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

Entry: Euclid - A13456082
Author: Gnomon - [ 3 stars - off to Budapest and Greece next week ] - U151503

A short entry on the great Greek mathematician.

I'm still reading a very 'brief' entry on Greek history, so this will have to wait

I'll give it a fuller read later this week...

who wrote 'Elements',
Euclid produced a huge work called 'Elements'
Much of Elements
Euclid's Elements is
(and so on)
-->
Elements

editors often tried to "correct" it
-->
editors often tried to 'correct' it

We call the geometry that he outlines "Euclidean Geometry"
-->
We call the geometry that he outlines 'Euclidean Geometry'

he proves that if you pick two points on a circle and join them with a line, then every point on that line is inside the circle
-->
join them with a straight line

It's obvious, innit?
-->
It is startlingly clear, wouldn't you say, old chap?

But assuming them to be false leads
But there is a great skill
But he doesn't know how
But there we come to the first
- my English teacher said never to start a sentence 'But'.

Alex

But Jimster did in his Muffin the Mule entry A17528321

But only once

It's OK to start a sentence with 'but'. But not too often.

I've tidied it up in line with people's comments. I left in one "But" at the start of a sentence.

The only change I didn't make was to the sentence "It's obvious, innit?" Can you e0xplain the reason for rewording this?

I think it was a joke.

Maybe this entry should be called "Euclid's Elements", considering there's very little in it about Euclid the man?

Hmmm. Possibly. What do other people think about a name change?

I was going to suggest the same thing, Gnomon.

I have some comments and suggestions, but I need to get them together when I get a few minutes...

I've changed the Entry title to:

Euclid's Elements

Excellent! Go to the top of the class . . . oh, you were there already.

This is rather severely compressed:

>Assuming them to be false, however, leads to an alternate equally valid description of the world, known as non-Euclidean geometry, which makes strange non-intuitive predictions for large distances.

I think "alternative" is a better choice than "alternate" here. "Equally valid" is dodgy, perhaps? Would "but also valid" be more prudent? Alternatively you could simply omit "equally valid" and continue "system, known as non-Euclidean geometry, which makes counterintuitive predictions that are valid nonetheless, for instance on non-plane surfaces or over very large distances"?

Your last sentence is a little too dismissive of recent advances: should you say we haven't advanced "much", rather than "at all"?

Good point!

Hi Gnomon

I'm glad you changed the title. Having read a lot of SWL's entries, I was on the point of suggesting "Here's Looking at Euclid", but then I sobered up.

I think the entry is really succinct, but if you wanted anything else, then here are a few interesting facts - use or discard as you think fit:

OUP A Dictionary of Scientists says "Some idea of the importance that has been attached to the Elements is gained from the fact that there have probably been more commentaries written on it than on the Bible."

"One of the most celebrated number theoretic results is Euclid's proof that there are an infinite number of primes."

Euclid wrote other things beside the Elements, but much of it has been lost. We have "Data", "Optics", "Phaenomena" (spherical geometry in astronomy) and an Arabic translation of "On Divisions [of Figures]". He's also (disputedly) written two treatises on music, "Section of the Canon" and "Harmonic".

Some refer to Elements as "Stoicheia".

One of his sayings has come down to us. When asked by Ptolemy I Soter, the reigning king of Egypt, if there was any quicker way to master geometry than by studying the Elements Euclid replied “There is no royal road to geometry.”

Euclid seems to have been the source of the words put at the end of mathematical proofs, in Greek, hper edei deixai, ‘which was to be proved’, but usually known in the Latin version, q(uod) e(rat) d(emonstrandum).

Why not list his axioms? It wouldn't take a lot of space:
1.a straight line may be drawn from any point to any other point,
2.a straight line segment can be extended indefinitely at either end,
3.a circle may be described with any centre and any radius,
4.all right angles are equal,
5.if a straight line (the transversal) meets two other straight lines so that the sum of the two interior angles on one side of the transversal is less than two right angles, then the straight lines, extended indefinitely if necessary, will meet on that side of the transversal.

And his 5 'common notions':
1.Things which are equal to the same thing are also equal to one another.
2.If equals are added to equals, the sums are also equal.
3.If equals are subtracted from equals, the remainders are also equal.
4.Things that coincide with one another are equal to one another.
5.The whole is greater than the part.


Hope this helps!

Icy

Yes, I might list the axioms and common notions. I've already listed the axioms in the entry on non-Euclidean geometry (Curved Space and the Fate of the Universe) but there'd be no harm listing them here too.

I thought Common notions were called Primitive, but that's beside the point. Actually I believe you use "postulate" where it should be "theorem". Postulate is something like axiom (I don't know if there is a difference actually).

My terminology is correct. Common notions and postulates are correct. Of course, they're only translations from the Greek, but they are good ones.

I am not yet convinced. According to Chambers, a postulate can be:

"1. a stipulation or prerequisite. 2 a position assumed as self-evident."

So it is not something which you prove based upon other postulates, and the terminology may be confusing here. That is to say, I was confused

I guess that "postulate" is the traditional English translation used for Euclid's Elements then? It might be worth stating that the meaning of the word has shifted. (Assuming it has shifted indeed - maybe I'm being trapped by the French meaning of "Postulat".)

"Here's Looking at Euclid"

Priceless!