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A monthly survey of math news
This month's topics:
"Can mathematicians learn from the narrative approaches of the writers who popularize and dramatize their work?" This is the sub-heading on a news feature piece by Sarah Tomlin in the August 4 2005 Nature. Tomlin is reporting on a conference held this summer on Mykonos, where a "select group of about 30 mathematicians, playwrights, historians, philosophers, novelists and artists" met to "find a common ground between story-telling and mathematics." The meeting was the brainchild of the poet and novelist Apostolos Doxiadis (Uncle Petros and the Goldbach Conjecture), who has formed a foundation (Thales & Friends) dedicated, according to its website, to "bridging the chasm between mathematics and human culture." Among the participants looking for that common ground from the mathematical side of the chasm, Tomlin quotes Timothy Gowers ("Most mathematics papers are incomprehensible to most mathematicians"), Perci Diaconis ("I can only work on problems if there is a story that is real for me") and Barry Mazur ("I don't think I personally understood the problem until I expressed it in narrative terms"). "Mazur," she tells us, "did not find a solution by using the narrative device of a cliff-hanger, but it helped him to frame the question - and that, he argues, may be as important." Mazur also is reported as suggesting "that similar narrative devices may be especially helpful to young mathematicians, who seem particularly poor at explaining their work to others." Tomlin also gives us a sobering quote from Diaconis: "To communicate we have to lie. If not, we're deadly boring."World's largest nano-deltahedron
The structure of [Pd2@Ge18]4-, after Goicoechea and Sevov. The Pd-Pd distance is about 3Å.
Deltahedron is chemists' name for a polyhedron with all faces triangular. These shapes occur as ions in cluster chemistry. Until recently, the largest one known had twelve lead atoms forming an icosahedral cage enclosing a platinum atom. Earlier this year, Jose Goicoechea and Slavi Sevov (Notre Dame) reported in the Journal of the American Chemical Society that they had assembled a deltahedral cage of eighteen germanium atoms around a palladium dimer. The structure is shown schematically on the left: two Pd-centered 9-atom Ge-clusters (blue) are joined with the interpolation of four (green) non-equilateral faces. The palladium dimer is shown in red, with the two palladium atoms approximately at the foci of the ellipsoidal cage. Goicoechea and Sevov report that the new cluster stays intact in solution. Their work was picked up under the Editor's Choice rubric in the May 20 2005 Science.
Self-assembled spherules produced by differential cooling of a silicon oxide shell enclosing a metallic silver core. The diameter of the shell is approximately 10 microns. Image courtesy Zexian Cao.
"Triangular and Fibonacci Number Patterns Driven by Stress on Core/Shell Microstructures" is the title of a report in the August 5 2005 Science. The authors, Chaorong Li, Xiaona Zhang and Zexian Cao (Chinese Academy of Sciences) used a physical process to produce a self-assembled regular pattern of spherules on a convex body about 10 microns in diameter. The ingenious process involved coating a droplet of molten silver with a silicon oxide shell, and then cooling the resulting object. The two materials have vastly different thermal expansion coefficients (off by a factor of more than 50); if the cooling is carefully controlled, the stress on the shell manifests itself in the formation of a very regular pattern of surface spherules. As the authors remark, they have raised the possibility of "designing an entire family of patterns through stress engineering." [It must be remarked that the appearance of Fibonacci-type spirals is quite spurious. An icosahedron bears five vertex-spirals and three face-spirals, in either direction, but these have nothing to do with Fibonacci numbers, and even less with phyllotaxis. -TP]