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

Well-spotted!

I've added a couple of links, including one to the Technical Article provided by Old Hairy. This is a PDF document. Is it acceptable to link to such a document?

What - the scary one? Excellent!

Nice entry. Like it.


Geggs

Yes, nicely written, and encouraging to those nibbling at the edge of the fascination of maths.

To get over the "counting numbers" that aggrieve Old H (or was that someone else) could you say "postitve integers"? Or better still "natural numbers" with a link to the entry on that?

And when you're counting up the factors, can't you stop at the square root? By the time you reach that you've got all the factors, since along with the factor 2 (say) comes the factor that's half-n and so on. And you don't have to find the squre root accurately either, just find what natural number exceeds it.

Yes this does take away from the avuncular chatty tone. Forget it. It is a nice entry, publish away!

Recumbentman, the square root will not do if you want all the factors. It can be used to get the PRIME factors.

Take 12 for instance. Square root 3 and something, but factors 4 and 6 too.

You are both right!

With 12, when you get 2, you also get 6
when you get 3, you also get 4
then you pass root(12) and are finished.

The last is needed for perfect squares, e.g. 16
With 16, when you get 2, you also get 8
3 is not a factor
when you get root(16)=4, you are finished.

Postscript: it was me that got fed up with counting numbers, and I gave the link.

In fact the entry only mentioned 'counting numbers' twice. I don't intend to change it, as I feel the term is more meaningful to the average reader than 'natural numbers', and certainly is equally accurate and understandable for the mathematicians.

The practical way of finding all the divisors would be to find the prime factors and then to construct the list of divisors from that. In doing this, you'd only have to search as far as the square root. But that's an unnecessary complication to the entry, so I'm not going to mention it.

Yeah, thought you wouldn't. Just being pedantic. To show that we care.

If the .pdf format is not allowed, the less technical (=less scary) http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Perfect_numbers.html might be useful. However, it would be nice to know the answer in respect of .pdf format for links in Guide entries, AND where this is recorded, for reference (e.g. what other formats are disallowed).

Nice one Gnomon!

And thanks to Recumbentman for the link

Nice entry, Gnomon.

Question: Did the Greeks have zero? I know that a lot of cultures did not consider the concept of zero until relatively recently. It might be worth mentioning whether they did or didn't when you talk about how they count.

Cheers!

Hi Gordon!

The Greeks knew about zero although they didn't consider it to be a number. They also were unsure as to whether 1 was a proper number or not. After all, when you say "there's a number of people at the door", you don't expect the answer to be 1 or 0, do you?

But I don't think it is worth putting in a note about zero in the entry. The entry is not about zero, and it's not really about the Greeks either.

I like this entry

On the pdf front I have had EG entries this year with pdf links. If the only worthwhile source on the net is pdf I'd say link to it. After all it is acceptable to provide references to articles not on the net at all - those odd things called books

A glance toward 'amicable' numbers, where the sum of factors of one equal the other, and vice versa would be an interesting sidenote. You could provide a reference of Chapter 12, Mathematical Magic Show, by Martin Gardner (published by Penguin 1985)

That reference also provides other interesting facts, such as that all perfect numbers are also triangular, can be easily written in binary (due to their close links to powers of 2), always end with a 6 or 8 (in base 10), the sum of the reciprocals of the factors (including the perfect number itself) will always equal 2.

Pimms

Has anyone found a crowd yet? (group of three numbers whose factors add up to the next in the group)

If you wish to add the fact about triangular numbers there is an entry about them: A649875 Triangular Numbers

You could also consider adding links to these (but I don't think they add much to the topic in question):
A405352 Integers and Natural Numbers
A385689 A History of Numbers

I can't find any disproof of existence of crowds or example of a crowd on the net, but that might just be me

Pimms

All those facts you quote apply only to even perfect numbers.

The fact that even perfect numbers are of the form M(M+1)/2 makes them automatically triangular, because that is the formula for triangular numbers, a fact which most of us encounter in our years in secondary school, and then promptly forget.

I'll think about putting some of that in to the entry.

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.

If you'd like to know what happens now, check out the page on 'What Happens after your Entry has been Recommended?' at EditedGuide-Process. We hope this explains everything.

Thanks for contributing to the Edited Guide!

Congratulations Gnomon!


F/b

Well done Gnomon

Congratulations.

What happens now. Does this thread continue, e.g. to address the remarks by Pimms, and how is it then altered?