Math Monday: Hexagonal stick arrangements By George Hart for the Museum of Mathematics Interpenetrating hexagonal arrangements of sticks are a challenging mathematical exercise to assemble from pencils. Four different directions are used, as color-coded here. The above sculpture, 72 Pencils, has tiny dots of glue to hold itself together, but you can easily use eight […]
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Build a challenging geometric puzzle out of wood then see if you can assemble it. Thanks go to George W. Hart for the original article in MAKE, Volume 17. To download The Egg Heads video click here and subscribe in iTunes. Check out the complete Egg Heads article in MAKE Volume 17 and you can […]
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Build a challenging geometric puzzle out of wood then see if you can assemble it. Thanks go to George W. Hart for the original article in MAKE, Volume 17. View the PDF of this project. and then subsribe to MAKE Magazine for other great projects you can do over the weekend.
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The problem of tiling a plane has fascinated builders and mathematicians alike since time immemorial. At first glance, the task is straightforward: squares, triangles, hexagons all do the trick producing well known periodic structures. Ditto any number of irregular shapes and combinations of them.
A much trickier question is to ask which shapes can tile a plane in a pattern that does not repeat. In 1962, the mathematician Robert Berger discovered the first set of tiles that did the trick. This set consisted of 20,426 shapes: not an easy set to tile your bathroom with.
With a warm regard for home improvers, Berger later reduced the set to 104 shapes and others have since reduced the number further. Today, the most famous are the Penrose aperiodic tiles, discovered in the early 1970s, which can cover a plane using only two shapes: kites and darts.
The problem of finding a single tile that can do the job is called the einstein problem; nothing to do with the great man but from the German for one– “ein”–and for tile–“stein”. But the search for an einstein has proven fruitless. Until now.
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Mathematical art in the lava By George Hart for the Museum of Mathematics Edmund Harris created this geometric sculpture on a 35 year old lava field in Iceland. It can be understood as a simple form composed of equilateral triangles, but the curved edges where the triangles hinge together soften the geometry, giving it a […]
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MacArthur fellow and MIT Media Lab alumnus Karl Sims brings us this great tutorial on how to build your own complex harmonograph (Wikipedia) for making cool…um…”geometric figures?” I’m looking for a 50-cent mathematician’s word (which may or may not exist) for these periodic spirally figures. Can anybody help me out? [Thanks, David!]
Continue ReadingThe relatively straightforward swing-hinged dissection of an equilateral triangle to a square in this video is called “Dudeney’s dissection” and has been known since 1902. For a gallery of hinged dissections, check out Tse-hsuan Yang’s page at Taiwan’s National Tsing Hua University.
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