## Search found 774 matches

- Sun Nov 04, 2007 9:22 pm UTC
- Forum: Mathematics
- Topic: Using Logs to Solve
- Replies:
**6** - Views:
**1265**

### Re: Using Logs to Solve

xlog(x)=log(x) x=1 Technically you can't even quite do this, since when you divide by log(x) you're assuming x isn't 1 (otherwise you're dividing by zero). So this actually shows a contradiction and proves that x can't be any positive number OTHER than 1, which you can then plug in and find that it...

- Sun Nov 04, 2007 3:29 am UTC
- Forum: Mathematics
- Topic: Pi repeats and the uncountable infinite set of numbers...
- Replies:
**14** - Views:
**2052**

### Re: Pi repeats and the uncountable infinite set of numbers...

SimonM wrote:Depends on whether or not the digits are perfectly randomly distributed

It's an open question as to whether they are, but the first 10 trillion or so (all we've calculated) seem to be (assuming you're using a reasonable definition of "random").

- Fri Nov 02, 2007 2:20 pm UTC
- Forum: Mathematics
- Topic: 2=1
- Replies:
**11** - Views:
**1661**

### Re: 2=1

Not sure if it's been done before so I'll just tack it onto this thread: 16 - 36 = 25 - 45----------------------------(Both are -20) 16 - 36 + 81/4 = 25 - 45 + 81/4----------(add 81/4 to each side) (4 - 9/2)^2 = (5 - 9/2)^2------------------(simplify the x^2 + 2xy + y^2 expressions) 4 - 9/2 = 5 - 9/...

- Fri Nov 02, 2007 1:55 pm UTC
- Forum: Mathematics
- Topic: Geodesics: Donuts are Delicious
- Replies:
**10** - Views:
**1587**

### Re: Geodesics: Donuts are Delicious

Well, it depends what sort of metric you have on the torus, but I'll assume it's the standard one you get from identifying the sides of a square with sidelength 1. Try drawing 9 copies of this sqaure in a 3x3 pattern, and put your first point in the middle square. Now you can put 9 copies of your se...

- Wed Oct 31, 2007 9:27 pm UTC
- Forum: Logic Puzzles
- Topic: City Planning
- Replies:
**19** - Views:
**2376**

### Re: City Planning

Token wrote:Given that it was big enough to scare him into running an entire kilometer, I assume it was the penguin queen, who resides exactly at the South Pole.

Ah, but if it was the penguin queen at the South Pole, then he didn't run at all, now, did he?

- Wed Oct 31, 2007 2:01 pm UTC
- Forum: Logic Puzzles
- Topic: City Planning
- Replies:
**19** - Views:
**2376**

### Re: City Planning

Ok, I've changed the statement of the problem to be a bit less obvious. If anyone's curious, the math concept that inspired this was that of a Cayley Graph (wikipedia has a nice writeup on what these are). The problem is actually asking you to find the Cayley graph of the group with presentation <a,...

- Wed Oct 31, 2007 12:13 am UTC
- Forum: Logic Puzzles
- Topic: City Planning
- Replies:
**19** - Views:
**2376**

### Re: City Planning

Indeed. Hm, 3 answers in 15 minutes... I guess it was too easy with the sports thing, maybe I should have just left out the 4th condition and instead asked what familiar graph the streets make.

Anyhoo, well done!

Anyhoo, well done!

- Tue Oct 30, 2007 11:53 pm UTC
- Forum: Logic Puzzles
- Topic: City Planning
- Replies:
**19** - Views:
**2376**

### City Planning

Here's a puzzle inspired by (though not requiring) some rather hefty mathematics: A city planner is given some odd requirements by a rather eccentric governor for the city he's designing. There are 4 requirements: - Each street corner must have exactly 3 streets (not the usual 4). Of these streets, ...

- Tue Oct 30, 2007 10:06 pm UTC
- Forum: Forum Games
- Topic: Count to 1 1000 times!
- Replies:
**1000** - Views:
**153686**

### Re: Count to 1 1000 times!

16836 rewritten in base 26

- Tue Oct 30, 2007 8:11 pm UTC
- Forum: Logic Puzzles
- Topic: 10 Word Puzzles
- Replies:
**17** - Views:
**3074**

### Re: 10 Word Puzzles

Guess for 4.

**Spoiler:**

- Mon Oct 29, 2007 9:32 pm UTC
- Forum: Logic Puzzles
- Topic: Circles on a plane
- Replies:
**33** - Views:
**3973**

### Re: Circles on a plane

I'm not certain, but it seems to me that if you're talking about open circles, then the fractal-ish pattern would leave out points, but if you're talking about closed circles, then everything gets covered. Neither was specified at the start of the problem, so I was using closed circles. quintopia: Y...

- Sun Oct 28, 2007 11:58 pm UTC
- Forum: Mathematics
- Topic: limit of a function defined in terms of another function
- Replies:
**18** - Views:
**1979**

### Re: limit of a function defined in terms of another function

Can't you interpolate a quadratic onto any 3 points? In particular, I think if you find the quadratic passing through (0, .5), (.5, .8 ), and (.8, .5), you'll get a quadratic function which satisfies the given conditions, but repeated applications of the function will keep oscillating between .5 and...

- Sat Oct 27, 2007 6:21 pm UTC
- Forum: General
- Topic: INTRO THREAD THE THIRD
- Replies:
**10891** - Views:
**2038330**

### Re: POST HERE FIRST - INTRO THREAD THE THIRD

Hi, I'm a math grad student in the US. Stumbled onto xkcd a while ago and loved it (I really identified with a lot of the comics in the archives). I really liked the math and logic puzzles parts of these forums, and finally got around to registering today.

- Sat Oct 27, 2007 6:12 pm UTC
- Forum: Logic Puzzles
- Topic: Circles on a plane
- Replies:
**33** - Views:
**3973**

### Re: Circles on a plane

I had to register just to comment on this. You never said all the circles had to be the same size. If they can get very small, you can cover the plane with a fractal-like pattern of circles so that each circle intersects only four others, and each point of the plane is contained in no more than two ...