
06664742
j
2016f.00932
Reed, Cameron
Computing logarithms by hand.
Math. Teach. (Reston) 109, No. 8, 633636 (2016).
2016
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
F50
N50
logarithms
numbers
mathematical concepts
interpolation
http://www.nctm.org/Publications/MathematicsTeacher/2016/Vol109/Issue8/ComputingLogarithmsbyHand/
Summary: How can oldfashioned 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)