# I need a formula for segmenting a circle

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• posted on June 27, 2005, 1:17 am

I can't remember the formula for the life of me. If a dish is almost 3 ft across and I want to segment it like an orange into 10 segments how do I calculate how wide each will be at the rim? So I end up with a dish that has 10 sides.:)
I'm math clueless.

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• posted on June 27, 2005, 1:20 am
Burt wrote:

perimeter = pi * diameter = 3.1415926 * 3 = 9.42478 ft
Or, just measure around and divide by 10...

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• posted on June 27, 2005, 1:20 am
Burt wrote:

perimeter = pi * diameter = 3.1415926 * 3 = 9.42478 ft
Or, just measure around and divide by 10...

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• posted on June 27, 2005, 1:34 am
wrote:

Thanks. I can't measure around because it ain't made yet.<g> I need to cut ten pieces of steel to form a ten sided form that will fit exactly inside a 3 foot circle. I need the distance between the points as a straight line. so if it section is shaped like a bow I need the length of the string. Does this make any sense?

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• posted on June 27, 2005, 3:11 am
Each segment will be 11.125" wide.

into 10

exactly
straight
string.

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• posted on June 27, 2005, 7:22 am

I get 11.3 inches.

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• posted on June 27, 2005, 1:28 pm

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

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• posted on June 27, 2005, 2:24 pm

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.

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• posted on June 27, 2005, 2:32 pm
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.

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• posted on June 27, 2005, 4:45 pm

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.

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• posted on June 27, 2005, 5:04 pm
"Burt" wrote in message

term
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. :)
--
www.e-woodshop.net
Last update: 5/14/05

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• posted on June 27, 2005, 8:07 pm

And if the gun was on a ship....... LOL. I don't think I will ever forget the length of the equation we used in Physics when determining when to pull the trigger and when will it hit if the seas were rough and the ship was traveling.

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• posted on June 28, 2005, 1:18 am
Can't help that. 11.1246 is the correct number.

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• posted on June 27, 2005, 9:14 pm
Keep an eye on alt.binaries.pictures.woodworking your quick formula will show up there as soon as I have it written.
-- PDQ
| wrote: | | >Burt wrote: | >> | >> I can't remember the formula for the life of me. | >> If a dish is almost 3 ft across and I want to segment it like an orange into 10 | >> segments how do I calculate how wide each will be at the rim? | >> So I end up with a dish that has 10 sides.:) | >> | >> I'm math clueless. | > | >perimeter = pi * diameter = 3.1415926 * 3 = 9.42478 ft | > | >Or, just measure around and divide by 10... | | Thanks. I can't measure around because it ain't made yet.<g> | I need to cut ten pieces of steel to form a ten sided form that will fit exactly | inside a 3 foot circle. I need the distance between the points as a straight | line. so if it section is shaped like a bow I need the length of the string. | Does this make any sense?

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• posted on June 27, 2005, 1:27 am
Try these sites, hope something here helps.
http://www.verifiedsoftware.com/goodturns/plans.htm http://www.delorie.com/wood/segturn.html

into 10

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• posted on June 27, 2005, 1:34 am
Burt (in snipped-for-privacy@4ax.com) said:
| I can't remember the formula for the life of me. | If a dish is almost 3 ft across and I want to segment it like an | orange into 10 segments how do I calculate how wide each will be at | the rim? | So I end up with a dish that has 10 sides.:) | | I'm math clueless.
Burt...
Each of the sides will be 36" * sin(360 degrees / 20) or approximately 11-1/8"
-- Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto/solar.html

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• posted on June 27, 2005, 1:57 am

Too much work and I don't get the same answer anyway. (PI * 36 / 10) PI * 3.6 = 11.3097312 etc. etc. etc. Significantly more than 1/8 inch difference, it's over 11 1/4 inches.
--
I can find no modern furniture that is as well designed and emotionally
satisfying as that made by the Arts and Crafts movement in the early years

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• posted on June 27, 2005, 2:17 am
Ed Clarke (in snipped-for-privacy@individual.net) said:
|| Burt (in snipped-for-privacy@4ax.com) said: || ||| I can't remember the formula for the life of me. ||| If a dish is almost 3 ft across and I want to segment it like an ||| orange into 10 segments how do I calculate how wide each will be ||| at the rim? ||| So I end up with a dish that has 10 sides.:) ||| ||| I'm math clueless. || || Burt... || || Each of the sides will be 36" * sin(360 degrees / 20) or || approximately 11-1/8" | | Too much work and I don't get the same answer anyway. (PI * 36 / | 10) = PI * 3.6 = 11.3097312 etc. etc. etc. Significantly more than | 1/8 inch difference, it's over 11 1/4 inches.
Not too much work if your calculator has trig functions. My Windows calculator came up with 11.124611797498107267682563018581", which misses 11-1/8 by only 0.0004".
Pi * 36 / 10 would be the arc length of the segment, while 36*sin(18) is the chord length. The difference is 0.18512175542514839078295316122472", somewhere near 3/16" - so the extra effort may be worthwhile :-)
-- Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto/solar.html

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• posted on June 27, 2005, 3:45 am

Your answer is to a question that was not asked. Had the OP asked what the length of the exterior of the segment was you would have been correct. However the OP asked how wide the segment would be. The widest part would be the distance between the two closest points of that triangle shaped segment. That distance between those two points is approximately 11.125".

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• posted on June 27, 2005, 2:10 am
said:

If he were building a 10 segment, flat circle you would be right on but he said "dish". I suspect he needs the other sides's dimension as well. More information is necessary to figure it out. How deep is the dish and does it have an elliptical section or is it part of a sphere? What is the dish for exactly? There are myriad possibilities when you say dish so there is no way to give a (complete) correct answer...
Phil Davis 247PalmBeachRE.com