So 57 years ago, there weren’t any programming books. Well, there was one. McCracken and Dorn, Numerical Methods and Fortran Programming. A kindly childless couple, Ben and Bluma Goldin, who lived in the same apartment house in Brooklyn, bought me this book as a gift.
An axiomatic lesson from the book was distrust of Taylor expansions, and the necessity of moving the expansion point of any function to a favorable location.
Because harmonic functions are very well behaved, it should also be obvious that even a very coarse lookup table + interpolation should converge to high accuracy quickly. Finally, use of trigonometric identities to zero in on the desired angle is helpful. OK I’ll shut up now.
Going on a tangent, as I understand it, the first programming book was "The Preparation of Programs for an Electronic Digital Computer: With special reference to the EDSAC and the Use of a Library of Subroutines", by Maurice Wilkes, David Wheller and Stanley Gill (1951).
They are long dead. It was sad. They doted on me and my sister because they had no kids. He was a salesman. He knew how to get books in Manhattan. He used to get my sister classics with the most beautiful color plate illustrations. In the sixties, these had little value. Today?
