Recent Additions to the Junkyard

• Applications of shapes of constant width. A Reuleaux triangle doesn't quite drill out a square hole (it leaves rounded corners) but a different and less-symmetric constant-width shape based on an isosceles right triangle can be used to do so. This web page also discusses coin design, cams, and rotary engines, all based on curves of constant width; see also discussion on Metafilter.

• Bamboo C.O.R.P.S.. Durable bamboo models of the Platonic and Archimedean polyhedra, offered for sale.

• Contortion Engineering. Some Escher-like impossible figures from Offworld Press.

• Crocheted Seifert surfaces by Matthew Wright. George Hart, Make Magazine.

• Dodecahedral melon and other fruit polyhedra, by Vi Hart.

• 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.
  

• Human Geometry and Naked Geometry. The human form as a building block of larger geometric figures, by Mike Naylor.

• Hyperbolic crochet coral reef, the Institute for Figuring. Daina Taimina's technique for crocheting yarn into hyperbolic surfaces forms the basis for an exhibit of woolen undersea fauna and flora.

• 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.

• Magazine Puzzle Fun. Fifteen years of back issues of an Argentine magazine about pentominoes (in English).

• Mathematical balloon twisting. Vi Hart makes polyhedra and polyhedral tangles from balloons.

• Mathematically correct breakfast. George Hart describes how to cut a single bagel into two linked Möbius strips. As a bonus, you get more surface area for your cream cheese than a standard sliced bagel.

• Origami proof of the Pythagorean theorem, Vi Hart.

• Packing Tetrahedrons, and Closing in on a Perfect Fit. Elizabeth Chen and others use experiments on hundreds of D&D dice to smash previous records for packing density.

• Platonic solids transformed by Michael Hansmeyer using subdivision-surface algorithms into shapes resembling radiolarans. See also Boing Boing discussion.

• 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.

• Sierpinski valentine from XKCD.

• 30 computers. Forrest McCluer makes polyhedral sculptures out of discarded electronics.

• Three spiral tattoos from the Discover Magazine Science Tattoo Emporium.

• Lun-Yi Tsai paints fine art of foliatied 3-manifolds, differentiable atlases, and other topological structures.

• Typeface Venus, Circle Marilyn, and Bubble Mona. village9991 uses quadtrees and superellipses to make abstract mosaics of famous faces.

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

• What to make with golf balls? Dale Seymour chooses a Sierpinski triangle and Sierpinski tetrahedron.

• Wooden polyhedra from Japan (but with English explanations). And more, in Japanese.

• Woolly thoughts, mathematical knitwear.

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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