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A mathematical function that is the inverse of the tangent function.

‘We can put this in words as ‘The final arctan is just 1 more than the product of the other two (whose denominators differ by one).’’

‘In the 14th century, Madhava, isolated in South India, developed a power series for the arc tangent function, apparently without the use of calculus, allowing the calculation of pi to any number of decimal places.’

‘When we find an arctan of a reciprocal of an even-indexed Fibonacci number, we can use to replace it by a sum of two terms, one an odd-indexed Fibonacci number and another even-indexed Fibonacci number.’

‘Using a bit more trigonometry, we can determine the angle between two subsequent samples by multiplying one by the complex conjugate of the other and then taking the arc tangent of the product.’

‘To see how this description of the series fits with Gregory's series for arctan see the biography of Madhava.’