Geometry on the Beach: Circling the Square

18, November 2013 § 1 Comment

Squaring-the-Circle small

by Jane Morris Pack

The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful. The ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics. –G.H. Hardy, A Mathematician’s Apology

Geometry, from the Greek γεωμετρία or “earth measurement,” was used by the Egyptians to reestablish the borders of farmed ground after the Nile had flooded and erased the previous year’s boundary markers.  This marking of the earth developed into a complex system of mathematics which was understood and amplified by the Greeks;  Pythagoras, Euclid and Archimedes are names we associate with geometry. In the Middle Ages mathematicians in medieval Islam contributed most of the further developments until once again the Europeans led the way in the 17th century.

“Squaring the circle” is an attempt to create a square with an area equal to a circle using only a straight edge and a compass.  Ancient geometers worked on this problem and it was only proven impossible in 1882.  Nonetheless the symbolism involved remains potent: that of combining the heavenly circle with the square of earth.  Leonardo explored this image in the famous Vitruvian man drawing which we were privileged to see in Venice this last September.

Steven Kosovac and I gathered with students on a blustery afternoon to draw out our attempt at a related conundrum.  With only pegs and a rope we followed the process from a book and arrived at a large and perfect example of circling the square. The circle we constructed had the same perimeter as a square.


The Rubens Project

12, November 2013 § 4 Comments

rubensdrawingsmallby Jane Morris Pack

This fall, six advanced painting students are working with me to discover Rubens’ painting technique. To delve into Rubens’ style we studied the twisted forms of a knotted rope and a gnarled stick to imitate his brushstroke which often follows a spiraling line. We see it in the manes of his horses and the fabric of capes, in beards and in clouds. It was also important to learn to highlight economically with white as this is the primary way in which Rubens creates dimension. So our first study involved working on toned paper with white conte (above) and looking for expression of the twisted form. We then continued this investigation with paint (below).


Copying a master work is the best way to educate the eye and hand so our next step was to copy a passage of Rubens’ work. An enlarged section is easily obtained by perusing his work on Google Art Project. It is quite clear what the layers are and how they are preserved or covered by subsequent paint. Rubens seems to do so little but each brushstroke is amazingly rich in information. Not only is the color of the object’s surface there but also its texture, tone, temperature, direction of thrust and lighting condition. He accomplishes with one stroke what others would with many.

We are adding chalk to the paint as recent scholarship has detected the presence of it in his work. Chalk adds a textural component to the paint and helps it to dry quickly.

Meanwhile we are composing a large canvas to include five or six figures which will give each student a chance to contribute to the piece.




4, November 2013 § 2 Comments


by Jane Morris Pack

Euphrosyne Doxiades is a painter and an expert on encaustic, the wax based painting method of the Ancient Greeks. She has been asked to contribute her knowledge of the technique to a conference in Athens which is examining the use of paint on marble surfaces, both architectural and sculptural.  She asked my help to recreate a figure which is on a marble disk thought to be from the mid fifth century.  The piece is in the museum in Paros and was found in the cemetery excavation near the sea.  It was the lid of an urn which may have held the ashes of an athlete who had won a competition for discus throwing.

What remains of the paint is vermillion pigment and there were traces of gold on the head and on the discus which are now missing.  We painted vermillion mixed with hot bees wax and mastic directly into the surface of the marble and added gold leaf to the hair and the circle of the discus.  The paint was “burned in” using a hot tool and then scraped and polished to a soft shine.  Euphrosyne had made previous tests which insured that the paint adheres to the surface even out of doors in full sun.

We had a joyful time recreating this beautiful remnant of ancient culture and perhaps it will contribute to the scholarship as well.


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