Simple question about curves

AARRRGH

Hello all

I am rewriting my elliptic curve cryptography thesis in mongo English so anyone can understand it.

I want to explain what a curve is in simple terms. Am I right in thinking the following?

If someone asked you to describe a curve, you would probably say it's a sort of bendy line, like a "c" or "s". This is because we are taught to believe curves are simply bendy lines. However in the world of mathematics it's quite possible to have curves which don't look anything like a bendy line - in fact, many can't be visualised at all. This is because mathematicans define curves by their mathematical properties rather than what they look like.

In other words, a curve doesn't necessarily look like a curve.

Am I right?!

Thanks

RoundTower

well it's correct, but it might leave your readers more confused than they started

LeixlipRed

Just use pictures of several different types of elliptic curves. That description is very bs to be honest.

Fremen

You could say a curve is a set of points which possess a common property, then give some examples
(say, f(x) = 1 if x is rational, 0 otherwise)

Are you writing this for simple.wikipedia.org?

MathsManiac

I agree with Leixlip Red. Since elliptic curves pretty much are just bendy lines, why would you want to undermine a reader's perfectly adequate intuitive understanding of what a curve is?

RoundTower

Fremen wrote: »

You could say a curve is a set of points which possess a common property, then give some examples
(say, f(x) = 1 if x is rational, 0 otherwise)

Are you writing this for simple.wikipedia.org?

hmm maybe someone can explain what a curve is to ME. I definitely didn't think that function was a curve.

seanybiker

mongo english , thats nice. And then ya cant even explain what your trying to do. Hate the word mongo

LeixlipRed

Fremen wrote: »

You could say a curve is a set of points which possess a common property, then give some examples
(say, f(x) = 1 if x is rational, 0 otherwise)

Are you writing this for simple.wikipedia.org?

Is a curve not generally consider to be a continuous set of points? Unless that's a counter example you were giving there? And less use of the word mongo OP. Just noticed that now.

Fremen

I was trying to deal with AAARGH's point that

However in the world of mathematics it's quite possible to have curves which don't look anything like a bendy line - in fact, many can't be visualised at all.

Wikipedia suggests that curves need to be continuous, so I guess I was mistaken. Maybe a path traced out by a point moving through an abstract space would be a better definition, but that's still a bit vague for the casual reader.

AARRRGH

Thanks for the replies everyone.

The elliptic curves used during cryptography don't really look anything like curves, or at least, not curves as the average programmer would visualise them. They are really just a sort of random looking series of points. So I want the reader to accept he is dealing with a lot of points rather than a curvey line...

But maybe it is confusing and I should just leave it as a curve.

seaneybiker wrote:

Hate the word mongo

I like the word. It's funny.

LeixlipRed

It's also slightly racist. Google it there. Last warning AARRRGH

LeixlipRed

Also, Elliptic Curves do look like curves when you consider them over the real numbers. You're just talking about Elliptic Curves over finite fields

AARRRGH

LeixlipRed wrote: »

You're just talking about Elliptic Curves over finite fields

Actually, you're right, thanks.

LeixlipRed wrote: »

It's also slightly racist. Google it there. Last warning AARRRGH

OK, I didn't realise some people would be offended by that word. I never even knew it was racist?! Always assumed it meant, at worst, "retarded".

LeixlipRed

Not a discussion for here. As I said, google it and you'll see the associations it has.