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July 21

Equally puzzling as prime numbers

Are there other phenomena on mathematics that are equally puzzling as the distribution of prime numbers? Mr.K. (talk) 10:10, 21 July 2008 (UTC)[reply]

I think a few phenomena in chaos theory can be very puzzling, for example that such complicated patterns as the Julia set and the Mandelbrot set arise with simple recursions. I'm sure there are many other examples. --Xedi^Talk 13:19, 21 July 2008 (UTC)[reply]

You might want to look at Unsolved problems in mathematics. When I read your question, the first one I thought of was the Riemann hypothesis which is one of the most famous unsolved problems ones, and is also related to the distribution of prime numbers. J kasd 14:51, 21 July 2008 (UTC)[reply]

Look at our page on the Collatz conjecture. The quote from Paul Erdős is rather entertaining, if also a bit scary. « Aaron Rotenberg « Talk « 10:26, 22 July 2008 (UTC)[reply]

Vectors

Please help me with the below question

A,B,C and D are four points in the space. They have position vectorsa,b,c and d respectively.

a=(2,4,-1) b=(4,1,0) c=(1,2,2) d=(3,3,3)

Find the value of K where, K=(AB*BC).(CA) using the value of K what can we say about points A,B and C? —Preceding unsigned comment added by 202.124.160.212 (talk) 14:20, 21 July 2008 (UTC)[reply]

The dot product and cross product articles have useful information on how these operations work (I assume the "*" in your question is the cross product), and should help you figure out the meaning of K. We can't do your homework for you, though! :-) --_{tiny plastic} Grey Knight ⊖ 14:48, 21 July 2008 (UTC)[reply]

Thanks for your advice, the value of K is zero. But I have no idea about the points by this value of K? —Preceding unsigned comment added by 202.124.160.212 (talk) 05:20, 22 July 2008 (UTC)[reply]

See also Triple product. Hope that helps. --CiaPan (talk) 06:23, 22 July 2008 (UTC)[reply]

Interpretation

I'm doing a question and I need a bit of help interpreting the meaning of it.

This is for a specific $f(x)$ and is not just a statements about all functions. One part of the questions says 'Either prove or disprove by means of a counterexample that $f(pq)=f(p)*f(q)$ if p and q are distinct prime numbers.' The next part of the question says 'Either prove or disprove by means of a counterexample that $f(pq)=f(p)*f(q)$ only if p and q are distinct prime numbers.'

What is the difference between these statements? 92.3.187.235 (talk) 21:27, 21 July 2008 (UTC)[reply]

I believe the second statement means you must prove (or disprove) the case where p and q are NOT distinct prime numbers (meaning they are either the same prime number or one or both are not prime). StuRat (talk) 21:40, 21 July 2008 (UTC)[reply]

Yes. The two claims to be proven or disproven are:

"p and q are distinct prime numbers" ⇒ "f(pq)=f(p)*f(q)"
"f(pq)=f(p)*f(q)" ⇒ "p and q are distinct prime numbers"

—Ilmari Karonen (talk) 21:54, 21 July 2008 (UTC)[reply]

One says "if"; the other says "only if". "A if B" means if B is true then so is A. "A only if B" means if A is true then B is true. Michael Hardy (talk) 04:31, 22 July 2008 (UTC)[reply]