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a and b are whole positive integers, which makes the following identity true. What are the values of a and b? Thanks.

Pi/4 =8arctan(1/10) - arctan(a/b)

 Dec 26, 2017

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 #1
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Pi/4 =8arctan(1/10) - arctan(a/b)

0.7853981634...... =0.79734921992... - arctan(a/b)

arctan(a/b) =0.79734921992  -  0.7853981634......

arctan(a/b) =0.0119510565318..........

Using "continued fraction" method:

a = 1,758,718

b=147,153,121

 Dec 26, 2017
 #1
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+1
Best Answer

Pi/4 =8arctan(1/10) - arctan(a/b)

0.7853981634...... =0.79734921992... - arctan(a/b)

arctan(a/b) =0.79734921992  -  0.7853981634......

arctan(a/b) =0.0119510565318..........

Using "continued fraction" method:

a = 1,758,718

b=147,153,121

Guest Dec 26, 2017
 #2
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The Guest made a copying error:

a =1,758,719.

 Dec 26, 2017

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