cosine

Haven't heard of that one... but I would just really really recommend you go to a library and see whats available on the shelf for free. In the Dewey Decimal system the mathematics books all have call numbers from 510-520. In the Library of Congress system they're sections Q-QA. Can you get to a library?

Hey, nice website. You seem to have a lot of interesting thoughts. You have more work to do before I could hope to comprehend your equations. First, you need to specifically define every variable in every equation you use, and explain why you are doing that which you are doing at each step of the derivation. Second, you need to actually program your code to see if it works. Honestly I don't see any reason why your loop will ever terminate. Can you prove that it will? You say that for this formula all you need to find the next prime number is the last prime number. Can you explain your result in terms of P2 = f(P1) ? Or if its simply to test if something is prime, please provide algorithm on how to check using your end result. Also, if you are just trying to check if a given number is prime, it would be very efficient to use something called Miller's Test. Please write everything out in as excruciating and mundanely detailed manner as possible!

Is Mathematics a Social Discipline? I think that mathematics is really one of the most social disciplines, in this day and age it seems that people seem to produce much better when working in cooperation. Maybe it is because one person's stupid mistakes are easily seen by another. Then again I can see counter arguements to this too. In the years they were working on their respective theorems, Weils and Perelman occasionally left their attics to go for walks. Yet I think these rather famous cases are rare and may be caused solely by the specific expertise needed. But what do you think?

I think what you are looking for are popularized mathematics books. Don't be fooled! Popularized books will often teach you a lot if you aren't already an expert on the subject I recommend a few books actually. Usually my number one out of hand recommendation is William Dunham's "Journey Through Genius: The Great Theorems of Mathematics". Besides that I think there are many great books but I would start with that one. It treats math theorems like works of art, discusses them in historical context as well as the other theorems used in proving them, and then tends to give the aftermath [pun intended!] of the proof.

Hmm I read through them again. First of all I think I understand your motivation for using the logarithmic spiral, but don't shoot the messenger when I tell you its not likely to be as accurate as you would imagine in the sense that you would like. Secondly, the variables in your derivations are VERY hard to follow. At the beginning, please declare and write the meaning of every variable. For example: Let S2 = the second prime That and also be a lot more rigorous when you say "the boxed in logarithmic spiral" You should give a picture and an equation as to what exactly that means. You seem to have put a lot of work into the site and I hope to see you work through these requests! In the worst case scenario where you find an error in the work, it will be a great learning exercise! And in the best case scenario you'll have discovered something new! (Though personally, I think at best what you have is a graphical interpretation of a famous theorem by Gauss, where the prime numbers less than or equal to N is approximately ln(N).

Nice!

if its true is a null hypothesis, so feel free to make up your own answer

Didn't all of your proofs rely on the converse of proposition 1 at some point?

Depending on how you interpret the question, its B, if they happen to all know the answer, or there is no answer if they don't know the answer.

Hey. So I checked out your equations and stuff. Its nice to see that you're thinking about this kind of stuff, but the truth is that your equations will "confirm" any numbers are prime. You can put any number into P1 and P2 and it will check. It works for 1 and 2, 9 and -9, even pi and i.

I really want to know the answer to Dhnondy's question!

If y=x + sin(xy) dy = dx + cos(xy)*(ydx + xdy) dy(1 - x*cos(xy)) = dx(1 + y*cos(xy)) so y'= (1 + y*cos(xy))/(1 - x*cos(xy)) yep

Hm, thats the first time I've heard it explained that way tree, I like it! An algebraic way of looking at it could go this way: For a positive*negative, multiplication is defined as addition of one number, summing with itself the number of times as the other number. So (-1)*a = -1 + -1 + -1... a times. For neg*neg here is a proof by contradiction: assume (-a)*(-b) =/= a*b then (-a)*(-b) - a*b =/= 0 so (-a)*(-b) + (-a)*b =/= 0 by the distributive law (-a)(-b + b) =/= 0 (-a)(0) = 0 =/= 0 is a contradiction. Therefore (-a)*(-b) = a*b And division works the same way because division is just multiplication by a multiplicative inverse, which has the same sign.

What kind of cipher system is it?

The March on May 1st did have millions of people. Several hundred thousands in the major US cities. (Approximately 400,000 in California and New York each). The article you cited referred to protests in March that were only in California.

I like Colbert's approach in the obviously and hilariously forced use of rhetoric to parody all political garble.

I once attended a presentation at SUNY Stony Brook where a professor presented how fractals represented the effectiveness of Newton's approximations when searching for zeros on the complex plane of a given polynomial.

The thing is when you already assume that x=y when you say "Consider the point P(x' date=' y) where [b']x=y[/b]=d" So of course it only holds when x=y, you assumed it so! Therefore your "proof" does not prove anything.

Where does 6.6 trillion USD number come from? Here is what we say people need to live: 5.15 an hour 40 hours a week 52 weeks a year 5.15 x 40 x 52 = 10712/yr Please explain how 2 cars + house + DVD player + TV + computer = 10712/yr

Hm interesting question. The first statement is T -> L, the second statement says that if we know you won the Lottery, then we know you bought a ticket. So it is L -> T. If you want to pursue this you can conclude that T <-> L Does this help? Also for mathematical topics I always reccoment Mathworld and Wikipedia, mathworld for more technical overviews, and wikipedia for everything else. So in this case I would reccoment searching "logic" on Wikipedia.

Joao Miguelo wrote a nice popular book about this called "Faster than the Speed of Light." It is a great read, even just to learn regular einsteinian physics. Its divided into two parts, Einstein, then VSL. I reccomend it highly.

Sounds like a modest proposal to me.

Thats a really good article, Pangloss, thanks for the link. I think he's concerns are important. Personally I don't have anything against earmarking and lobbying, its how we petition our government and get things from it. I wonder if perhaps the problem is less lobbying reform and more campaign finance reform. Because its when money controls who wins elections that the corporate representative lobbyists outstage the public interest lobbyists, (although there have been impressive lobbyist showings by nonprofits in the past).

In Mathematics here its about 60:40 Females to males. Maybe a little more even, but thats the gist of it.

"What's 2+2?"