Search found 162 matches

by ptveite
Mon Apr 14, 2008 4:50 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0410: "Math Paper"
Replies: 92
Views: 31188

Re: "Math Paper" Discussion

I've definitely given a talk before in which, using the fact that Bernstein sets (a type of nonmeasurable set) didn't have the property of Baire, we asserted that there were no Bernstein Baires. It was horrible. A whole slide, with a picture of the Berenstein Bears. With an X through it. HAHAHAHA
by ptveite
Mon Mar 24, 2008 4:59 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0400: "Important Life Lesson"
Replies: 242
Views: 49235

Re: "Important Life Lesson" Discussion

I didn't laugh until I read the alt-text. Then I really did lol, and I don't do that much. I heart Monty Python.
by ptveite
Thu Jan 03, 2008 6:34 am UTC
Forum: Mathematics
Topic: Is the Koch Snowflake compact?
Replies: 17
Views: 3138

Re: Is the Koch Snowflake compact?

SlyReaper wrote:What's the Koch anti-snowflake?


http://mathworld.wolfram.com/KochAntisnowflake.html
by ptveite
Wed Jan 02, 2008 5:11 pm UTC
Forum: Mathematics
Topic: Is the Koch Snowflake compact?
Replies: 17
Views: 3138

Re: Is the Koch Snowflake compact?

Interestingly, though, the Koch anti-snowflake IS compact. That's pretty trivial though as it's expressible as the intersection of closed sets.
by ptveite
Mon Dec 31, 2007 11:22 pm UTC
Forum: Mathematics
Topic: Need help with a *trivial* proof
Replies: 8
Views: 1817

Re: Need help with a *trivial* proof

I know that with squares, any number can be represented as the sum of no more than 4 squares. 15 needs that many.
by ptveite
Sun Dec 23, 2007 4:02 am UTC
Forum: Mathematics
Topic: Trisecting an angle
Replies: 63
Views: 11248

Re: Trisecting an angle

In fact, I think that you can n-sect a 90 degree angle (or at least you can construct a regular n-gon) exactly when n=2ip1p2...pj where the pk's are distinct Fermat primes 2^(2^n)+1
by ptveite
Sat Dec 22, 2007 6:34 pm UTC
Forum: Logic Puzzles
Topic: Robots on a Plane(t) [SOLUTIONS + SPOILERS THREAD]
Replies: 96
Views: 27690

Re: Robots on a Plane(t) [SOLUTIONS + SPOILERS THREAD]

The interesting part about the sphere case versus the cube case that makes this answer work is, not only is it a continuous transformation, it's an isometry (i.e. - distance-preserving). Fixed points under a continuous transformation that was not distance-preserving would not necessarily help us at ...
by ptveite
Thu Dec 20, 2007 7:17 am UTC
Forum: Logic Puzzles
Topic: Robots on a Plane(t) [SOLUTIONS + SPOILERS THREAD]
Replies: 96
Views: 27690

Re: Robots on a Plane(t) [SOLUTIONS + SPOILERS THREAD]

By the way, how can you be at the north pole facing west? At the north pole, every direction is south....

I just wanted to say, I really like the fixed-points solution, very elegant, albeit absurdly inefficient.
by ptveite
Wed Dec 12, 2007 5:39 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0356: "Nerd Sniping"
Replies: 376
Views: 159637

Re: "Nerd Sniping" Discussion

Wow, the more I think about it, the cooler/more disgusting this problem becomes.
by ptveite
Tue Dec 11, 2007 5:40 pm UTC
Forum: Logic Puzzles
Topic: Oracle [Solution]
Replies: 11
Views: 2100

Re: Oracle [Solution]

i think that hix mixed up white and black a couple times, but i think that what he proposes is, indeed, a workable solution.
by ptveite
Tue Dec 11, 2007 5:28 pm UTC
Forum: Logic Puzzles
Topic: Simple Puzzle
Replies: 27
Views: 6039

Re: Simple Puzzle

I like 1,2,4,7 Number of pieces that the plane is divided into by n lines, with no 3 intersecting at a point, and no 2 parallel or 1,2,4,8,15 Number of pieces that space is divided into by n planes, with no 4 intersecting at a point, and no 2 parallel or 1,2,4,8,16,31 Number of pieces a circle is di...
by ptveite
Thu Dec 06, 2007 2:58 pm UTC
Forum: Logic Puzzles
Topic: Small values of 20
Replies: 42
Views: 5527

Re: Small values of 20

Spoiler:
In golf?
by ptveite
Mon Dec 03, 2007 7:43 pm UTC
Forum: Logic Puzzles
Topic: Ambiguous times
Replies: 11
Views: 2860

Re: Ambiguous times

Half-assed answer
Spoiler:
Analog clocks are imprecise enough that you can never tell with certainty, so around every "legit answer" there is a continuum of possibilities that are indistinguishable, so there are c-many times that you could have woken up :)
by ptveite
Mon Dec 03, 2007 7:35 pm UTC
Forum: Logic Puzzles
Topic: Ambiguous times
Replies: 11
Views: 2860

Re: Ambiguous times

My answer comes about by taking a normal clock, and adding a third hand that is where a minute hand would be if the current minute hand were the hour hand. Every time this new hand crosses the hour hand, we have an undistinguishable time. This hand revolves 288 times per day, and the hour hand goes...
by ptveite
Mon Dec 03, 2007 7:19 pm UTC
Forum: Logic Puzzles
Topic: Ambiguous times
Replies: 11
Views: 2860

Re: Ambiguous times

I believe that this basic question has been done before....altho phrased differently.

I believe that the answer is
Spoiler:
264
I'm way too lazy to try to list all the times though.
by ptveite
Mon Dec 03, 2007 2:59 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0351: "Trolling"
Replies: 179
Views: 36053

Re: "Trolling Discussion"

XKCD has it's finger to the pulse of american culture. This week's new Family guy make a Rick Astley reference :)
by ptveite
Thu Nov 29, 2007 8:59 pm UTC
Forum: Logic Puzzles
Topic: Hooray for Hats! [solution thread]
Replies: 13
Views: 2077

Re: Hooray for Hats! [solution thread]

It's interesting that a resolution comes earlier in the straight-line case, when the people guessing actually have less information
by ptveite
Thu Nov 29, 2007 4:32 pm UTC
Forum: Mathematics
Topic: William Lowell Putnam Competition
Replies: 73
Views: 8816

Re: William Lowell Putnam Competition

There are two sets of questions, 6 problems each, 3 hours each. Section A, you have A1,A2, etc. and likewise with B, there is no substantive difference between A questions and B questions, and there is no real consistency with any given question number from year to year, but in general the lower num...
by ptveite
Thu Nov 29, 2007 1:33 am UTC
Forum: Mathematics
Topic: William Lowell Putnam Competition
Replies: 73
Views: 8816

Re: William Lowell Putnam Competition

I scored a 31.7 last year, just good enough to break the top 200. I got that taking only the second half of the test (stupid math GRE scheduling), but probably would not have done much better even with the first half, after looking at it. I would say that practicing off of old tests is in some ways ...
by ptveite
Fri Nov 23, 2007 6:12 am UTC
Forum: Mathematics
Topic: Amusing answers to tests
Replies: 393
Views: 58778

Re: Amusing answers to tests

The impression I got, though, was that the teacher wanted students to take the arithmetic mean of the two quantities, instead of the geometric mean. Wat he said. You're right, my method was not exactly efficient, altho it was right. The point is that the teacher was just retarded and had no idea wh...
by ptveite
Wed Nov 21, 2007 8:13 pm UTC
Forum: Mathematics
Topic: Amusing answers to tests
Replies: 393
Views: 58778

Re: Amusing answers to tests

I have a couple here.... First, if I don't know exactly how to do a proof in a math class, I will usually write a bunch of stuff that's true and assert that the rest is trivial. It actually works pretty often. Second, and more interestingly, I took very accelerated math through a program at our loca...
by ptveite
Wed Nov 21, 2007 7:32 pm UTC
Forum: Logic Puzzles
Topic: Variation on the Monty Hall Conundrum
Replies: 16
Views: 2872

Re: Variation on the Monty Hall Conundrum

I think it's pretty obvious that if the second door you choose has a prize, we're in the exact situation of the original problem. From there it only takes a little bit of logical extension to get the second half (if the door you pick has no prize then we are in a sort of "reverse-m...
by ptveite
Tue Nov 20, 2007 12:59 pm UTC
Forum: Mathematics
Topic: Show us your articles! Or what's your Erdos number?
Replies: 185
Views: 266741

Re: Show us your articles! Or what's your Erdos number?

Hmmm....we'll see if this works....
by ptveite
Sat Nov 10, 2007 2:39 am UTC
Forum: Logic Puzzles
Topic: What is the formula?
Replies: 18
Views: 2949

Re: What is the formula?

ya, that's the same thing
by ptveite
Sun Nov 04, 2007 8:18 pm UTC
Forum: Logic Puzzles
Topic: The Marching Soldiers
Replies: 18
Views: 2743

Re: The Marching Soldiers

Spoiler:
Image
This path gets you to every box....
by ptveite
Fri Nov 02, 2007 4:11 pm UTC
Forum: Mathematics
Topic: millionth derivative
Replies: 18
Views: 2744

Re: millionth derivative

I don't think that's true: The derivative of x 2 sin(1/x) is defined everywhere, but it's discontinuous at zero. How is -cos(1/x) + 2x*sin(1/x) Defined everywhere? It's still discontinuous at x=0. This is, indeed, the canonical example, but you have to define f(x)=0 at x=0, then the function is con...
by ptveite
Fri Nov 02, 2007 4:04 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0337: "Post Office Showdown"
Replies: 155
Views: 28209

Re: "Post Office Showdown" Discussion

I always find myself thinking, "oooh, maybe I should try this crazy/stupid thing. I'll quicksave first though!"
by ptveite
Fri Nov 02, 2007 3:45 am UTC
Forum: Logic Puzzles
Topic: Hole-finding.
Replies: 83
Views: 9790

Re: Hole-finding.

Spoiler:
I think that doing either my strategy or the reverse of my strategy (left instead of right and vice versa), each with probability one-half works as a solution to 2 and 3.
by ptveite
Fri Nov 02, 2007 3:41 am UTC
Forum: Logic Puzzles
Topic: Hole-finding.
Replies: 83
Views: 9790

Re: Hole-finding.

ptveite: What I'm looking for is not an expected ratio of 7 when the whole is at an arbitrary h , but rather an expected ratio of 7 when the hole location is chosen by an adversary, i.e. when the hole is in the worst possible place. I'm quite certain your algorithm can't make that guarantee just by...
by ptveite
Thu Nov 01, 2007 11:57 pm UTC
Forum: Mathematics
Topic: millionth derivative
Replies: 18
Views: 2744

Re: millionth derivative

Can you find a function that has a derivative that's defined everywhere, but discontinuous on a set of positive measure?
by ptveite
Thu Nov 01, 2007 6:44 pm UTC
Forum: Logic Puzzles
Topic: Hole-finding.
Replies: 83
Views: 9790

Re: Hole-finding.

Alright, I believe pretty strongly that my solution, unaltered, gives an expected value of w(h)/|h|<7, where w(h) is the wear and tear produced by an algorithm if the hole is at position h feet. Here goes, using the fact that if -2*4 n <= h < -2*4 n-1 , w(h) = 4 n+1 - 2 + x ...
by ptveite
Thu Nov 01, 2007 12:54 pm UTC
Forum: Logic Puzzles
Topic: Four gods [solution]
Replies: 15
Views: 3183

Re: Four gods [solution]

Well, 1 seems simple enough, ask "If I was to ask you is that the door to heaven while you were in your current mental state, would you say yes?" until you get the same answer from two gods. If it's yes, then go through it, if it's no, then don't. It doesn't seem like we can do any better ...
by ptveite
Thu Nov 01, 2007 12:50 pm UTC
Forum: Logic Puzzles
Topic: Hole-finding.
Replies: 83
Views: 9790

Re: Hole-finding.

Greedy's is no more efficient than mine, for h=-22, the robot must travel 1 + 2 + 4 + 8 + 16 + 32 + 64 + 65 = 192 = 8.73|h|. In fact, for any h = -(1 + 4 + 16 + ... + 4 n + 1), the robot will have to travel 9|h| - 6 feet, and so you can't be guaranteed to do any better than 9|h|. That being said, I'...
by ptveite
Thu Nov 01, 2007 1:42 am UTC
Forum: Mathematics
Topic: millionth derivative
Replies: 18
Views: 2744

Re: millionth derivative

Not all functions are polynomials, obviously finite polynomials have derivatives that eventually become zero, but that still means that their millionth derivatives are defined.
by ptveite
Thu Nov 01, 2007 12:59 am UTC
Forum: Logic Puzzles
Topic: Hole-finding.
Replies: 83
Views: 9790

Re: Hole-finding.

Alright, I think that calling it a proof would be a bit generous, but "worst case" for my solution would be that the hole is one more than an odd power of 2-many feet to the left or 1 more than an even power of 2-many feet to the right. The calculation is basically the same either way, as...
by ptveite
Wed Oct 31, 2007 11:21 pm UTC
Forum: Logic Puzzles
Topic: Hole-finding.
Replies: 83
Views: 9790

Re: Hole-finding.

GreedyAlgorithm wrote:
Spoiler:
Go right 1 unit, go left 2 units, go right 4 units, go left 8 units, etc. You are guaranteed to find a hole with h<=2^n within sum(2^i,i=0..n+1)=2^(n+2)-1 units. [2^(n+2)-1] < 4h < 9h.


Your answer is right, but your calculation leaves a lot to be desired.
by ptveite
Wed Oct 31, 2007 11:18 pm UTC
Forum: Logic Puzzles
Topic: Hole-finding.
Replies: 83
Views: 9790

Re: Hole-finding.

1)
Spoiler:
Go 1 foot to the right, 3 feet to the left, 6 feet to the right, 12 feet to the left, etc.
by ptveite
Wed Oct 31, 2007 1:32 am UTC
Forum: Logic Puzzles
Topic: City Planning
Replies: 19
Views: 2557

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! Ya, I think it might be better if the question seemed like more of a non-sequitur, jus...
by ptveite
Tue Oct 30, 2007 11:56 pm UTC
Forum: Logic Puzzles
Topic: City Planning
Replies: 19
Views: 2557

Re: City Planning

Spoiler:
soccer
by ptveite
Mon Oct 29, 2007 8:24 pm UTC
Forum: Mathematics
Topic: A regular pentagon
Replies: 4
Views: 2026

Re: A regular pentagon

I think you mean point 1 = (1,0) point 2 = (rcos(theta),rsin(theta)) point 3 = (rcos(2theta),rsin(2theta)) point 4 = (rcos(3theta),rsin(3theta)) point 5 = (rcos(4theta),rsin(4theta)) with theta = 72 degrees. altho that will be the wrong orientation I guess, so what you're really looking for is: poin...

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