Sunday, October 08, 2017

[wbmowbjw] Print your own log tables

Ceate a device to print out log tables, inspired by Babbage's Difference Engine.  Obviously, a modern computer and printer.  There exist many fine details.

How much precision in input?  Printed tables of logarithms are already unwieldy (compared to calculators and computers) so go for the max and make it many volumes, maybe 90.  This will be very expensive.  How much precision in output?  The logarithm function changes rapidly near 1.0 but slowly near 9.9 so perhaps more gradations in input around 1.0 and more precision in output around 9.9.  We need that precision to invert (exponentiate).  Sampling along arc length seems like the right thing to do, but not so convenient for actual use of the table, typically doing interpolation.  Around 9.9 perhaps express output as 1-output.

All this assumes base 10.  Maybe binary, octal, or hexadecimal is better.  Perhaps invent new robust compact notation for those bases.   Previously, base 100.

Many many fine printing and bookmaking details of exactly how to format the tables to make it quick to find a desired entry.  A fancy dictionary has a thumb index.

What functions other than log?  Sine and cosine seem appropriate as the continuation of exponentiation into the complex plane.  Tangent and arc tangent?

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