I Need A Formula for PI Using ArcTangents And Real numbers... Anyone?
2007-03-19 16:42:04 · 7 answers · asked by Amrit S. 2 in Science & Mathematics ➔ Mathematics
pi/4 = 4arctan(1/5) - arctan(1/239)
2007-03-19 16:49:41 · answer #1 · answered by tryzub91 3 · 2⤊ 0⤋
Pi = 4 arctan(1)
Pi = 6arctan(1/sqrt(3))
Pi = 3arctan(sqrt(3))
Pi = 2(arctan(x) + arctan(1/x)) if x >0 (you can plug in anything for x! 100, 147.325, it doesn't matter, as long as it's positive)
2007-03-19 23:49:53 · answer #2 · answered by mitch w 2 · 0⤊ 0⤋
4 arctan 1 = pi
This and many others from
http://www.primepuzzles.net/puzzles/puzz_050.htm
The formula involving arctan can be found by scrolling about 2/3 of the way down the page. There are many good approximation formulas on this page, enjoy!
2007-03-19 23:49:28 · answer #3 · answered by Joni DaNerd 6 · 0⤊ 0⤋
There are LOTS of such formulas. Tryzub91 (answerer 3) should get "Best Answer" because he gave one of the best and most popular, called Machin's formula:
pi/4 = 4 x arctan(1/5) - arctan(1/239)
2007-03-20 08:50:13 · answer #4 · answered by bh8153 7 · 0⤊ 1⤋
ArcTan(1) = Ï/4, because the tangent of 45° is 1. You can take it from there.
2007-03-19 23:50:54 · answer #5 · answered by Scythian1950 7 · 0⤊ 1⤋
tan Ï/4 = 1
arctan tan Ï/4 = arctan 1
Ï/4 = arctan 1
Ï = 4 arctan 1
2007-03-19 23:52:12 · answer #6 · answered by novangelis 7 · 0⤊ 1⤋
I would guess that 2*tan^-1(0) would equal PI, but I could be wrong.
2007-03-19 23:47:50 · answer #7 · answered by Anonymous · 0⤊ 1⤋