Recent Additions to the Junkyard

• Carnival triangles. A factoid about similar triangles inspired by a trigonometric identity.

• Eight foxes. Daily geometry problems.

• Fermat's spiral and the line between Yin and Yang. Taras Banakh, Oleg Verbitsky, and Yaroslav Vorobets argue that the ideal shape of the dividing line in a Yin-Yang symbol is formed, not from two semicircles, but from Fermat's spiral.

• Flat equilateral tori. Can one build a polyhedral torus in which all faces are equilateral triangles and all vertices have six incident edges? Probably not but this physical model comes close.
  

• Greg's favorite math party trick. A nice visual proof of van Aubel's theorem, that equal perpendicular line segments connect the opposite centers of squares exterior to the sides of any quadrilateral. See also Wikipedia, MathWorld, Geometry from the land of the Incas, interactive Java applet.

• Hyperbolic games. Freeware multiplatform software for games such as Sudoku on hyperbolic surfaces, intended as a way for students to gain familiarity with hyperbolic geometry. By Jeff Weeks.

• The HyperSphere, from an Artistic point of View, Rebecca Frankel.

• Hyperbolic shortbread. The Davis math department eats a Poincaré model of a tiling of the hyperbolic plane by 0-60-90 triangles.

• Nested Klein bottles. From the London Science Museum gallery, by way of Boing Boing. Topological glassware by Alan Bennett.
  

• Non periodic tiling of the plane. Including Penrose tiles, Pinhweel tiling, and more. Paul Bourke.

• Platonic solids and Euler's formula. Vishal Lama shows how the formula can be used to show that the familiar five Platonic solids are the only ones possible.

• Rectangular cartograms: the game. Change the shape of rectangles (without changing their area) and group them into larger rectangular and L-shaped units to fit them into a given frame. Bettina Speckmann, TUE. Requires a browser with support for Java SE 6.

• Santa Fe Ribbon, painting by Connie Simon featuring a rhombic Penrose tiling.

• Sierpinski cookies. Actually more like Menger cookies, but whatever.

• Sierpinski gaskets and Menger sponges, Paul Bourke. Including stacks of coke cans, radio antennas, crumpled sponges, and more.

• Sierpinski valentine from XKCD.

• sneJ made a Mandelbrot set with sheet plastic and a laser cutter.

• Voronoi diagrams at the Milwaukee Art Museum. Scott Snibbe's artwork Boundary Functions, as blogged by Quomodumque.

• The Water Cube swimming venue at the 2008 Beijing Olympics uses the Weaire-Phelan foam (a partition of 3d space into equal-volume cells with the minimum known surface area per unit volume) as the basis of its structure.
  

From the Geometry Junkyard, computational and recreational geometry pointers.
Send email if you know of an appropriate page not listed here.
David Eppstein, Theory Group, ICS, UC Irvine.
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