A minor nitpick: It was Andrew Wiles who proved Fermat's last theorem. Andre Weil was another incredible mathematician (responsible for, among many other things, the celebrated Weil conjectures), but did not prove…
I'm sorry to be so pedantic, but your math doesn't seem quite right. Should it instead be (1/100,000 chance of burning down each year) * ($200,000 cost if it does) = $2 per near expected damages?
This property of Piedmont is not even unique within the Bay Area! Fremont (the fourth-largest city in the Bay Area) has an enclave of its own, Newark, which is its own city yet completely surrounded by Fremont.
I use it for my weekly to-do list (since it then syncs across all computers and my phone), and it is a convenient way for me to keep track of my different projects. I type up a short summary for myself after meetings…
To belabor the point: Keeping one of the prices fixed, you should prefer that it be 20 percent more expensive on the weekend. Assume for example that the price on Saturday is $10 and the price on Tuesday is $8. It is…
If you're handy with simple algebra (and can remember that the derivative of x^2 is 2x) then you can remember the picture. If f(x) = x^2 - N, then you're looking for the (positive) zero of f. You take a succession of…
Just to nitpick a bit -- your final three numbers add to 110, not 100. Perhaps you meant 49/31/20? I point it out only because 49/31/30 seemed too good to be true.
Or simple contraposition :-P Please correct me if I am wrong, but if the relevant part of the article is "I do not have insurance, so it is important that I maintain my health", then the contraposition would be "It is…
The 30% profit margin sometimes also signals that there are high barriers to entry. (You already mention what I think is the big one: accreditation.)
I haven't read Smolin's paper, so I'm not sure exactly what this article is getting at. Is he suggesting that there should be a different connection (i.e., not the Levi-Civita one) on the cotangent bundle of spacetime…
I'm sorry I wasn't more clear, but your interpretation is what I meant. Per your rule of thumb, seeing \tau should suggest that it has to do with circles or polar coordinates, and the square root points to how to get…
I'm not a big fan of introducing a new constant (though I believe \pi should have been 2\pi), but I love thinking of the integral you wrote down as \sqrt{\tau / 2} because then the answer practically tells you how to…
You should never end a sentence with a preposition. The mathematician Paul Halmos loved issues like these and once constructed a sentence that ends in five prepositions: "What did you want to bring that book that I…
I'm having trouble determining whether you are serious, but I suspect the original poster was referring to reddit's programming community.
I was aware of the group structure of the Rubik's cube (it is, after all, a subgroup of the permutation group on 54 elements), but apparently I had never given it much thought beyond that. Thanks!
Oh, fair enough! That's a fun example.
I don't follow -- what is the structure being preserved in this example?
I'm assuming you want non-trivial examples of non-bijective homomorphisms, but you can create a trivial one using the <= relation: Consider the two element set {0, 1} and the function f from {0,1} to {0,1} so that…
The a-ha answer still works, but the orignal answer given has you sum 2^(d-k) from k =0 to d, so in this example would be 2^1 + 2^0, suggesting that you would need 3 games to determine the winner.
Nobody, but it was implicit in the solution proffered by the post I replied to. If the game they are playing has 5623 participants with one winner and 5622 losers, you only need a single game!
"If you had 5,623 participants in a tournament, how many games would need to be played to determine the winner?" Let d = Log_2 N. Sum 2^(d-k) for k = 0 ... d The a-ha solution to this puzzle is to realize that every…
I don't know whether this is the Lorenz they are referring to, but there was another Lorenz who worked in optics. http://en.wikipedia.org/wiki/Ludvig_Lorenz In fact, there is a Lorentz-Lorenz equation. Somewhat more…
It's only somewhat related, but This Week's Finds in Mathematical Physics #234 discusses some of the math behind music theory. It's a nice article if you're familiar with basic group theory.…
I'm confused by your statement -- in the quaternions, i, j, and k are all square roots of -1.
I have great personal affinity for Texas but am having trouble coming up with a list of half a dozen top notch universities. I can come up with three (UT, TAMU, Rice) and a few more if you set the bar a bit lower, but…
A minor nitpick: It was Andrew Wiles who proved Fermat's last theorem. Andre Weil was another incredible mathematician (responsible for, among many other things, the celebrated Weil conjectures), but did not prove…
I'm sorry to be so pedantic, but your math doesn't seem quite right. Should it instead be (1/100,000 chance of burning down each year) * ($200,000 cost if it does) = $2 per near expected damages?
This property of Piedmont is not even unique within the Bay Area! Fremont (the fourth-largest city in the Bay Area) has an enclave of its own, Newark, which is its own city yet completely surrounded by Fremont.
I use it for my weekly to-do list (since it then syncs across all computers and my phone), and it is a convenient way for me to keep track of my different projects. I type up a short summary for myself after meetings…
To belabor the point: Keeping one of the prices fixed, you should prefer that it be 20 percent more expensive on the weekend. Assume for example that the price on Saturday is $10 and the price on Tuesday is $8. It is…
If you're handy with simple algebra (and can remember that the derivative of x^2 is 2x) then you can remember the picture. If f(x) = x^2 - N, then you're looking for the (positive) zero of f. You take a succession of…
Just to nitpick a bit -- your final three numbers add to 110, not 100. Perhaps you meant 49/31/20? I point it out only because 49/31/30 seemed too good to be true.
Or simple contraposition :-P Please correct me if I am wrong, but if the relevant part of the article is "I do not have insurance, so it is important that I maintain my health", then the contraposition would be "It is…
The 30% profit margin sometimes also signals that there are high barriers to entry. (You already mention what I think is the big one: accreditation.)
I haven't read Smolin's paper, so I'm not sure exactly what this article is getting at. Is he suggesting that there should be a different connection (i.e., not the Levi-Civita one) on the cotangent bundle of spacetime…
I'm sorry I wasn't more clear, but your interpretation is what I meant. Per your rule of thumb, seeing \tau should suggest that it has to do with circles or polar coordinates, and the square root points to how to get…
I'm not a big fan of introducing a new constant (though I believe \pi should have been 2\pi), but I love thinking of the integral you wrote down as \sqrt{\tau / 2} because then the answer practically tells you how to…
You should never end a sentence with a preposition. The mathematician Paul Halmos loved issues like these and once constructed a sentence that ends in five prepositions: "What did you want to bring that book that I…
I'm having trouble determining whether you are serious, but I suspect the original poster was referring to reddit's programming community.
I was aware of the group structure of the Rubik's cube (it is, after all, a subgroup of the permutation group on 54 elements), but apparently I had never given it much thought beyond that. Thanks!
Oh, fair enough! That's a fun example.
I don't follow -- what is the structure being preserved in this example?
I'm assuming you want non-trivial examples of non-bijective homomorphisms, but you can create a trivial one using the <= relation: Consider the two element set {0, 1} and the function f from {0,1} to {0,1} so that…
The a-ha answer still works, but the orignal answer given has you sum 2^(d-k) from k =0 to d, so in this example would be 2^1 + 2^0, suggesting that you would need 3 games to determine the winner.
Nobody, but it was implicit in the solution proffered by the post I replied to. If the game they are playing has 5623 participants with one winner and 5622 losers, you only need a single game!
"If you had 5,623 participants in a tournament, how many games would need to be played to determine the winner?" Let d = Log_2 N. Sum 2^(d-k) for k = 0 ... d The a-ha solution to this puzzle is to realize that every…
I don't know whether this is the Lorenz they are referring to, but there was another Lorenz who worked in optics. http://en.wikipedia.org/wiki/Ludvig_Lorenz In fact, there is a Lorentz-Lorenz equation. Somewhat more…
It's only somewhat related, but This Week's Finds in Mathematical Physics #234 discusses some of the math behind music theory. It's a nice article if you're familiar with basic group theory.…
I'm confused by your statement -- in the quaternions, i, j, and k are all square roots of -1.
I have great personal affinity for Texas but am having trouble coming up with a list of half a dozen top notch universities. I can come up with three (UT, TAMU, Rice) and a few more if you set the bar a bit lower, but…