Mercury's Three Halos

In which Venus' orbit is determined from Mercury's by just three circles

In this simple construction, a circle is drawn which represents Mercury's mean solar orbit. Three equal circles are drawn from the first circle with radii such that they touch each other like three coins. The circumcircle (containing circle) around these three touching circles then represents Venus's mean heliocentric (sun-centred) orbit with an astonishing 99.9% accuracy. This is an easy solution to remember and can be practised in restaurants or at home; it can also be discovered drawn up in the tracery of many church windows. It is important to remember that Venus and Mercury swapped positions in the order of things as a result of the shift to the heliocentric cosmos.