Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Lemmas

Just a really quick question. I understand what lemmas are, but I am trying to explain them in a fairly simple way to people in their last year of pre-university maths education - so they have a good knowledge of basic mathematical principles and methods, but probably haven't considered mathematical reasoning in much depth. My question is would it be correct to think of some of the trig identities, such as something as simple as:

In a proof of a trigonometry relation, as a lemma. I know lemmas are usually thought of as being perhaps a little more difficult and a little more interesting - but unless I've woefully misunderstood, this certainly serves the purpose of a lemma, since it is a relation which has already been proven and is used as a 'stepping stone' to a more complicated relation.

Thanks

P.S. If this is not suitable, I wonder if anybody could suggest an alternative. I was thinking of using Bézout's identity:

Now Bézout's lemma states that such coefficients exist for every pair of nonzero integers (a,b), with in addition d > 0. It's just that something like a trig identity suggested itself to me as something really easy that A-level mathematicians have used before and would therefore see how lemmas work and what they are.

Last edited by Au101 (2011-04-17 11:16:07)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Lemmas

Hi;

That trig identity looks like it could be called a lemma, though I have never seen it called that. It is the fundamental trig identity from which all trig identities are derived.

You are right about Bezouts.

Here is a list of a bunch more:

http://en.wikipedia.org/wiki/List_of_lemmas

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Lemmas

Ooooh, that's good, thanks for the further examples .

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Lemmas

There are some nice ones there. Most I never heard of.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.