Geometric problem that's been driving me crazy...

[Dory]

Incredible! This is exactly the same problem. Thanks Tigg!

Well, using (what I thought) Gawdzilla suggested I got 2.82. The answer in your link is 2.76. They used a far more complex method. I'm not sure what they mean by "no elementary solution".

[Tigger]

Incredible! This is exactly the same problem. Thanks Tigg!

Well, using (what I thought) Gawdzilla suggested I got 2.82. The answer in your link is 2.76. They used a far more complex method. I'm not sure what they mean by "no elementary solution".

You can't use basic (or even fairly complex) trig to do it.

[The Curious Squid]

The way they worked it out on that forum is the same method Larry suggested here, the reason your answer is slightly off is because as he mentioned, there's no definitive answer since the method used is an approximation. I think that's what they meant by "no elementary solution".

[Xamonas Chegwé]

Incredible! This is exactly the same problem. Thanks Tigg!

Well, using (what I thought) Gawdzilla suggested I got 2.82. The answer in your link is 2.76. They used a far more complex method. I'm not sure what they mean by "no elementary solution".

You can't use basic (or even fairly complex) trig to do it.

Yep. I was going along the same path. Basically, you need to use some kind of iterative method to get a solution, you can't end up with a simple numeric formula for r.

You need to feed values of r into , and use trial and error to get closer to the exact value.

Nasty problem.

[Dory]

This is math, how come we're talking about trial and error...isn't this supposed to be exact? I see numbers in a formula, it's not as though we're measuring stuff with a ruler here.

[Xamonas Chegwé]

This is math, how come we're talking about trial and error...isn't this supposed to be exact? I see numbers in a formula, it's not as though we're measuring stuff with a ruler here.

You cannot rearrange the formula to give you r as the subject. All you can do is get as close as you can to the answer by educated trial and error.

Maths isn't always exact. Every value of π ever calculated is an approximation!

[Dory]

Should I try to "get as close as I can by educated trial and error" or is it too high a math? Not that I have a problem learning new math... I do that all the time...

[Xamonas Chegwé]

Should I try to "get as close as I can by educated trial and error" or is it too high a math? Not that I have a problem learning new math... I do that all the time...

Iteration IS maths. Some of the iterative methods used to find approximate solutions to a given accuracy are extremely sophisticated.

http://en.wikipedia.org/wiki/Iterative_method

[Dory]

I....see. I'll have to read tonight then thanks, Xas...helped a lot.

[Linus]

By no "elementary solution" I think the guy means that there is no explicit answer of the form

r = [some expression in terms of the most well-known functions like polynomials, exponentials, trigonometric functions, etc.]

Instead, the answer has be expressed in the more implicit form f(r) = 0 for some f. Of course, nothing prevents you from inventing a name for the inverse of f in an interval around 0 and writing r = f^-1(0), but f^-1 wouldn't count as an "elementary" function.

[Seth]

This help? http://www.sosmath.com/CBB/viewtopic.ph ... 26c2487a88

Measure the fucking diameter of the pipe with a tape-measure and be done with it...

[Seth]

This is math, how come we're talking about trial and error...isn't this supposed to be exact? I see numbers in a formula, it's not as though we're measuring stuff with a ruler here.

You cannot rearrange the formula to give you r as the subject. All you can do is get as close as you can to the answer by educated trial and error.

Maths isn't always exact. Every value of π ever calculated is an approximation!

Which is why math sucks and tape-measures rule....

[Xamonas Chegwé]

This is math, how come we're talking about trial and error...isn't this supposed to be exact? I see numbers in a formula, it's not as though we're measuring stuff with a ruler here.

You cannot rearrange the formula to give you r as the subject. All you can do is get as close as you can to the answer by educated trial and error.

Maths isn't always exact. Every value of π ever calculated is an approximation!

Which is why math sucks and tape-measures rule....

Tape measures are maths.

[Seth]

This is math, how come we're talking about trial and error...isn't this supposed to be exact? I see numbers in a formula, it's not as though we're measuring stuff with a ruler here.

You cannot rearrange the formula to give you r as the subject. All you can do is get as close as you can to the answer by educated trial and error.

Maths isn't always exact. Every value of π ever calculated is an approximation!

Which is why math sucks and tape-measures rule....

Tape measures are maths.

Er...tape-MEASURES...RULE...get it?

[JimC]

This is math, how come we're talking about trial and error...isn't this supposed to be exact? I see numbers in a formula, it's not as though we're measuring stuff with a ruler here.

Not all maths will allow for exact solutions, or even an algebraic solution of any sort. Polynomial equations of degree 5 or beyond have (aside from some special cases), no algebraic solution, so approximations via successive iterations are the only reasonable way to go. The same is true for something as simple as:

x + sin (x) = 2