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

Entry: Constructions with a Ruler and a Compass - A24020506
Author: toy box - U208464

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When you link to Gnomon's entry on Euclid's Elements you'll need to use the Edited version: A23999494.

OK, done

Hi Toybox

Overall, it's a lot 'heavier' than I expected from the title.

It's too long for me to review in one go, but here are a few typos to be getting on with:

kept

I don't think 'it raises the question...' is right here.. How about 'loosely speaking, it involves...'?

...all the mathematics...

..was as follows:

sequel? I don't understand.

...practice

I'll get back to it when I get a minute.

Icy

Well, it is heavier than I had expected too

The sequel, the sequel... I meant the remaining bit of the entry. I changed it into: 'the following two axioms are the more relevant to the construction problems'. I meant that maybe they justify the fact that one wonders about constructions with a ruler and compass.

Ah, and I made the typo modifications too

Good Entry, though parts of it might be a little tricky to understand without an idea of what to expect.

The complete list can be found in this entry.
-->
The complete list can be found in the Entry on Euclid's Elements.

circumcentre, orthocentre - what are these? There are more terms further down that could also do with some explaining.

Mathematicians say that F is a field. - this footnote comes a little late in the sentence.

Alex

The complete list can be found in the Entry on Euclid's Elements.

Done, but I then removed the link. I wasn't extremely satisfied with double-linking to an entry anyway.



Circumcentre, orthocentre - I didn't include a definition for a number of reasons. First, the circumcentre (as well as the centre of gravity) is defined in the Triangle entry - though curiously I didn't see the orthocentre. Giving a proper definition would take us too far (by introducing more definitions which would just make the entry heavier without really gaining anything from them, and which are, I believe, already given in the Triangle entry.)

Second, these are terms which French people would have learned at school, as well as how to construct them actually (I don't know about other countries - it seems dissection is commonplace in British schools, while I've never seen it done in France for instance). However, apart from a few geometry enthousiasts, most people have certainly forgotten about those terms and what they stand for. The idea is that these should still ring a bell, so that the reader might think: 'Oh, these annoying points which I always confused, these were examples of Constructions with ruler and compass! I'll be a monkey's uncle!'.

I'm not sure I am very clear about what was I said above. In any case I would be happy to clarify these points in the entry; I just don't want to introduce too much additional abstract stuff.



Mathematicians say that F is a field. - this footnote comes a little late in the sentence.

I quite like it where it is. At most I would understand if you said it came late, but early? Where would you have thought of placing it?

I have to say that 'field' means a non-empty set enjoying these properties (and some more technicalities, never mind these). Just defining F as we did (with distances and such) doesn't make it a field.



I'll have a look at other terms which might need defining. Of course feel free to point these out to me.

>>>Of course feel free to point these out to me.<<<

No, that's ok. I value my life too highly to do such a thing

That's too late anyway. Just try to avoid the hootoo meets I might attend in the future

No no, I meant it. Sometimes I'm a bit unaware of what might put people off. At least, those few who haven't run away when hearing the words 'mathematics'

Ok then:

construct a square which has the same area as the surface delimited by the circle - delimited?

Perpendicular bisector of a segment - while the footnote helps, there's no mention of what a segment is

a finite amount of pairwise distinct prime Fermat numbers - erm...

You don't want to get me started, toy box

I was able to follow the first part by getting out the ruler and compass and follow it. (I can't visualise these things).
After that, you lost me. What does it mean:
>>It was only until the 19th century that the last two constructions were indeed proven to be impossible.<<

That sounds as if it was proven before the 19th century, but afterwards, there was no proof?

Finite amount of pairwise distinct Fermat primes - that's why it is a footnote. I could make the statement less accurate ('it involves Fermat numbers' or something)

Segment - Maybe there's a better term for it. It is a piece of straight line delimited by 2 points.

The 19th century: I'll clarify the sentence then. It means people had never succeeded in finding a construction and some thought that maybe it was impossible, but never came up with a proof that it was so. In the 19th century, Lindemann and others found a proof.

I'll make the corrections when I have time, sorry about that. Thanks for the comments though!

Oh, and 'delimited' - that's encompassed. I would write 'the same are as the circle', but the circle is just the line so it doesn't have an area. You should speak of the area of a disc, rather than of a circle.

to have lost you in the later part B'elana!

As for updates: it seems that 'delimited' was just a bad translation from the French, I replaced it with 'encompassed'. I explained the 'segment' bit and simplified the Fermat primes story.

I rephrased what happened in the 19th century, hope it is clearer now.

Thanks toy box, that reads much better now.
I hope the mathmaticians will come and review this soon. Did you leave a PR alert in the maths forum?

I think I did. You never know, maybe I left it in the wrong forum

No, I've just checked, you left it in the correct forum all right.
Maybe they're all on their summer holidays?

"Algebra is often used as a powerful machinery to tackle systematically and in an abstract fashion more concrete problems, such as those arising from geometry"

I don't think that sentence will encourage the reader to go on. Either that or the reader will just skip over it. And is it really necessary? If it is, it could do with being simplified.

I'm not sure how others feel about this, but there is some mathematical turns of phrase in there which might put the layman reader off. For example "Let F be the set of constructible numbers". It just *sounds* tricksy, if you get my meaning. It would be better if it was more conversational, like 'Take the set of all constructible numbers, which we will call F', or something.
(I always thought some mathematical notation and phrasing was unnecessarily difficult. I've just finished my Maths A-level and we are supplied with a booklet of common formulae in the exams. But I hardly used it because most of them are written in such a counter-intuitive way I found it easier to learn the same formula in a simpler form. Sorry for rambling...)

On the 'Properties of Constructible Numbers' section:
It all seems to be a bit of a roundabout way of saying things - fine for mathematicians, but I think it should be more direct for h2g2.
"If x and y are in F, then x+y and x-y are in F."
could be 'If the numbers x and y are constructible, then x+y and x-y are constructible.'
It's a little longer, but clearer and more direct, I think.

"The second and third one require a bit of proof"
For those not familiar with mathematics in general or proof specifically this would not be possible.

I am pleased to offer you something that's not to do with mathematics:
'less instruments' should be 'fewer instruments'.

This is a tricky subject to talk about, and ideally it would have a few illustrations. A little bit heavy in places, I thought. Interesting, though . I haven't had a proper mathematical think since my exams, and I cocked those up.

>>I don't think that sentence will encourage the reader to go on. Either that or the reader will just skip over it. And is it really necessary? If it is, it could do with being simplified.<<

I modified a little that paragraph. Is it any better? I'm not sure about the last sentence for instance.



>>I'm not sure how others feel about this, but there is some mathematical turns of phrase in there which might put the layman reader off. For example "Let F be the set of constructible numbers". It just *sounds* tricksy, if you get my meaning. It would be better if it was more conversational, like 'Take the set of all constructible numbers, which we will call F', or something.<<

Well, that's how we mathematicians speak every day. I think you just highlighted one of the reasons why people seem to run away whenever they hear us speak of mathematics

Anyway I fixed it. I completely removed any mention of 'F' anyway (I always strive to avoid notation unless it is very useful, which wasn't the case here).



>>On the 'Properties of Constructible Numbers' section:
It all seems to be a bit of a roundabout way of saying things - fine for mathematicians, but I think it should be more direct for h2g2.
"If x and y are in F, then x+y and x-y are in F."
could be 'If the numbers x and y are constructible, then x+y and x-y are constructible.'
It's a little longer, but clearer and more direct, I think.<<

Changed



>>For those not familiar with mathematics in general or proof specifically this would not be possible.<<

Actually it wasn't meant to be possible. I thought of putting a footnote in the spirit of 'Don't try this at home, kids' ('Left to the reader as an exercise' means a little bit the same in mathematician lingo ), but then I thought that a) it wasn't a dangerous thing to do and b) it is actually a very noble activity to do so. So I replaced it.



>>I am pleased to offer you something that's not to do with mathematics:
'less instruments' should be 'fewer instruments'.<<

Aargh
I should have known, it was in the 'Language bugbears' thread not too long ago! Thanks



>>This is a tricky subject to talk about, and ideally it would have a few illustrations.<<

Yes, but since it is elementary geometry (i.e. the sort you learn at school - this doesn't mean it is easy!) I thought it would be a good idea to include this in the Guide.

Originally I wanted to put more constructions, but I think the interested reader can get them on the 'net; just that one example is enough. Only while I was writing the entry did I think it would be a good opportunity to introduce a bit of algebra, how you get from geometry to algebra, and why it is useful (proving some impossibilities).

Ah, if only I had a black board to draw some constructions