There is an equation as below.
where a, b and c are arbitrary real numbers.
We have found that the above equation displays the envelope of a rectangle in the case that the absolute values of b and c take sufficiently large (over about ten).
If we rewrite Eq.(1), the following equation is led to
where the defined region is given as
In the case of a=1, if we calculate Eq.(2) as varying the several values of and with the use of computer, the each rectangle is drawn as shown in Fig.1 to 8. The each length of longitudinal and horizontal sides of a rectangle is about and respectively.