The Thousand Islands Arts is an association of artists and artisans providing support to its members for tours and shows as well as a link to the community of the Thousand Islands as well as the arts community at large.
The Kingston Arts Council is an umbrella organization devoted to promoting the creation, production, presentation and appreciation of the arts in Kingston and the surrounding region.
Artists in Canada is an on line directory of Canadian artists, art galleries, associations and art resources.
Robert Genn is not only a prolific talented artist but he produces engaging twice weekly letters as well as a forum for discussion at http://www.painterskeys.com.
In my mixed media work I use art cloth painted by fiber artist Kit Vincent to create backgrounds or collages that are laminated to hardboard.
Mathematics and art have been intertwined ever since their beginnings. Both are driven by imagination and both try to explain reality. From early on, artists and architects accepted that the geometry of Plato, Pythagoras and Euclid were describing an underlying harmony of the universe. Judi Loach1 expresses it elegantly, "For the artist, mathematics does not consist of the various branches of mathematics. It is not necessarily a matter of calculation but rather of the presence of a sovereign power; a law of infinite resonance, consonance, organisation." In what follows I try to give a brief, though far from exhaustive, description of how mathematics has influenced art and, vice versa, how art has influenced the development of mathematics with links to further information.
Proportion
Perhaps the most famous of all proportions is the Golden Ratio (or sometimes called the golden section, the divine proportion, the golden mean, etc). It has been used from early Greek architecture to Renaissance art to more recent work of LeCorbusier or Dali. This ratio has deep roots in Mathematics and has been popularized recently in Dan Brown's The Da Vinci Code. Though there is some dispute over this ratio being at the base of some work or even over its aesthetic appeal, it has, along with other geometric constructions, become part of an established toolbox for design and composition. Today artists, such as Alex Colville, use these structures as an armature that provides this harmony in their compositions. Painter Ian Roberts has good instructional material, which covers the importance and use of an armature in a painting.
Perspective
Artists for a long time have pursued techniques to create the impression of three dimensional space on a two dimensional canvas but it wasn't until the Renaissance that Perspective was developed to enhance this capability. Filippo Brunelleschi a sculptor and architect (1377-1446) was the first to recognize the geometry required but humanist Leon Battista Aberti and artist and mathematician Piero della Francesca (1412-1492) were the first to publish mathematical principals behind the geometry of vision. Other artists, like Leonardo Da Vinci and Albrecht Dürer, continued these developments along with mathematicians Luca Pacioli and Guidobaldo del Monte (an excellent description of this history can found at the site School of Mathematical and Computational Sciences University of St Andrews ). In the 17th and 18th century French mathematicians (inspired by Girard Desargues and developed by Gaspard Monge, Jean Victor Poncelet and Michel Chasles) formalized this knowledge into a branch of mathematics called Projective Geometry, which not only reset geometry on a new footing but has been important in the study of algebraic equations in mathematics and quantum field theory in physics. With the advent of the Expressionism and Cubism, which distort reality in favour of emotional content, perspective lost its central role in painting carved out by the Renaissance artists (as Leonardo put it, " without perspective nothing can be done well in the matter of painting"). Artists like William Hogarth and M.C. Escher, inpsired by Penrose's stairs (see his Road to Reality for everything you have ever wanted to know about the mathematics of reality), destroy perspective while appearing to use it. However, if traditional artists have abandoned perspective, all is not lost as computer graphic artists now use the wealth of geometrical construction (commonly called Descriptive Geometry) and computational methods of linear algebra in 3-D computer games and ray tracing, as well as Computer Aided Design (CAD) software used by sculptors and architects such as Frank Gehry to demonstrate complex forms that are difficult, if not impossible, to articulate otherwise.
In 2-D work, patterns in fabric, mosaics or on pottery that include repeating geometric forms go back to ancient times. Though studied by early Greek mathematicians (500 - 400 BC), these patterns, known today as Regular or Semi-Regular Tillings (or Tessellations), were used by artists from the period for their inherent structural and aesthetic beauty. It wasn't until the Renaissance that these patterns were revived for their formal structures by artists like Piero della Francesca and Albrecht Dürer. This regenerated interest by mathematicians whose studies of these patterns contributed to the development of a branch of mathematics called Group Theory and in particular Symmetry Groups, which are important in physics and chemistry. More recently Escher,in close communication with mathematicians(H.S.M. Coxeter, Roger Penrose), has represented tessellations in many of his works. Salvador Dali, likewise influenced by science, introduced mathematical objects in his religious paintings of the 1950's to reflect his view of a modern faith infused with the vision of science. In his Last Supper, whose dimensions form a golden rectangle, Christ appears to be at the centre of a dodecahedron, whose 12 pentagons ostensibly represent the 12 apostles. The crucifix in his Crucifixion (Corpus Hypercubus) is the surface of a 4-D hypercube, unfolded into 3-D (similar to unfolding the surface of a 3-D cube into a flat cross).
In 3-D work in recent years sculptors, some of whom are mathematicians, have been creating complicated mathematical surfaces in various materials, producing beautiful intriguing forms, for example Helaman Ferguson, C. Goodman-Strauss, Charles Perry and George Hart. Dick Termes paints on spheres using 6-point perspective. There are even mathematical fiber artists who knit, weave and quilt topological surfaces.
The American Mathematical Society has an excellent article on mathematics and art and the Bridges Organization, which promotes and organizes conferences on connections between mathematics and art, displays many art works from their juried art exhibitions. There are more links at this site and for those who want to play with models or with games on topological surfaces, Jeff Weeks has extraordinary programs, which are free downloads.
As for everything else, so for a mathematical theory: beauty can be perceived but not explained. Arthur Cayley (1821 - 1895) Quoted in J R Newman, The World of Mathematics (New York 1956)