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From: Jon on 8 Aug 2010 07:00
The angle subtending arc A and chord B on a circle is,

angle = 4arccos( {B/A}^(100/131) ) 2/pi <= B/A <= 1

This is an approximation good for 2-3 decimal places.

Development:

http://jons-math.bravehost.com/arc.html




From: William Elliot on 9 Aug 2010 04:03
On Sun, 8 Aug 2010, Jon wrote:

> The angle subtending arc A and chord B on a circle is,
>
> angle = 4arccos( {B/A}^(100/131) ) 2/pi <= B/A <= 1
>
What's the radius?

> This is an approximation good for 2-3 decimal places.
>
radius r; angle in radians a
arc length s = ra
cord length c = 2r.sin a/2

Given s and c, find a?

c/s = 2(sin a/2)/a

> Development:
>
Numerical approximation?

From: achille on 9 Aug 2010 04:50
On Aug 8, 7:00 pm, "Jon" <jon8...(a)peoplepc.com> wrote:
> The angle subtending arc A and chord B on a circle is,
>
> angle = 4arccos( {B/A}^(100/131) )    2/pi <= B/A <= 1
>
> This is an approximation good for 2-3 decimal places.
>
> Development:
>
> http://jons-math.bravehost.com/arc.html

By matching the taylor expansion of cos(at) and
(sin(t/2)/(t/2))^b,

angle = 2*sqrt(5)*arccos( {B/A}^(3/5) )

will give a better approximation for angle < 0.85 pi.
For angle < pi/2, this approximation is accurate up
to around 4 decimal places.
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