Separated from my activities with the Regional Institute, I am also looking into issues involving enzyme kinetics. When the number of enzyme molecules and substrate molecules was high, mass action equations were an adequate mathematical model of the dynamics of the enzyme reactions. As biochemistry is learning more about enzymatic reaction in which the number of molecules is smaller, the stochastic or random effects are playing a more important role. Here we will be writing programs that find the importance of these effects and looking into the experimental data for verification. But all numbers, rational and irrational numbers, have unique continued fraction expansions.
Some irrational numbers have continued fractions that consist of a repeating pattern of numbers .
The problem concentrates on the continued fraction expansions of numbers of the form where n is an integer. These numbers have repeating continued fraction expansions. Some of these expansions can be expressed by a formula that can easily be verified. The interesting formulae are those where the number of terms in the repeating pattern grows larger as the number under the square root grows larger. These formulae are harder to pick out and more difficult to verify.