(no subject)

[chess]

Gah, evil maths.

I have:
L=2r*sin(l/2r) (that's a small L, not a 1)
h=r(1-cos(l/2r)) (before the cos is a 1, after is a small L)
I know L and l, and I want h in terms of these.

*mutters about nasty Engineering projects and people who are meant to be helping who don't have email at home*

Comments

[sath.livejournal.com]

umm you're trying to end up without an r in it?

[chess]

yup. I've kinda given up now, tho - no-one else is doing any work on this stupid project, so I don't see why I should waste my Saturday on it.

[naath.livejournal.com]

Divide one by the other and you'll get rid of the r's at the start...

L/h = 2sin(l/2r)/(1-cos(l/2r)

but I can't see how to get rid of the other r...

[stipe.livejournal.com]

It's been too long since I did any of this stuff, but my guess is that 2sin(x)/(1-cos(x)), or some rearrangement thereof, is an identity and can be simplified.

Re:

[naath.livejournal.com]

possibly... I can't remember anything of that form though.

[passage.livejournal.com]

sin(x)=2sin(x/2)cos(x/2)
1-cos(x)=2sin^2(x/2)
=> 2sin(x)/(1-cos(x))=2cot(x/2)

I don't think this helps however ...

Neil

[passage.livejournal.com]

Where did this crop up?

If it was a reuslt of normal A level stuff then I suspect you've made an error in deriving these formula.

These forumula do have exact answers in the sense that "exact solutions exist" but you can't write down those answers in closed form.

The way these problems are dealt with is iteration which can achieve an arbitary degree of accuracy: adaquete for most real life purposes.

The way you'd start an interation would be to first derive the statement:
L^2+4h^2=8rh
Sub that back into the h= ... expression and then use something like the Newton Raphston (sp?) method. However, this kind of stuff was only covered at the end of my further A level so I suspect you don't know what I'm talking about at this stage.

If you want me to explain how I derived that forumla or more about iteration then just email me or ask me on a talker and I'll try and explain.

Neil

[chess]

It's for the Engineering project.

I found the answer (well, the iterative formula) online, plugged that in, and it seemed to work fine.