All quadratic surds
have continued fractions in which the terms repeat after a certain point, i.
I now wondered if other rational sequences exist which converge to a surd value.
Finally, trial values for the numerator and denominator of the second fraction are entered and systematically altered until the fractions converge to the sought after surd as they have in Figure 1.
Each student could then be given the task of determining a sequence which converges to their own given surd.
It is essentially a lesson in number pattern but includes work with surds
, coordinate geometry and some elementary use of complex numbers.
This is distinct from less everyday aspects of school mathematics, especially as it emerges during secondary school, including algebra, trigonometry and surds.
For example, most people do not ordinarily use algebra, trigonometry, coordinate geometry, surds, or combinatorics (except at an almost trivial level of choosing different combinations of clothes or menu items)--in short, in my view, most of secondary school mathematics.
Thus, these are not surd
quantities, but rather rational numbers.