I need a formula for segmenting a circle

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On Mon, 27 Jun 2005 21:17:05 -0000, snipped-for-privacy@host122.r-bonomi.com (Robert Bonomi) wrote:
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What do you mean by the "dimension of a circle"? A circle of radius 1[arbitrary] unit is called the "unit circle". Dropping it here would give the distance of a hord in the unit circle. Then you could use similarity for the one in question ...a fancier way of saying multiply by 36. I think I got it right this time. :-)
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On Mon, 27 Jun 2005 19:08:49 -0400, Guess who

...or even a chord.
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wrote:

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.
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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.
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On Mon, 27 Jun 2005 13:32:38 GMT, "Leon"

That became apparent a little later in the thread. I was going to throw the chord length in there, but I don't have a scientific calculator handy, and I was too lazy to dig around on the net for the value of sin(18)!
Of course, others nailed it, so there is no point in my posting it as well.
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The question required a bit of thought. I was going with the 11.3" until I saw the other answers being lower and ended up solving the problem with a drawing on AutoCAD.
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wrote:

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.
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You might want to reread the question. The diameter is 36" not 72".
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Scales linearly. Divide by 2, get the same result as many others. Hasn't this been beaten to death yet?
Steve
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On Mon, 27 Jun 2005 13:55:42 GMT, "Leon"
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.
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LOL. I thought you may have done what I have been known to do and read the 3' diameter as the radius.
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On Sun, 26 Jun 2005 18:17:56 -0700, the opaque Burt

Buy Charlie Self's new book and figure it out yourself. ;) Woodworker's Pocket Reference : Everything a Woodworker Needs to Know at a Glance ($10 + s/h at Amazon.com)
From a chart in Lee Valley's copy of Handyman In-Your-Pocket, the chord is 0.3090170 times the diameter of the circle, or 11.124612".
On a lighter note, read this:
Teaching Math -------------
Teaching Math in 1950: A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit?
Teaching Math in 1960: A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit?
Teaching Math in 1970: A logger exchanges a set "L" of lumber for a set "M" of money. the cardinality of set "M" is 100. Each element is worth one dollar. Make 100 dots representing the elements of the set "M". The set "C", the cost of production contains 20 fewer points than set "M." Represent the set "C" as a subset of set "M" and answer the following question: What is the cardinality of the set "P" for profits?
Teaching Math in 1980: A logger sells a truckload of lumber for $100. Her cost of production is $80 and her profit is $20. Your assignment: Underline the number 20.
Teaching Math in 1990: By cutting down beautiful forest trees, the logger makes $20. that do you think of this way of making a living? Topic for class participation after answering the question: How did the forest birds and squirrels feel as the logger cut down the trees? There are no wrong answers.
Teaching Math in 1996: By laying off 40% of its loggers, a company improves its stock price from $80 to $100. How much capital gain per share does the CEO make by exercising his stock options at $80? Assume capital gains are no longer taxed, because this encourages investment.
Teaching Math in 1997: A company outsources all of its loggers. The firm saves on benefits, and when demand for its product is down, the logging work force can easily be cut back. The average logger employed by the company earned $50,000, had three weeks vacation, a nice retirement plan and medical insurance. The contracted logger charges $50 an hour. Was outsourcing a good move?
Teaching Math in 1998: A laid-off logger with four kids at home and a ridiculous alimony from his first failed marriage comes into the logging-company corporate offices and goes postal, mowing down 16 executives and a couple of secretaries, and gets lucky when he nails a politician on the premises collecting his kickback. Was outsourcing the loggers a good move for the company?
Teaching Math in 1999: A laid-off logger serving time in Folsom for blowing away several people is being trained as a COBOL programmer in order to work on Y2K projects. What is the probability that the automatic cell doors will open on their own as of 00:01, 01/01/2000?
- DANCING: The vertical frustration of a horizontal desire. --------------------------------------------------------- http://diversify.com Full Service Web Programming
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LOL. Too much truth
Steve
spake:

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