h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Bearing in mind the limitations of GuideML, I would suggest φ for the one you called Φ, and φ–1 for the one you called &phi, because the product of the two is 1. GuideML does not allow a caret on a Greek letter. This is just my opinion though.

Your Guide Entry has just been picked from Peer Review by one of our Scouts, and is now heading off into the Editorial Process, which ends with publication in the Edited Guide. We've therefore moved this Review Conversation out of Peer Review and to the entry itself.

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Geggs

Congrats!

Congratulations.

Is this entry finished? It does not appear to be.

Well, the italics thought it was... how is it not finished?

The continued fraction at the end was downloaded from me for future use, and is just sat as a meaningless appendage at the end of the entry at the moment.

The notation change that the author enquired about recently may not have been acted upon, or the use of Φ may have been adhered to - I do not know.

The author may have been busy lately, or may have struggled with some of the feedback from peer review, because updates have not been very quick to occur. For these reasons, I doubt it is finished.

Sometimes the Italics pick an entry before it is actually finished. Old Hairy, are these the sort of things that can be sorted out by a sub-editor? If so, then we can leave it to the sub-ed to make any necessary changes. On the other hand, if there are major problems with the content of the entry, then it might be best to leave it untouched until the author has sorted them out. What do you think?

Oh damn I forgot to update it...

*ah!*

No it isn't finished.
I've got to do that.
Like,right away.
**

see I got caught up in RL for a while...

AK, if you update it now (in the next day or so) and let us know, we can have a last look over it to check it seems OK, then you can give the nod to the sub-editor who will whisk it away and do sub-editing things to it.

If you need more time, I'm sure the sub-ed can be put on hold - Jimster just needs to press the SLO-MO button and the sub-ed will be slowed down to one hundredth normal speed, giving you plenty of time to make the final changes. Just let us know what you want.

I shall try my best to finish tonight, but I don't know. my internet conenction must have deleted the last update. (faulty wireless). I'm workin' on it!

Is it just conincedence or something that (sqrt5-2)^3-1=Phi, and that Phi^3-2=sqrt(5)...
and Phi-.5=sqrt(1.25).
Random things I found playing with a calculator

btw what's the entity for the little squiggly approximately sign?

Hello everyone, but especially Cyzaki and Gnomon.

I have done what little I can to help this entry along, and very much look forward to it appearing on the front page. My warning that the entry was possibly unfinished has now been confirmed by the author. Perhaps the subbing process proceeding in 'slo-mo' will ensure all turns out as the author would wish, so I need say no more for now.

Thank you,

but

could you look at it now?
The only thing I didn't get involved in is the symbols for Phi and phi, I want to get the entry done-ish first.... try to ignore it for now

Hello AK.

For approximately equal you could try ≈ which is #8776.

The questions about your expressions I will not answer for the moment. More relevant to the entry are:-

x^2-x-1=0, so that x^2=x+1, and then x=1+1/x=1+1/(1+1/x)=1+1/(1+1/(1+1/x)) and so on. (That is one way to get the continued fraction).

x^2-x-1=0, so that x^2=x+1, and then x=sqrt(1+x)=sqrt(1+sqrt(1+x))=sqrt(1+sqrt(1+sqrt(1+x))) and so on. (That is one way to get the interminable square root expression).

In both the above, it is really necessary to show that both expressions converge. In each case that can be done by showing that the x which is always associated with a one has less effect than the one, so that a small error in x is diluted. (That is very rough, but if you do maths you can see what I mean.)

Hint about your question is, don't mess about with sqrt(5)-2, but instead put sqrt(5)=x. then (x-2)^3 is easy to do, giving x^3-6x^2+12x-8=x(x^2+12)-6x^2-8, then you can replace x^2 with 5.

Alternatively, using p for phi, as p=(sqrt(5)+1)/2 then 2p=sqrt(5)+1 so that sqrt(5)=2p-1, which works better in expressions involving both p and sqrt(5). You can have endless fun (?) with these.

By converge do you mean if you solve it after each substitution for x, it converges on Phi?

Converge means get closer and closer to the final result, eventually (after an infinite number of steps) give a constant value.

In my last posting it means that the influence of the single x on the right hand side becomes so small that it does not matter what value that x has, so that the iteration performed on a calculator gives the answer phi whatever number (x) you start with, up to a point. The answer at each stage gets closer and closer to phi, so that eventually (depending on the precision of your calculator), the displayed result does not change, although in theory the true answer is obtained only after an infinite number of iterations.

The continued fraction says, repeatedly, invert then add one (so that excludes 0 as the starting value, and some negative values if you are not to run into trouble later). The square root iteration says add one then square root (so excludes starting values less than -1). In either case, just keep going and the value phi emerges as if by magic.

As in either case the number one has to be repeatedly entered into the calculator, it is simplest to start with x=1 for both methods.

But hey, its your entry. I just mentioned where the methods you state have come from, because someone is bound to ask.

I've alerted the Editors, at F47997?thread=386962.

or even F47997?thread=386962