The power of math: 17 Equations That Changed the World - a one table summary of the book by Ian Stewart FRS. Business Insider gives its interpretation of the importance of each equation. Brain pickings (2012) on this book and equations, and another extract from the book. [more inside]
In 1909, American architect and cartographer Bernerd J.S. Cahill published An Account Of A New Land Map Of The World (and at The Internet Archive), in which he described a novel way of projecting a map. [more inside]
Polyhedra and the Media - On the new polyhedra of Schein and Gayed, and mathematical journalism.
Beaded Polyhedra ❂ More beadwork (mathematical and otherwise) by Gwen Fisher ❂ Still more beadwork galleries at beAdinfinitum ❂ Three-dimensional finite point groups and the symmetry of beaded beads [pdf - some algebra, but lots of illustrations]
Let's say you're me and you're in math class, and you're supposed to be learning about factoring. Trouble is, your teacher is too busy trying to convince you that factoring is a useful skill for the average person to know with real-world applications ranging from passing your state exams all the way to getting a higher SAT score and unfortunately does not have the time to show you why factoring is actually interesting. It's perfectly reasonable for you to get bored in this situation. So like any reasonable person, you start doodling.[more inside]
Geometry, Surfaces, Curves, Polyhedra (many of which are beautiful) l Google Earth Fractals l fractals and chaos. [more inside]
Polyhedral Maps is a website that explores unconventional methods of mapping the surface of the earth. The most famous of these unusual maps was Buckminster Fuller’s Dymaxion map, which used the net of an icosahedron. Da Vinci had experimented with this technique in his “Octant” map of 1514, which used Reuleaux triangles as map elements. This process is now being used by photographers and artists in manipulating panoramic images. A good example is Tom Lechner’s The Wild Highways of the Elongated Pentagonal Orthobicupola.
Walter Randelshofer's Pretty Patterns collection (for Rubik's cubes up to 5x5x5) is one of the nicest twisty puzzle sites going. It's based on his CubeTwister software, which you can download (including a lovely OS X standalone). If you really want a treasure trove of twisty polyhedra, check out gelatinBrain's enormous collection of java applets (which unfortunately don't do so well on macs). Are those things even physically possible? Really? Mini bonus: Randelshofer also hosts an archive of fondly-remembered Amiga animations.
Here are some beautifully rendered views of polytopes, and a few more. The rendering program, Jenn 3D, is free and downloadable, (OS X, Linux, Win) and includes some really dazzling fly-about and camera effects as well as tons of high-dimensional models to explore. There's also a mind-boggling possibility of playing Go on boards in projective space. Via the Math Paint blog, which leads to other interesting places...
The Spidron is an interesting geometric construction that seems to lend itself to folding, dissection, and space-filling in two and three dimensions.
Friday Folding Fun! Paper models of polyhedra (most of which I had never heard of before). When finished they look like this. In many cases it's a toss up as to whether they're easier to fold or to pronounce; dodecicosidodecahedrons, anyone? Also: polyhedra info, indexes; and stellated icosahedra by shape and plan.
Prof. George W. Hart, of the Computer Science Department at SUNY Stony Brook, has an enviable web presence. His Encyclopedia of Polyhedra alone is worth the visit, his geometric sculptures make the nerd in me weep at their beauty, and his trilobite recipe looks mighty yummy.