Mathematics poll

[ciphergoth]

Inspired by a similar poll in palmer1984's journal.

About the "proof" question below: examples of the kind of proof I mean would be a proof that there are infinitely many primes, or that the square root of two is irrational, or of Pythagoras's Theorem. A proof in computer science counts too. By "know a proof off by heart" I mean that you'd be able to convince someone of it at a party, if they had the background to follow the proof.

If you know lots of proofs, feel free to choose one you particularly like in the last question...

[Poll #1351621]

Comments

[alextiefling.livejournal.com]

How would you prove Pythagoras' Theorem? Isn't it really a metric axiom rather than a genuine theorem?

[wildeabandon.livejournal.com]

You can start with Euclid's axioms and from there derive Pythagorus' Theorum - I think that counts as a proof.

[fizzyboot.livejournal.com]

Fuck Euclid. The best way to do geometry (and geometrical proofs) is cartesian coordinates.

[ciphergoth.livejournal.com]

Depends on whether you use R² or Euclid's axioms to define the plane I guess. The proof I have in mind is the variant on proof #4 here, for example.

[skx.livejournal.com]

Cute page - the one I knew is listed as #3.

[adjectivegail]

I just read proofs 1 and 2 and found them interesting, right up until the author said "obviously the resulting shape..." Because, no, it's not obvious, some of us actually have to sit and think a while before we realise that it's the case. And this is My Huge Button about maths, which has grown ever-larger through the years as people have said "but it's obvious that..." about a million different things, none of which have been obvious.

It puts me right off, as evidenced by my immediately clicking away from the page and going to do something more fun instead.

[ciphergoth.livejournal.com]

Try Proof 9, which is almost entirely visual.

The thing that makes the proof work is that in both cases, the side of the big square is the long and short sides of the triangle put together. The four triangles are just moved from one place to another between the two, so they cover the same area. That means the area remaining - blue in one case, red in the other - is the same. The blue area is exactly the square on the hypotenuse, and the red area is the sum of the squares on the other two sides.

Is that any clearer?