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

Entry: Euclid Father of Geometry - A761294
Author: dwight - U193722

Howdy... this is the intro for A745760 - Equality and Similarity Euclid's Elements...

for an online Elements, try: http://aleph0.clarku.edu/~djoyce/java/elements/elements.html(uses java)

You're right that no-one has proved Euclid's 5th axiom. The existence of non-Euclidean geometry shows that the 5th axiom cannot be proved from the other four: non-Euclidean geometries satisfy the first 4, but not the 5th. A proof of the 5th axiom would amount to a contradiction in those non-Euclidean geometries, and although nobody has proved that there cannot be a contradiction in those geometries, they *have* proved that if there is one, then there is also a contradiction back in the usual Euclidean geometry (the non-Euclidean geometries are relatively consistent - they are consistent if and only if Euclidean geometry is consistent).

This looks promising, dwight. It might benefit from a short introduction to Euclid the man, to put him into context, ie when did he live (and maybe what he built on). Was he before or after Pythagoras? I assume after, but it would be nice to show him in his lineage.

There is a reason that postulate 5 (also know as the parallels postulate) has never been proved.

it is because it is an assumption.

It is true for ordinary planar euclidean geometry.

spherical geometry includes ordinary euclidean geometry as a special case.

the other one (there are only three, as together they cover the entire range of possibilities) includes spherical geometry as a special case, and approximates to the structure of spacetime (at least topographically speaking).

I hope that helps.

I think this entry needs to be broken up into sections with headings. For example, Euclid the Man, Postulates, Constructions, etc. You'd be surprised how much clearer the article is both to the reader and to the author once you put in headings.

If you can do GuideML, then you can make your headings stand out by using the tags. If not, don't worry, just put the headings on a separate line with a blank line before and after them.

I think the start bit needs to be rearranged. We need to be told that Euclid wrote the Elements before we're given the quote. The quote doesn't define Euclid, it just provides his place with respect to other philosophers. First tell us that he wrote the Elements. Then say something like "Euclid did not invent or discover everything in the elements himself. Rather, he built on a solid foundation of mathematics provided by ...". Then put the quote.

I wouldn't include the quote translated from Proclus. It's not as though you are reviewing the work that you are quoting from. If you want to include that information, put it into your own words. That's if you need it at all.

Hey Dwight, are you still working on this? Are you back in Annapolis for the fall? (If so, and if you meet a freshman from Dallas named Claire, tell her Tony says hi. That'll surprise her.)

If you're still interested in working on this entry, drop a post in here to let us know. It's a really good start, and it'd be great to see it in the Edited Guide!


GTB, SF '99

Hey, I'm back... I haven't met Claire, but If I see her I'll tell her you said hi...