June 29, 2009
THE MATH PROBLEM LEONARDO COULDN’T SOLVE
The artist Uffenbach’ss extremely rare tract on squaring the circle
UFFENBACH, Philipp. De Quadratura circuli mechanici. Das ist: Ein newer Kurtzer, hochnützlicher und leichter mechanischer Tractat und bericht von der Quadratur dess Circkels, etc. in Verlegung dess Authoris: Franckfurt, 1619. 19th cebtury marbled boards. VERY RARE. No copies in 30 years of the ABPC auction records.
Philipp Uffenbach (1566–1636) was a German painter and etcher. He was born in Frankfort-on-the-Main, and trained under Hans Grimmer. One of his pupils was Adam Elsheimer.
This very rare tract attacks the great Renaissance problem of squaring the circle. Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. In 1882, the task was proven to be impossible, as a consequence of a theorem which proves that pi (π) is a transcendental number.
That an artist and engraver like Uffenbach would be interested in this mathematical problem is not unusual and is in keeping with a tradition of other great artists attacking this important philosophical conundrum. Dürer in his treatise, Unterweisung der Messung mit dem Zirkel und Richtscheit, the first mathematics book published in German, provides approximate methods to square the circle using ruler and compass constructions. Also, Klaus Schröer (Das Geheimnes der Proportionsstudie, Waxmann Publisher, Germany, 1998) recognized that Leonardo, in his Vitruvian Man, is actually attempting to square the circle and establish the rational proportional relationship that was a favorite obsession of Renaissance mathematicians for use in painting and architecture (hence the name Vitruvian). It must have been frustrating for Leonardo not to solve a problem whose solution would have crowned him as the greatest mathematician of the Renaissance. Well, at least it was a problem that actually had no solution.
