pi/(pi - (1/2)) approx = 2^(1/4)

[Greg Rosser]

hello,
can anyone help me to locate this approximation in the history of mathematics:

pi/ (pi - (1/2)) approx = 2^(1/4)

where can I find the first mention of this approximation?

 

[Greg Rosser]

Area circle = pi
Area square = 1/2

circle / (circle - square) = approximately 2^(1/4)

 

[JeffM]

Are you sure that anyone used this to approximate the fourth root of 2?

Why?

 

[JoeyW]

I've never personally seen this approximation before. Perhaps there's a geometrical explanation for it (maybe not). If it's any consolation, you can arbitrarily approximate [math]\frac{\pi}{\pi - \frac{1}{2}}[/math] using any base greater than one. For example, [math]3^{\small \frac{15778803}{10^8}}[/math], which can easily be found by taking [math]\log_3 \bigg( \frac{\pi}{\pi - \frac{1}{2}} \bigg)[/math].

 

[HallsofIvy]

Where did you see this?