Greg Egan's Home Page
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|Information, illustrations, and Java applets that supplement some of the works of the science fiction author. The Applets Gallery includes groups of rotations in three dimensions and in four dimensions; Escher, inspired by the artist's conflicting orientation cues; Cantor, a 2-dimensional Cantor set; Laplace, solutions of Laplace's equation in three dimensions, sampled on the surface of a sphere; Schwarz, two successive Schwarz-Christoffel transformations of the complex plane; Gummelt, a quasiperiodic tiling of the plane with overlapping decagons; QuantumWell, a wave function in either a square well or a harmonic oscillator potential; LiquidMoon, a reflection of a moon in water; SoapBubbles, interference effects in soap films; deBruijn, tilings chosen from a plane in n-dimensional space and projecting selected points from a hypercubic lattice onto the plane; Prisms, white light refracted by a ring of rotating prisms; Lissajous, the locus of a point driven by sums of harmonic waves; KaleidoHedron, symmetries of an icosahedron used to replicate a pattern across the surface of a sphere; Syntheme, ways of partitioning the 12 vertices of an icosahedron into 3 sets of 4, so that each set forms the corners of a rectangle in the Golden Ratio; Dirac, a demonstration of the topological "Dirac belt trick"; Spin, the matrices of complex numbers that represent rotations in quantum mechanics; Platonic, a rotating, translucent Platonic solid (tetrahedron, cube, octahedron, dodecahedron or icosahedron), with the faces rendered opaque where they lie inside a second, independently rotating Platonic solid; Solid, two independently rotating copies of the same Platonic solid; Wythoff, uniform polyhedra, using Wythoff's kaleidoscopic construction to compute the locations of the vertices; Slice, 3-dimensional slices through the regular 4-dimensional polytopes, as they rotate; and kaleidoscope. Other applets illustrate Egan's science fiction stories: Diaspora; Oceanic; The Planck Drive; Schild's Ladder; Teranesia; and Border Guards, which features quantum soccer. Foundations is a series of articles, first published in the magazine Eidolon, on some of the theories of twentieth-century physics that have most influenced modern science fiction, such as special relativity, general relativity, black holes, and quantum mechanics. Also, over a dozen complete science fiction stories.|
|Levels:||High School (9-12), College, Research|
|Resource Types:||Graphics, Articles, Recreations, Web Interactive/Java|
|Math Topics:||Modern Algebra, Dynamical Systems, Polyhedra, Symmetry/Tessellations|
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