprise that this problem is a somewhat classic problem that has a name. Here's a sketch of what I consider the best solution I've come up with: With the help of the Pythagorean theorem and similar triangles, one can get 1/5 = 1/sqrt(144-x^2) + 1/sqrt(100-x^2) In ...
Sun Mar 06, 2011 6:23 pm UTC
Forum: Mathematics
Topic: Geometry puzzle with a complicated solution
Replies: 2
Views: 704

### Geometry puzzle with a complicated solution

Here's a geometry puzzle that superficially looks like it should be easy to solve. Find x. http://i.imgur.com/jfgec.jpg (Note: I interpret "10 ft" to refer to the line segment extending all the way from the left "wall" to the lower right corner. Similarly for "12 ft". S...
Sun Mar 06, 2011 2:57 am UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 158163

### Re: A very interesting Mathematical Paradox

Let's say that 0 is a point (length = 0), and 1 is the line segment [0,1] (length = 1). They're not, though. Those subsets of the real line have some properties that are analogous to the integers 0 and 1, but not all the same properties. You can't "prove" unorthodox results about addition...
Fri Mar 04, 2011 9:15 pm UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 158163

### Re: A very interesting Mathematical Paradox

Real numbers don't have predecessors nor successors. This is key. The 0.999...=1 deniers sometimes describe 0.999... as the number immediately next to 1, so it's infinitesimally close but not equal. The intuition that infinitesimals should exist is not, in and of itself, such a bad thing. That intu...
Thu Mar 03, 2011 11:22 pm UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 158163

### Re: A very interesting Mathematical Paradox

Also, ofc .99... = 1. I think the misconception that it does not, stems from not quite grasping that the sequence of 9 is in fact never-ending, as in it NEVER ends. I think the intuitive idea is when one says "never-ending" is that one just means "really really long" but that it...
Thu Mar 03, 2011 7:25 pm UTC
Forum: Mathematics
Topic: Copy :Does anybody knows why people always pick number 3???
Replies: 28
Views: 5470

### Re: Copy :Does anybody knows why people always pick number 3

Of course, with the specific example where 1 and 10 are mentioned, some people will assume 1 and 10 are permissible simply because 1 to 10 inclusive is a common scale on which to measure things. If you said "between 43 and 157", maybe people are more likely to assume that 43 and 157 are ex...
Wed Mar 02, 2011 8:27 pm UTC
Forum: Mathematics
Replies: 10
Views: 2087

I would be interested in what the actual probability distribution is if you asked someone to pick any real number "at random". Would probably look very strange! Something in a similar spirit, which wouldn't be that difficult to try: For each of the 10000 expressions 0.0001 to 0.9999 (or e...
Wed Mar 02, 2011 1:39 am UTC
Forum: Mathematics
Topic: Copy :Does anybody knows why people always pick number 3???
Replies: 28
Views: 5470

### Re: Copy :Does anybody knows why people always pick number 3

Anecdotally, I've heard that when people are asked to pick a number from 1 to 100, 37 is extremely popular.
Tue Mar 01, 2011 8:27 pm UTC
Forum: Mathematics
Replies: 10
Views: 2087

The uniform probability density on [0,1] is a pretty standard thing in mathematics. But I suppose you're correct that there's something a little fishy about randomly "selecting" one real number from that interval, as though it's an action to be performed. This is drifting from math into ph...
Tue Mar 01, 2011 2:50 pm UTC
Forum: Mathematics
Replies: 10
Views: 2087

An analogy I've used before: Consider a straight or curved line in the plane. Its area is zero. That doesn't mean it doesn't exist at all; it just means it makes no quantifiable contribution to area. Or, pick a random point on the Trans-Canada highway. What's the probability that your point lies on ...
Sun Feb 27, 2011 6:18 pm UTC
Forum: Mathematics
Topic: 7's and 9's
Replies: 5
Views: 1430

### Re: 7's and 9's

Here's my answer to the 7's and 9's problem. First, notice that 0, 9, 18, 27, 36, 45, and 54 are all attainable. These are all incongruent mod 7 (this is a relatively easy consequence of 7 and 9 being relatively prime). We claim that the seven consecutive integers 48, 49, 50, 51, 52, 53, 54 ...
Sun Feb 27, 2011 12:57 am UTC
Forum: Mathematics
Topic: 7's and 9's
Replies: 5
Views: 1430

### Re: 7's and 9's

This general result was first proved by JJ Sylvester. Cool, I didn't know that. I've always liked this problem, but never knew what to call it or how to credit it other than "mathematical folklore". Do you have a reference, by any chance? Here, for what it's worth, is my suggestion for so...
Sat Feb 26, 2011 11:34 pm UTC
Forum: Mathematics
Topic: 7's and 9's
Replies: 5
Views: 1430

### Re: 7's and 9's

In a sense, the multiples of 10 are a red herring. It may help you visualize things and make good guesses, but multiples of 10 are only convenient because we're used to counting that way. More fundamentally, the structure of this problem doesn't really have anything to do with the number 10. I'm pre...
Sat Feb 26, 2011 11:04 pm UTC
Forum: Mathematics
Topic: "Oh no! We forgot how to say... math... stuff!"
Replies: 294
Views: 93066

### Re: "Oh no! We forgot how to say... math... stuff!"

My reason for asking the question was not so much that I wanted an answer, but more to make the point that notational conventions do matter. Probably nobody here would enjoy using f to denote a real number and x to denote a function on the real numbers. Yes, at a fundamental logical level, we can us...
Sat Feb 26, 2011 9:43 pm UTC
Forum: Mathematics
Topic: "Oh no! We forgot how to say... math... stuff!"
Replies: 294
Views: 93066

### Re: "Oh no! We forgot how to say... math... stuff!"

BlackSails wrote:He has no point. Conventions are arbitrary by nature.

Let x be the function from the reals to the reals defined by x(f) = f^3. Find dx/df.
Fri Feb 25, 2011 7:48 pm UTC
Forum: Mathematics
Topic: "Oh no! We forgot how to say... math... stuff!"
Replies: 294
Views: 93066

### Re: "Oh no! We forgot how to say... math... stuff!"

I hope you consider this both relevant to the thread title and interesting: When teaching calculus, it has struck me that I wish there was a short name for "the natural logarithm of the absolute value of". That function is, of course, the most natural antiderivative of 1/x which is defined...
Wed Feb 23, 2011 1:02 pm UTC
Forum: Mathematics
Topic: Problems that seem difficult but aren't
Replies: 75
Views: 9102

### Re: Problems that seem difficult but aren't

For example, when n=18, n 2 +n+1=343=7 3 . But what sort of answer are you looking for? Are you suggesting that there are only finitely many integer solutions to y 3 =x 2 +x+1? That was indeed my guess, and more specifically that there are none with n > 18. I asked this question on Mathoverflow, an...
Tue Feb 22, 2011 11:26 pm UTC
Forum: Mathematics
Topic: Problems that seem difficult but aren't
Replies: 75
Views: 9102

### Re: Problems that seem difficult but aren't

This is all a bit subjective, of course, but I found it appropriate for this thread because (1) I was naturally led to consider possible approaches that seemed like they might be subtle or difficult, but (2) once I got the answer, it could be expressed concisely as a brief "aha!" moment. A...