Napier's Logarithms — Build a Paper Slide Rule and Multiply by Sliding

In 1614 John Napier published logarithms, which turn hard multiplication into easy addition. The slide rule mechanised the trick and did the world's calculating for 300 years. You will build one from paper.

Cut two identical strips of card. On each, mark 1 at the left and 10 at the right, but space the numbers so that 2 sits about 30% along, 3 about 48%, 5 about 70% -- these positions are the logarithms. (Mark 1,2,3,...,10 at the log positions; a printed log scale helps.) These uneven marks are the secret.

To multiply, say, 2 by 3: slide the 1 of the top strip to sit above the 2 on the bottom strip. Now look above the 3 on the top strip -- it points at 6 on the bottom. You just multiplied by ADDING two lengths. Try 2 by 4, or 3 by 3. Sliding adds the log-distances, and adding logs multiplies the numbers.

What your slide rule teaches. (1) A logarithm answers 'what power of 10 gives this number?', and the one law log(a times b) equals log(a) plus log(b) is why sliding (adding lengths) multiplies. (2) Equal MULTIPLES sit at equal DISTANCES on a log scale -- that is why the marks bunch up toward 10. (3) From Kepler's orbits to the Apollo programme, science ran on log tables and slide rules until electronic calculators retired them in the 1970s. (4) Logarithms never left: they measure sound in decibels, acidity in pH, earthquakes on the Richter scale and information in bits.