Decimal Periods and their Tables: A German Research Topic (1765-1801)

At the beginning of the 18th century, several mathematicians noted regularities in the decimal expansions of common fractions. Rules of thumb were set up, but it was only from 1760 onwards that the first attempts to try to establish a coherent theory of periodic decimal fractions appeared. J.H. Lambert was the first to devote two essays to the topic, but his colleagues at the Berlin Academy, J. III Bernoulli and J.L. Lagrange, also spent time on the problem. Apart from the theoretical side of the question, the applications (factoring, irrationality proofs and computational advantages) as well as the tabulation of decimal periods aroused considerable interest, especially among Lambert’s correspondents, C.F. Hindenburg and I. Wolfram. Finally in 1797-1801 the young C.F. Gauss, informed of these developments, based the whole theory on firm number-theoretic foundations, thereby solving most of the open problems left by the mathematicians before him.