In our professional practice, we are often called to perform rapid, approximate calculations without a calculator. Any available scrap of paper such as an envelope will do to scribble on. These calculations are more than guesses but less than accurate mathematical proofs. Such scribblings can become the stuff of legend. How many times have we heard stories about successful and influential startup companies being born on the backs of napkins in the pub?
One consummate performer of such approximate calculations was the physicist Enrico Fermi, who famously estimated the TNT energy release equivalent of the first atomic bomb test in the New Mexico desert in July 1945 by dropping scraps of paper and measuring how far they moved as the shock wave passed by. Fermi had a quick approximation formula and the movement of the paper was its parameter. While his estimate had to be corroborated by more rigorous methods, the use of these so-called "back-of-the-envelope" calculations can often lead to startlingly useful results.
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