The connection between mathematics and
art goes back thousands of years. Mathematics has been
used in the design of Gothic cathedrals, Rose windows,
oriental rugs, mosaics and tilings. Geometric forms were
fundamental to the cubists and many abstract expressionists,
and award-winning sculptors have used topology as the
basis for their pieces. Dutch artist M.C. Escher represented
infinity, Möbius ands, tessellations, deformations,
reflections, Platonic solids, spirals, symmetry, and
the hyperbolic plane in his works.
Mathematicians and artists continue to
create stunning works in all media and to explore the
visualization of mathematics--origami, computer-generated
landscapes, tesselations, fractals, anamorphic art, and
more.
Last additions - Notices of the American Mathematical Society :: Cover Art
Dyadic icosahedraThis image exhibits fanciful renderings of the dyadic icosahedra discussed in the article "The p-adic Icosahedron," by Gunther Cornelissen and Fumiharu Kato (Notices of the American Mathematical Society, August 2005, p. 720).
--- Bill CasselmanJul 12, 2006
Coxeter groupsThis image illustrates two types of infinite Coxeter groups and algorithms involved in computation within those groups: one which generates elements of the group one by one, the "Shortlex automaton," and others, more conjectural, which seem to describe the Kazhdan-Lusztig cells of an arbitrary Coxeter group.
The illustration is described in detail and was created to accompany the article "Cells in Coxeter Groups," by Paul E. Gunnells (Notices of the American Mathematical Society, May 2006, p. 528). The explicit finite state machines required to draw the Kazhdan-Lusztig cells were supplied by Gunnells.
--- Bill CasselmanJul 12, 2006
Kleinian PearlsPeople have long been fascinated with repeated patterns that display a rich collection of symmetries. The discovery of hyperbolic geometries in the nineteenth century revealed a far greater wealth of patterns, some popularized by Dutch artist M. C. Escher in his Circle Limit series of works.
This cover illustration portrays a pattern which is symmetric under a group generated by two Möbius transformations. These are not distance-preserving, but they do preserve angles between curves and they map circles to circles. The image accompanies "Double Cusp Group," by David J. Wright (Notices of the American Mathematical Society, December 2004, p. 1322).Mar 28, 2006
"Kissing in Motion""Kissing in Motion" shows the motion of the "shadows" of kissing spheres in a deformation pointed out by J.H. Conway and N.J.A. Sloane, following an observation of H.S.M. Coxeter. The sequence is left-right, right-left, left-right (sometimes called boustrophedon). The image accompanies "Kissing Numbers, Sphere Packings, and Some Unexpected Proofs," by Florian Pfender and Günter M. Ziegler (Notices of the American Mathematical Society, September 2004, p. 873).