Thread: Diameter Of A Circle

Originally Posted by RayG

Depends how you draw it I guess, I took it as the spacing between hole centers was 36mm measured along the arc.

Well no wonder you got the "wrong" answer

Time for some shed time I think.

Stuart

Originally Posted by Stustoys

Well no wonder you got the "wrong" answer

Hehe..

26th may and 0746am cst...and your still arguing about which way (if any) is the right way to come up with the correct answer

Originally Posted by eskimo

26th may and 0746am cst...and your still arguing about which way (if any) is the right way to come up with the correct answer

Very true, it looks like you'll have to help us out after all..

Ray

Originally Posted by Stustoys

Originally Posted by ian
and is the easiest to set out !
how does that come into it? once your picked your answer the set out is the same.

yes you're right, both method one and method two are equally easy to set out

Originally Posted by Stustoys

Originally Posted by ian
although when the hole diameter is small and n gets very large there's no real difference between RayG's solution 1 and 2.

There's a very simple explanation why that is so, would anyone care to say why?

Sooner or later you end up with an "almost" straight line and(I think) all the while Rays solutions move closer to the U and S solution?

Method 1 (polygon touching the outside of the circle) and method 2 (polygon touching the inside of the circle) is how people work out the value of pi to great precision -- the true value of pi lies between the perimeter of both polygons


but back to the OP

I need to know the diameter of a circle that needs to be divided into 18mm sections, I attach a rough diagram to help illustrate what I am saying.
If someone can help me out and save me going mad from trying to figure it out I would be most appreciative.

I read this to mean that the 18mm holes are separated by 18mm virtual holes or spaces, so out of the entire thread I posit that there are only two solutions that meet OP's request

Solution 1 — the circle is divided into an even number of 18mm chords and an 18mm hole is placed at the every second vertex (is that the correct name for the point where two chords meet?) The holes can be set out with compass and a pair of dividers.

Solution 2 — the circle is divided into an even number of 18mm arcs and a hole slightly less than 18mm in diameter is placed at every second arc intersect -- which results in the same outcome as Solution 1, but the holes are less than 18mm.


and Eskimo
because it's fun

Originally Posted by ian

although when the hole diameter is small and n gets very large there's no real difference between RayG's solution 1 and 2.
There's a very simple explanation why that is so, would anyone care to say why?

The answer I was thinking of, is to look at the two equations.

Solution 1. D = h/sin(pi/2n)

Solution 2. D = h/tan(pi/2n)

When the angle is small, sin(x) = x Also when the angle is small tan(x) = x

So the angle between segments is pi/2n, will get smaller as n gets larger, and sin(pi/2n) gets closer in value to tan(pi/2n)

Eventually all the solutions converge on the D = 2nh/pi which is the where you just measure along the arc.

Ray

Originally Posted by ian

because it's fun

not for the rest of us...we have NFI what your supposedly having fun with..if we knew we might be crapping on also.

But it is sad to see that a consensus as to which is correct method to arrive at correct answer has not been reached....how am i gunna work it out if you lot cant get it right...I wont be able to trust you

Originally Posted by eskimo

But it is sad to see that a consensus as to which is correct method to arrive at correct answer has not been reached....

Hey its not our fault. Each of the answers are correct(or at least pretty close)......in the end it just depends on what question you think the OP is asking.
Of course I like my method better as (I think) it matches the drawing best(though really "bigger than XXX" isn't much of an answer lol). But it doesn't match his written question.

Stuart

Originally Posted by Stustoys

Hey its not our fault. Each of the answers are correct(or at least pretty close)......in the end it just depends on what question you think the OP is asking.
Of course I like my method better as (I think) it matches the drawing best(though really "bigger than XXX" isn't much of an answer lol). But it doesn't match his written question.

Stuart

I am still at a loss as to how one can have 4 different answers but yet they are all correct at the same time..oh yeah I forgot...roughenuff is goodenuff
I just hope the others are taking note should they wish to ever contemplate to get some precision machining carried out by you....is pretty close going to be good enough?

but ...you had a try at solving it..more than what I can do

Originally Posted by eskimo

I am still at a loss as to how one can have 4 different answers but yet they are all correct at the same time..

Don't stress about it, lots of problems have more than one correct answer... Skinning cats.

Ray

Originally Posted by RayG

Don't stress about it,

no no no I am not stressed...I am supposed to be having fun...so I have been told ...dont know how when or where but