id: 06664742
dt: j
an: 2016f.00932
au: Reed, Cameron
ti: Computing logarithms by hand.
so: Math. Teach. (Reston) 109, No. 8, 633-636 (2016).
py: 2016
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: F50 N50
ut: logarithms; numbers; mathematical concepts; interpolation
ci:
li: http://www.nctm.org/Publications/Mathematics-Teacher/2016/Vol109/Issue8/Computing-Logarithms-by-Hand/
ab: Summary: How can old-fashioned tables of logarithms be computed without
technology? Today, of course, no practicing mathematician, scientist,
or engineer would actually use logarithms to carry out a calculation,
let alone worry about deriving them from scratch. But high school
students may be curious about the process. This article develops a
straightforward technique for computing common logarithms by
establishing a few successive square roots of 10. Because the
logarithms of these values are by definition just the power to which 10
has been taken ($1/2$, $1/4$, $1/8$, etc.), these values can be used to
construct a table of logarithms in which the increment in the logarithm
is $1/2^N$, where $N$ is the number of square roots computed. By
interpolating between these accurately computed points, we can build a
standard log table. This method should help reinforce rules of
logarithms and powers for students. (ERIC)
rv: