17. Gregory's Arc Tangent Series

Ratio comparison of two arc tangents.

Using the given inequality, calculation of the mean value of function 1/(1+x²) allows series expansion of arc tan x in powers of x. _________________________ Gregory's Arc Tangent Series [b]Proposition: [/b][i]To determine the angles of a triangle from the sides without the use of tables.[/i] This is problem #17 in Heinrich Dorrie's [i]100 Great Problems of Elementary Mathematics[/i]