Hi MathsisFun;
I don't know of an overall definition, I don't think there is one.

MathsisFun wrote:

But I would prefer this: (x+1)(x+2)
To this: x^2 + 2x + 2

I would prefer the factored form also. It gives more info and uses less operations.

This: 2x + 2/(x-3)
Or this: (2x^2 - 6x + 2)/(x-3)

This one really looks like the first is simpler.

Is this: 1/√2
Better than this: √2/2 (rationalized denominator) ... ?

Like the √2/2 better and it's a bit more numerically stable.

Last edited by bobbym (2009-08-13 23:00:26)

hmm it's kinda hard to define...
Every form is useful for some purpose... and I guess that would be my definition: The simplest form is the form which is most useful for a specific purpose, so the notion is relative.

For example, you could argue that

is more simplified than

, but it would be easier to integrate the second rather than the first.

And take for example

If you wanted the asymptotes you would go for

but if you wanted to integrate you would go for

Even with

, while most people would say that

is the most simplified form, that's only because it's easier to evaluate. If we aren't worried about evaluating, but simply math theory, then there's there's no reason why we couldn't say

is more simplified.

Hi MathsisFun;

Same problem as simpler. How do you define easier to use? Less operations, less terms, shorter in length, smaller numbers? The best simplification depends on what you are trying to do.

Look at this:

or

Now, supposing you wanted to evaluate them numerically so you would know how much something costs.
The first one certainly is shorter and simpler but the second one which is a truncated Taylor series of e^x allows you to calculate values like e^(1/2) in your head. While the first one is useless for computation. Which is better 3.14159265... or the symbol π? Depends on what you require. I think you can only suggest some general guidelines.

Last edited by bobbym (2009-08-17 12:22:17)

Hi MathsisFun;

Looked at the page, looks good to me. Maybe somebody else has an opinion about it.