dividing circle's circumferance with wrt to n llel secants

[muruga86]

how to divide a circle cicumferance with respect to n equidistant parallel secants?

the problem is as follows..........

i have a circle of diameter 138 inches when calulating its circumferance comes to 433 inches. 32 eqidistant lines or secants of which are parallel to each other with 3 inch gap pass through the circle each intercesting the circle at two places on both sides. of the 32 lines 16 lines are on the oneside of the center of circle and the remaining on the another side. the center of the circle is half way between the 16 and 17 lines (i.e 1.5 inch). now my aim is to divide the circumferance of the circle such that it is more or less eqidistant with respect to secants cutting it. i can't do the genearal way of dividing the circumferance of circle by 360 and use because at both end of the parallel lines i.e 1 and 32 lines the arc width is more between the 3 inch gap than at the center i.e 16 and 17 lines.

given attached the image of the question.......
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can any one give me a solution?

thanks in advance

 

[echo47]

Re: dividing circle's circumferance with wrt to n llel secan

my aim is to divide the circumferance of the circle such that it is more or less eqidistant with respect to secants cutting it

That's confusing. Please rephrase. What's stopping you from drawing lines on your circle wherever you need them?

If you happen to have a CAD program such as AutoCAD, it can be very helpful for weird geometry calculations.

 

[kalyanram]

Re: dividing circle's circumferance with wrt to n llel secan

Hi Murugan,
Here is the solution if you need a geometric construction.Join the points formed by the intersections of two adjacent secants. And bisect all such chords. Extend the bisector to the circumference and you will have the result.

If you need a generic algebraic formula. Here is the method.

Firslty draw the diameter parallel to these set of secants. Now the angles I talk of are wrt this line.
Now assume there are 2n line which are equidistant with seperation 'r' between them and 'R' is the radius of the circle. Now you see that the diameter has already bisected the arcs between nth and n+1 secant.

Now in general start drawing lines with angles 0.5*(arcsin[(2n-1)r/2R]+arcsin[(2n-3)r/2R]).

If you need a proof for the above formula please feel free to ask.

Kalyan.

 

[muruga86]

Re: dividing circle's circumferance with wrt to n llel secan

hai kalyan,
thanks for your help, but i can't undersatand what do u say. kindly give more elobrate answer from which i can procedd for solution

murugan