I need a formula for segmenting a circle

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Not.
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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.

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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
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On Wed, 29 Jun 2005 05:02:39 -0500, Prometheus

Perhaps they aid in some, but calculators don't "solve the calculus problems" I've seen. That's just it; they are an aid, not "the answer." Solution of problems in calculus involves a pretty thorough knowledge of calculus and all that precedes it, and most of that is done with the calculator we're born with.

That's what I mean.
All said and done, the calculator is a tremendous asset *after* an understanding of basic principles of the subject it is supposed to assist. Same with woodworking [thought I'd throw that in.] The tools don't make the master woodworker, but good tools sure help. Lots of people have much better tools than some superb craftsmen stuck with less, but all they do is build stepstools. The calculator [ or CAD program or whatever] is good in the right hands and next to useless in the wrong ones, and really not all that necessary, as you pointed out.
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Not true at all. You can have any device you want, that will give you any answer you want, but it will just sit there and act stupid if you don't know what to ask it. Even then, you have to now if it is giving you the right answer. Take the segmented circle problem under discussion. There is no way that any calculator is going to figure that out for you. You have to know what you are wanting to do, lay it out and devise a formula (whether it is a standard one or one you devised yourself). Only then, fed the correct formula, is that calculator of any use and all it is then doing is replacing the trig tables that yo feel are better. When ariving at and asnswer, before commiting time and wood to that number, you will want to turn that formula around, work it backwards and see if it is still correct. Many mistakes can be found this way. The calculator is a dumb slave to the human brain commanding it. If you don't know what you are doing, that device will do nothing.
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Prometheus (in snipped-for-privacy@4ax.com) said:
| 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.
Hmm. I studied math through an advanced course in partial differential equations - and, when it comes to solving even simple trig problems, I'm one of those who're lost without a calculator.
I suppose I could do a little (lot of?) review and calculate my own trig function values:
sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...
[ Anyone who did this in their head for sin(18 degrees = pi/10 radians) to solve Burt's problem can pat themselves on the back and disregard the remainder of this post. All of those who evaluated /pi/ with a series approximation have a surplus of brain cells and a serious need to "get a life".]
Ah. Glad I'm not alone :-)
It's a Good Thing, IMO, to understand the math - but I don't think it's bad to not understand the math. Mathematics *and* calculators are both tools.
Burt has a formula and, presumably, a calculator - and can grind out whatever chord lengths he wants. He doesn't /need/ to understand the mathematics. It wouldn't hurt if he did, but all the understanding in the world won't produce any better results.
-- Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto/solar.html
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Nobody needs to understand math. Well, that's just...
Hm... Hum... What to say?
I fart in your general direction. Your mother was a hamster and your father smelled of elderberries.
I despise your comment as quoted above, and the attitude that allowed it to be verbalized/typalized.
It's, simply, despicable. IMO.
No more to say on this topic, except "SOHCAHTOA".
--
~ Stay Calm... Be Brave... Wait for the Signs ~
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Dave Balderstone (in 290620052217077499%dave@N_O_T_T_H_I_S.balderstone.ca) said:
| || Burt has a formula and, presumably, a calculator - and can grind || out whatever chord lengths he wants. He doesn't /need/ to || understand the mathematics. It wouldn't hurt if he did, but all || the understanding in the world won't produce any better results. | | Nobody needs to understand math. Well, that's just...
...not what I said at all. :-)
Not all people can be all things; and everyone has different aptitudes and talents to develop. It took me a long time to internalize that not everyone needed to become a programmer in order to use a computer to good advantage. The same applies to mathematics.
| Hm... Hum... What to say? | | I fart in your general direction. Your mother was a hamster and your | father smelled of elderberries.
Well, ok - but the smell hasn't reached Iowa yet. In case you hadn't noticed, the prevailing wind is from the southwest this time of year - I would caution you against over-exerting yourself. :-D
My mother would have smiled and assured you that she did her best to be a proper /Scottish/ hamster. From what I've been told, I think my father would have grinned and said that he'd been told worse. (I wish he'd had a chance to become elder-than-26.)
| I despise your comment as quoted above, and the attitude that | allowed it to be verbalized/typalized. | | It's, simply, despicable. IMO. | | No more to say on this topic, except "SOHCAHTOA".
I had to go to Google for that one. Neat. I wish you'd told me about that a half century ago, when I was struggling to keep all of those straight in my head.
-- Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto/solar.html
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wrote:

You didn't have that? Ah, that's just criminal. When one of the other guys at work found out that I was helping one of our co-workers learn trig, he screwed up his face a bit, thought about it for a minute, and then came up with "Do you mean SOHCAHTOA?" It was hilarious. Useful acronym, though.
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wrote:

The struggle was worth it. Those who memorise the "trick" never really understand the main ideas. You are a lot better off having learned to look for the sides and angles and ratios in each working problem. You might not realise it, but you gained a lot more insight, never mind the struggle.
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*snort* who needs a series approximation?? I've had the numerical value of pi, out to _20_ decimal places, memorized for more than 35 years.
I have, however, *rarely* needed more than 6-place accuracy for same.
Now, the numerical value for 'cornbread', THAT's a different matter. <grin>
Note; I also used to have a handful of common log values memorized. And a dozen or so trig values. With that, and a 'half-angle' formula, you can do faily impressive pencil-and-paper 'approximtions'.
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Robert Bonomi (in snipped-for-privacy@corp.supernews.com) said:
| *snort* who needs a series approximation?? I've had the numerical | value of pi, out to _20_ decimal places, memorized for more than 35 | years. | | I have, however, *rarely* needed more than 6-place accuracy for | same. | | Now, the numerical value for 'cornbread', THAT's a different | matter. <grin> | | Note; I also used to have a handful of common log values memorized. | And a dozen or so trig values. With that, and a 'half-angle' | formula, you can do faily impressive pencil-and-paper | 'approximtions'.
Lucky you! I've never been able to memorize stuff like that; but somehow managed to remember basic formulas like the series approximations. I can remember thinking early on that the actual numbers weren't as important as the relationships that produced them. Now I see 'em as two ends of the same stick that different people feel comfortable grasping in different places.
Heh heh. Just remembered the physics prof who got repeated cases of the heebeegeebies because I started nearly all problem solutions with "F = ma" and derived whatever I needed from that. It was my first real clue that we're not all wired alike.
Pencil and paper works - but (IMO) there are better tools like slide rule, calculator, and computer to make calculations faster and easier.
A side note: a couple of years ago I wrote a tiny/fast sine/cosine subroutine that divided a quadrant (quarter circle) into 256 parts and used a table of 256 16-bit numerators and a common denominator of 65535. The subroutine folded all angles into the first quadrant and interpolated to produce sine and cosine values accurate to +/- 0.0000005; it made me wish I could memorize the table.
Cornbread is good. I have the formula around here somewhere...
:-)
-- Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto/solar.html
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wrote:

See, somehow I knew you saw it my way- even if you don't agree with the calculator bit, you just proved you're math nerd. Reminds me of my TI-OS program for simulating synthetic division. Worked great, but everyone who saw it thought I was nuts.

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It is said that you only need to know two things to be an engineer; 1) F = ma 2) you can't push on a rope.
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wrote:

Okay, I fold. I still like the trig table in the context I needed it for though. Let me fill it in a little, so I'm not completely nuts to you all. We're working these problems on the motor cover of a huge vertical CNC bandsaw amid tons of coolant and steel swarf. The employer provides regular four-function calculators- not scientific versions. A calculator only lasts a couple of weeks, on average. A trig table lasts for 6 months or better once it's laminated (if the fraction-decimal charts are anything to go by), and it allows us to solve the problems in question without having to buy a much more expensive calculator every couple of weeks because some dummy knocked it into the coolant or the keys got jammed up by tiny steel chips.
The guy I'm teaching appreciated it as well- even though he is aware that calculators that will evaluate sin/cos/tan values exist, he's got 4 kids at home that (evidently) like to break things, so he doesn't have one of them.
Same logic applies to calipers- Sure, it's easier to use a dial or digital caliper when measuring, but I still use a vernier. It's not because it's inherantly better, it's just better for the environment I'm using it in, and lasts a heck of a lot longer!

I suppose there's an argument for just dropping in here again and asking if the application changes, but to me it's one of those Give a man a fish V. Teach a man to fish senarios. And, if the equation is not being used properly because of some difference in the problem, it can lead to some pretty large errors pretty quickly because he didn't know how to double-check it. As another poster noted, you can have any machine you want, but it won't do anything if you don't know what to put in it.
I see your point, though.
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On Thu, 30 Jun 2005 06:16:50 -0500, Prometheus

That argument is always good. If you use a vernier constantly, you'll be just as good with that as someone with an electronic instrument. That doesn't mean everyone should dash out and buy an abacus.
OK, if people promise not to throw things ...I used to teach math, and at years end would show others how to use their calculator effectively, or how to use a spreadsheet or suitable program, or make up one for them if they felt the need but didn't know how. I used a slide-rule myself. Why? I could use all of the above and more, but had used the slide-rule so often that it was second nature; much easier for me in the long run, if not for the others.
Moral: Use whatever works! Just build the bloody thing. It's woodworking, not brain surgery.
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Can't use a calculator unless you understand the math.
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*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*
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Robert Bonomi (in snipped-for-privacy@corp.supernews.com) said:
| *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 http://www.iedu.com/DeSoto/solar.html
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The dimension of a circle is *always* "1", when the unit of measure is a "radius", and thus it drops out of the formula. <*GRIN*>
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