geometry

Topology Tuesday:  Klein’s Quartic

Topology Tuesday: Klein’s Quartic

If you are looking for a subject likely to inflame the hearts of mathematicians, make them slightly weak in the knees, and induce some distinctly poetical sentiments, Kleinโ€™s Quartic, first described by German mathematician Felix Klein in 1878, seems like a pretty good bet. Though the surface itself, per Wikipedia, “does not have a (non-trivial) 3-dimensional linear representation,” several prominent math-bloggers have produced models, projections, and plain-language written explanations attempting – and doing a pretty good job of it, IMHO – to communicate their passion for the construct…

Mini Post-It Menger Sponge

Mini Post-It Menger Sponge

OK, so, itโ€™s a level 3 approximation of a Menger Sponge, actually, incorporating 8,000 unit cubes, each of which starts as one-sixteenth of a โ€œminiโ€ size Post-It. Its creator, Nicholas Rougeux, likes Post-Its for this work because they โ€œoffer surprisingly [sic] structural durability and are easy to get in large quantities making them ideal for assembling structures like these.โ€

Scott’s Pentagonal Dragon Tiling on a Dodecahedron

Scott’s Pentagonal Dragon Tiling on a Dodecahedron

Each face of “DodecaHedron of Dragons II” by California artist Scott Van Note is identically patterned, hand-carved on a pentagonal tiling designed by Scott himself. I had the pleasure of meeting Scott at BAMF 2011, where he was helping out at the Explorable Microscopy booth. We started talking, and he handed me this amazing object. I caught up with him, after the Faire, and got him to answer a few questions about it.