This is an accessiblle investigation recommended for year 8 or 9 learners who are comfortable evaluating expressions involving fractions and brackets when subsituting positive integer values of $n$. See teacher sheet for specific expressions.

It is not recommended for learners who already have knowledge of quadratic sequences or arithmetic series.

Writing and evaluating expressions (whole number values of $n$) involving brackets.

The premise of the investigation is simple: to investigate the number of lines in a mystic rose. A mystic rose is constructed by drawing straight lines connecting every point on the circumference of a circle to every other point.

This investigation does not go into regions which should be studied in year 9 or afterwards. Similarly this investigation only considers points to be equally spaced. The Lines and Regions investigation is therefore an extension of the Mystic Rose investigation to be studied in year 9 or afterwards.