chk out these mathematical curiosities

[blurredvision]

AAAAAAGGGGGGGGGHHHHHHHHHHHH!!!!! Too much thinking for so early in the morning!!!! I would solve each and everyone of these problems, but I'd hate to show everyone up on such a fine morning. 😉

 

[thEnEuRoMancER]

Shalmanese, edit your post and reverse the inequality signs 😉

0>x>10 and 0>y>10


a = n^2 (perfect square), n is an integer

b = 2*a = 2*n^2 = m^2 -> m = sqrt (2) * n -> m is not an integer -> b is not a perfect square

impossible.

 

[Shalmanese]

neuromancer: proving why sqrt 2 is not rational is what I am after as well as telling me who exactly died proving this 🙂

most of thats commonly around in literature so it shouldnt be that hard.

 

[troglodytis]

<< I will seriously buy someone a 128MB stick of micron RAM if they solve the second one >>





<< 2. find an even number apart from 2 which is not the sum of two primes >>




-2

-1 + -1 = -2


shall i email the address to which you can send the ram?

 

[reitz]

<< 2. find an even number apart from 2 which is not the sum of two primes >>


Ummmm...6+6=12...am I missing something here?

 

[Shalmanese]

12 is the sum of 5 and 7.

 

[thEnEuRoMancER]

I don't have a clue why someone should die proving sqrt(2) is irrational 🙂

Let's assume sqrt(2) is a rational number:

sqrt(2) = a/b , where a and b are integers

so

2 = a^2/b^2

and

a^2 = 2 * b^2

Now if we expand a and b into product of prime factors:

a = k1*k2*...*kn

b = l1*l2*...*lm where ki and li are prime numbers:

we get

k1^2*k2^2*...*kn^2 = 2 * l1^2*l2^2*...*lm^2 or

k1*k1*k2*k2*...*kn*kn = 2*l1*l1*l2*l2*...*lm*lm

There are 2n factors on the left side and 2m+1 factors on the right side. There cannot be an even number of prime numbers on one side and an odd number of prime numbers on the other side and this means the initial assumption is not correct and sqrt(2) isn't rational.
Now why is sqrt(a^2) rational? Because it is possible to expand a^2 into a product of an even number of primes.

 

[Shalmanese]

Guess I finally found something you dont know about neuromancer 😉, do some reading on the history of irrational numbers.

BTW: John Brunner kicks Gibsons ass in cyberpunk writing. predated him by at least 15 yrs and is still a better read

 

[Mday]

i already solved that problem.

a+bi

is prime if
1) a^2+b^2 = prime, a, b /= 0
2) b = 0, a is = 4 (mod 3)

see, 2 is not a gaussian prime.

i am hoping that underlined = sign is the triple bar congruence. =)

BTW, i am doing this in a Euclidian Ring, so you forgot the associates =) ;-)

 

[thEnEuRoMancER]

Hehe, Shalmanese, there are many things I don't have a clue about...
Besides, I said I don't know why someone should die proving sqrt(2) is irrational, I didn't say I don't know who died proving it 🙂

Listen, maybe I made a mistake calling you a troll. Time to do a search on John Brunner ...

 

[Shalmanese]

hmm... neuromancer apology accepted *mutters* damn, the price of bribing someone to keep your reputation clean is increasing every day, really gotta look into that insurance scheme Mday and BiggieN have got going*mutter*

also, there a lot of things that would look ridiculous with our &quot;modern&quot; outlook but Im willing to bet that plenty of things we hold sacred will be ridiculed in 100 years

John Brunner was THE person who invented cyberpunk. sad thing is he predated the coinage of the word &quot;cyberpunk&quot; by about 10 years (shockwave rider was 1975) so he sank into oblivion while the popular writers made a fortune plagurizing his ideas. Fortunatly, some of his works are being reprinted again but you local university library would be the best place to find him IMHO.

and another question:

using the following rules:
1. If the number is even, halve it
2. If the number is odd, multiply by 3 and add 1
find a positive, finite integer which does not have a finite number of iterations before it reaches one(eg. it loops) or prove that there is none.

eg.
for 2, it would go 2,1
for 3: 3,10, 5, 16, 8, 4, 2, 1
for 4: 4, 2, 1
etc..

also if you make a graph of n vs no of iterations for n, it makes a very nice semi-chaotic graph if your into that kind of thing

 

[thEnEuRoMancER]

This is another yet unsolved problem...

 

[shadowfaX]

uh oh... *BOOM* *shadowfax's head explodes*

 

[Shalmanese]

for some odd reason, Ive always known this problem as the hilbert problem.

maybe Ive got the two mixed up 🙁

 

[nullshark]

<do some reading on the history of irrational numbers>

I never, ever... ever thought I'd read anything like that sentence in my life 🙂

 

[Shalmanese]

but then again, You probably never ever thought that over 40,000 hardware addicts, losers and general nerds with no life could converge in one place and wonder about the deep mysteries of the universe like how old are you and how many times do you shower a day

 

[nullshark]

No... I read that would happen in a William Gibson book years ago 😉

 

[Shalmanese]

Bah, Gibson My @ss, read some decent cyberpunk. dont even get me started on this topic.

too late, read this

 

[nullshark]

I'm just pushing your buttons 😉


<...John Brunner kicks Gibsons ass in cyberpunk writing. predated him by at least 15 yrs and is still a better read>