I need a formula for segmenting a circle

[Larry Jaques]

On Sun, 26 Jun 2005 18:17:56 -0700, the opaque Burt spake:

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

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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.

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Full Service Web Programming

[Steve Peterson]

LOL. Too much truth

Steve

[Leon]

LOL. I thought you may have done what I have been known to do and read the

3' diameter as the radius.

[Leon]

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.

[Guess who]

Don't worry about it. Aside from a stupid error reading the original post, I usually do math like you can breathe, but put a dollar sign in front, and my eyes glaze over.

If you want to *understand* trig, you should first study ratio and proportion and then similarity, triangles being the simplest example. Then move into trig ratios, involving sides and angles of a special triangle, the right triangle.

[PDQ]

Keep an eye on alt.binaries.pictures.woodworking your quick formula will = show up there as soon as I have it written.

--=20 PDQ

| wrote: |=20 | >Burt wrote: | >>=20 | >> 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.:) | >>=20 | >> I'm math clueless. | >

| >perimeter =3D pi * diameter =3D 3.1415926 * 3 =3D 9.42478 ft | >

| >Or, just measure around and divide by 10... |=20 | Thanks. I can't measure around because it ain't made yet. | 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?

[Robert Bonomi]

The dimension of a circle is *always* "1", when the unit of measure is a "radius", and thus it drops out of the formula.

[Guess who]

|

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. :-)

[CW]

Can't help that. 11.1246 is the correct number.

[CW]

[Prometheus]

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.

[Prometheus]

Whew, just the whole degrees! I'm not doing global surveys or anything... Actually, after posting this, I found one online and posted it into an excel spreadsheet. It's just a quick reference to hang on the bandsaw at work, while I help a guy learn trig. (He's pretty sharp, but never took it in school) We just double check the prints to make sure the first piece in a run doesn't end up as scrap. Sometimes the engineers mess up the short length on a print with angled sides- kinda hard to do with AutoCAD, I'd think, but some of them manage to do it anyhow.

I'll keep an eye out for it! I had a lot of math in HS and college, but it's been a while now, and it's all getting a little fuzzy. A reference tool probably wouldn't hurt...

[Prometheus]

least. :)

[Prometheus]

Hmm... yeah. But then what happens when you don't have a calculator handy? People like to walk off with the $2 ones as it is! Nobody wants to steal a trig table, though if they do, you can print another off for almost nothing.

That, and dependancy on calculators seems to interfere with people fully understanding the math. If it's important to do a thousand calculations very quickly, then it's important to have automated help. But I'm talking about one or two problems a day- so the time savings is trivial.

[Leon]

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.

[CW]

Not.

[Guess who]

...or even a chord.

[Robatoy]

Can't use a calculator unless you understand the math.

[Prometheus]

You don't think so? I've got a calculator from 1996 laying around somewhere that can solve just about any calculus problem by typing in solve( and then the problem. Same for algebra, trig, or any other branch of math you care to name. I don't imagine that they've gotten less powerful over time.

But that's the extreme case- I know a lot of people who can't do long division, and don't care to know how because they have a calculator. But then when they don't have a calculator handy, they're lost. That would indicate to me that they don't understand the math, they just know how to operate a calculator.

[Ace]

Wish I had one of those back when..... However, it occurs to me that the real challenge is stating the "problem" in the correct mathematical form.

Just a thought, Ace