SUPER-FUN-HAPPY-MATHS-TIME

[zzdfa]

^lol
the other threadz are dead so ill post here:



b) and c) are quite simple, but my answer for a) is looooooooong . im wondering if i missed something simple.

any ideas?

[kamil9876]

BONUS QUESTION FOR 1e1000000 points.
Consider the function of complex variable s

Show that all non-trivial zeroes have real part 1/2

Haha some people think they can:

http://www.google.com.au/search?hl=en&q=proof+of+riemann+hypothesis

Fermat's last theorem is funny too:

http://www.fermatproof.com/

[Cthulhu]

BONUS QUESTION FOR 1e1000000 points.
Consider the function of complex variable s

Show that all non-trivial zeroes have real part 1/2

Haha some people think they can:

http://www.google.com.au/search?hl=en&q=proof+of+riemann+hypothesis

Fermat's last theorem is funny too:

http://www.fermatproof.com/

I'm glad someone caught on.

It's always funny when people make websites with "proofs" of things like the Riemann Hypothesis or when they have a Theory of Everything.

If you're interested here is a documentary about the proof of Fermat's Last Theorem. IIRC the final proof was over 100 pages long.

Interesting fact: Andrew Wile's was knighted for the proof.

Edit: Here: Have the article as well.

[/0]

For a) isn't the locus the perpendicular plane bisector of line XY excluding the midpoint of XY? So z could be anything on the plane?

[zzdfa]

nah, in 3d it's like the intersection of the surface of 2 spheres with radius r around points x and y,:


i think you passed over the fact that r is fixed

[d0minicz]

BONUS QUESTION FOR 1e1000000 points.
Consider the function of complex variable s

Show that all non-trivial zeroes have real part 1/2

Haha some people think they can:

http://www.google.com.au/search?hl=en&q=proof+of+riemann+hypothesis

Fermat's last theorem is funny too:

http://www.fermatproof.com/

I'm glad someone caught on.

It's always funny when people make websites with "proofs" of things like the Riemann Hypothesis or when they have a Theory of Everything.

If you're interested here is a documentary about the proof of Fermat's Last Theorem. IIRC the final proof was over 100 pages long.

Interesting fact: Andrew Wile's was knighted for the proof.

Edit: Here: Have the article as well.

the guy in the vid was fcking crazy

[ryley]

I'm surprised (and depressed) that I actually recognised the zeta function and the part that followed, I gotta stop wasting time on wiki and mathworld and do more english/life.

[evaporade]

^lol
the other threadz are dead so ill post here:

(Image removed from quote.)

b) and c) are quite simple, but my answer for a) is looooooooong . im wondering if i missed something simple.

any ideas?

[zzdfa]

nice drawing, but the bottom left corner of the triangle should be touching the circle ;p
but yeah, pretty much my proof was:
(1) that if k>=3 then there are infinite number of unit vectors perpendicular to x-y
(2) that for every unit vector perpendicular to x-y there is a z that satisfies |z-x|=|z-y|=r

looking back over my proof i realize most of it was showing (1). probably shouldve just prepended 'clearly' to the statement and be done with it.
surprisingly I don't think i used the triangle inequality for a) b) or c)

 

[evaporade]

No, the circle extends to infinity, z is just a member.

[zzdfa]

This is what the question asks you to show:
      for any given r>d/2,
      there exists infinitely many z such that |z-x|=|z-y|=r

This is what I think you think the question asks:
      there exists infinitely many z such that |z-x|=|z-y|>d/2

they are different.

look at the red lines. their lengths are greater than r. so they don't satisfy the condition that  |z-x|=|z-y|=r.
if the circle extends to infinity then it'd just be a plane.


edited to make the point i was trying to make clearer

[evaporade]

you used the word circle, so I used the word circle. Yes it is a plane in 3D but the same idea in higher dimensions and it would be difficult to illustrate with a diagram.

Don't know what you meant by 'there exists infinitely many z such that |z-x|=|z-y|>2d'
The diagram clearly shows 2r > d

[evaporade]

The diagram also explains parts (b) and (c).

[zzdfa]

made a few typos in the previous post, fixed now

[evaporade]

The set of z is the shaded plane.
r is the 'distance' from any z on the plane to x or y.
r is not a constant as you tended to suggest in quote "look at the red lines. their lengths are greater than r. so they don't satisfy the condition that  |z-x|=|z-y|=r".