Maths Problem [Resolved]

[taxes]

Hi,

I wonder if anyone can help with the following.

I have to calculate the graduations on a dipstick used to measure the amount of liquid remaining in a tank with an oval section. This appears to be a problem of Integration (maths meaning).

What I have to do is to calculate the area of that part of an ellipse between a line parrellel to the horizontal axis and the circumference.

I don't suppose there are any predefined VB.NET functions. Any ideas??

[taxes]

Help!! (Please)


I have been given the Integration formula but I do not know how to implement Integration! Any one know if I could find enlightenment on the Internet?

[tom_hotspur]

Hi

Is it requirement that you must use vb to solve this problem?

If not i would advise you to use a high level language maths package such as mathematica or maple.

Using VB means not just solving the problem but implementing any mechanisms to do so, this is possible but sounds a little like a University Dissertation project or something (i.e too much work)

not the answer you were hoping for i suspect...

[nswan]

What's the formula?

[taxes]

HI,

"Is it requirement that you must use vb to solve this problem?"

No, but once I understand what the formula requires, re-iteration should be a breeze in VB.


"What's the formula?"

I have difficulty in posting the formula, which is not a formula as we are used to in programming. It is a re-iteration of an infinite calculation until a negligible result is achieved.

The following shows how the formula is derived (if it means anything to anyone!!)


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let's say your ellipse has it's centre on the origin, and goes through the points

x=0,y=b; x=0,y=-b; x=a,y=0; x=-a,y=0

i.e. it has width 2a and height 2b. now the equation of the ellipse is given by

(x/a)^2 + (y/b)^2 = 1

i can prove this from something else if you want, but usually it is taken as the defenition of an ellipse.

now you want to find the area between the line y=k and the ellipse, k<b. to do this rearrange the equation:

x=a@(1 - (y/b)^2 ) ("@" should be a square root sign which I do not have on my keyboard)

and concentrate on y and x both greater than 0. now the area between the "top" of the ellipse and the line y=k is given by

y=b y=k a@(1 - (y/b)^2 ) dy. ("y=b" & "y=k" are interlined and preceded by a squiggle which looks like a vertically extended "S")

you should be able to do this integral with a simple substitution - let y = bsinq ("q" is the greek letter Theta which stands for an angle)

-----------------------------------------------------------------------------------

Any help would be greatly appreciated!!!

[nswan]

i'm afraid that's a bit beyond me. it's been a few years since I did A-level maths!

Try the maths forum:
http://www.vbforums.com/forumdisplay.php?s=&forumid=20

[taxes]

Hi,


I could handle A level maths, but this is way beyond that. It is more like a Degree Thesis!!

I did not realise there was a Maths Forum here
I have taken up your suggestion, Many thanks.