I need a formula for segmenting a circle

[bw]

I get 11.3 inches.

[Morris Dovey]

| I can't remember the formula for the life of me.

Me too. I've stashed a number of "cheat sheets" on the web so I can look up what I can't remember.

Now all I have to do is remember that they're at

Dovey DeSoto Solar DeSoto, Iowa USA

[Robert Bonomi]

*sigh*

The length of a side of an "n-ogon" inscribed in a circle is: 2*sin(180/n)

If you consider the angle out from the center of the circle, to the ends of the section (which is called the 'chord') it's easily remembered as: "twice the sine of half the angle".

How to confuse people -- note that you scale the above by the radius of the circle. *BUT* there is that little '2x' factor sitting in front of things. 2x the radius is the diameter. so you can use diameter*sin(angle/2) and seriously confuse the spectators.

*GRIN*

[Prometheus]

Pi (3.14) x diameter will give you the circumference. Divide that by ten, and it's the number you need.

In your example, 3.14 x 36" = 113.04" This is the total length of the outside edge. If you divide that into ten equal segments, each outside edge will be 11.3" inches long. That is the length of the curve.

[Prometheus]

at work trig, and that will come in very handy. Any chance anyone has a link to a printable version of the old-style sine/cosine/tangent tables? We don't have those umm... "fancy" calculators in the shop :)

[Prometheus]

Nah, you're making it too complex. The difference in the two answers given is that one is the length from point to point on the circle (Morris's answer, approx 11.125"), useful if the OP is making ten segments with straight edges, and the other is the length of the curve (approx 11.3"), useful if the segments need tobe curved to fit the rim exactly. We don't need to know how deep the dish is to figure it out.

[Leon]

11.3 is 1/10th of the circumference of the circle, not the width of that segment.

[Guess who]

You've received a lot of replies to sort through. Personally, if i had your apparent background in math, I'd go for using a CAD program [recommend DeltaCad as good and very intuitive]. However, it never hurts to know how and why: Here's one more:

The general formula for the chord length, or side of the polygon, is C = D*sin(180/N) [angle in degrees] where D is the diameter, and N is the number of sides.

For N = 10, D = 72", you have C = 72*sin(18)

On the calculator use the following order of keypress:

18 sin x 72 =

Ans: 22.249...

Now subtract 22

- 22 =

Now change the decimal to 16ths

x 16 = Ans: 3.98...

That is, about 4-16ths, or 1/4"

So .... 22 1/4", near as dammit is to swearing.

[Leon]

He does not want the circumference of the circle or the length of arc of that segment. He wants the total width of that segment which is less than the length of the arc.

[Morris Dovey]

| Any chance | anyone has a link to a printable version of the old-style | sine/cosine/tangent tables?

That could represent a /lot/ of bandwidth and either server processing time or file space if you want full tables at degree, minute, and seconds. Would you settle for an application that creates the file on your machine? If so, how much precision do you want?

You might consider hunting down a copy of Richard S. Burington's _Handbook_of_Mathematical_Tables_and_Formulas_ (McGraw-Hill). I think you can still find copies for less than US$10 on-line. It's one of my most-used shop tools.

-- Morris Dovey DeSoto Solar DeSoto, Iowa USA

[Leon]

You might want to reread the question. The diameter is 36" not 72".

[Burt]

Thanks for the responses guys. The circles are all less than my example of 36", the biggest is just over 35 3/4 on the inside. Some are as small as 12"

I will try some of the formulas and see if I can figure out which one is easy to use. I also need to calculate on 6, 8 and 12 segments.

[Morris Dovey]

| *sigh* | | The length of a side of an "n-ogon" inscribed in a circle is: | 2*sin(180/n)

I /almost/ hate to do this to you, but the length of a side of an "n-gon" inscribed in a circle of radius r is: 2*r*sin(180/n)

| *GRIN*

:-)

-- Morris Dovey DeSoto Solar DeSoto, Iowa USA

[Leon]

I can confirm with AutoCAD your findings on the different setups if you like or can send you a PDF file with drawings using your sizes.

[Steve Peterson]

Scales linearly. Divide by 2, get the same result as many others. Hasn't this been beaten to death yet?

Steve

[Guess who]

ut 4-16ths, or 1/4"

Sigh. Thanks. I was half awake, I guess, so half right. I had started to use 36" then decided that was the radius. To the OP: Just put 36 in place of 72 and use the same method.

[Guess who]

This might be of some help:

[Burt]

Thanks I'll keep that in mind if I can't figure this out. Like pumpkins the sizes will always change. I would like to be able to do segments that are not equal as well. If I can't figure out the formulas I will fire up a cad program and see if it helps. It's the math terminology that drives me crazy. Beyond the terms radius and circumference I'm clueless. I'm sure somewhere there was a term posted for the straight line distance between two points on the edge of a circle but I'm still unsure what that term is. I haven't had time to digest all the posts yet.

[Burt]

The problem for me is the terminology of math. Financial formulas I can use but I have no clue what the trig terms mean.:)

[Swingman]

A "chord", as opposed to the curved part, which is generally called the "arc".

An old Artilleryman will tell you that one mil of angle will subtend an "arc" of 1 meter at 1000 meters .. but, as in your case, it is really the "chord" that is the distance on the ground you're after when adjusting artillery fire. With the roughly 50 meter effective zone of a HE 105mm round, the difference between the "chord" and the "arc: is moot ... but you need a bit more precision than that.

... I mean, ya gotta put this stuff in perspective with those things of which you are intimately familiar. :)