Circling a square: The geometry of Beinecke MS408 folio 86v and how to construct the scaffold of the Rosette map with compass and straightedge

2015-04-07T19:35:37Z (GMT) by Juergen Wastl

This paper describes two possibilities on how to construct the scaffold of the Beinecke MS408 f86v ‘Rosette map’ (i) in a simple fashion and (ii) in only a few step process with compass and straightedge: A ‘circle’-based process requires four straight lines. Following onto that two circle settings (linked via golden ratio) are sufficient to produce the main scaffold in f86v.
Simple though it is, the geometric design leads to a highly symmetric ‘picture’ with a further pattern worth mentioning: the medieval mind’s love of squaring the circle. Literally, circling the square is easily achieved in this construction. Comparison and overlays with circles and squares in other medieval diagrams and maps suggests that this way of constructing diagrams can be applied to not only the Rosette map, but to other contemporary diagrams and maps, too.
The important question, if the use of the golden ratio (1.618) is deliberate or a coincidence, can’t be unequivocally answered, however the overlays described in this paper indicate the knowledge and the use of the application of golden ratio based geometric construction in the Rosette map in at least two instances:
The diameter of the central disc itself (in comparison to the overall folio’s dimension) and
the ratio of the central disc versus the eight outer circles.
These two processes give rise to the position of the outer circles in relation to the central disc (via the ‘circle’-based construction)