5. Fra Luca Paccioli

The platonic solids and the Golden Proportion underwent a revival during the Renaissance as shown in the painting by J. De Barbari, of Fra Luca Paccioli. This painting illustrates 5 different facets of the Golden Proportion.

A copy of a painting of Fra Luca Paccioli, studying The Platonic Solids and Euclid's work, has been used as the front cover of Robert Lawlor's book "Sacred Geometry - Philosophy and Practice", which contains two excellent chapters on the Golden Proportion. This painting has also been included in an article on dental aesthetics written by the author in the USA journal of Prosthetic Dentistry Sep 1978 and Dental Aesthetics Indepentent Dentistry. London The Golden Proportion Jan 1997.

Leonardo da Vinci, together with his mentor, Fra Luca Paccioli, one of the leading scientists and mathematicians of the Renaissance, were both fascinated with the Golden Proportion and together wrote a dissertation on the golden Proportion. The dissertation was printed in 1509 under the title of the Divine Proportion", reprinted in Milan in 1896, (Gardner Pelican 1961), the frontispiece of which is shown below.

The Divine Proportion frontispiece illustrated by Leonardo da Vinci   Leonardo da Vinci's famous study of the square and the circle

Amongst Da Vinci's abundant studies is his famous squaring of the circle. So fascinating that variation have become the logo of a number of organisations, each with slight modifications. It shows the figure of a man contained within a square as well as within a circle. Its connection with the Golden Proportion is that the centre of the circle is in the umbilical navel which divides the body into a larger part and a smaller upper part, the two parts in the Golden Proportion' as in the above copy of the study.