Monday, March 19, 2012

[xzpqsgea] 0.239 degrees

A curious coincidence of digits when calculating trigonometric functions in degrees instead of radians:
0.239 degrees ≈ arctan (1/239) made famous in Machin's formula for pi.  Equality happens at approximately 239.364672.

It leads to a pi approximation of 3.14164, though you can't convert from degrees to radians without knowing the value of pi.

Newton's method: x = x - (tan(x/1000*Pi/180) - 1/x) / (Pi/180/1000/cos(x/1000*Pi/180)^2 + 1/x^2)

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