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, Klein’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, it’s a level 3 approximation of a Menger Sponge, actually, incorporating 8,000 unit cubes, each of which starts as one-sixteenth of a “mini” size Post-It. Its creator, Nicholas Rougeux, likes Post-Its for this work because they “offer surprisingly [sic] structural durability and are easy to get in large quantities making them ideal for assembling structures like these.”

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.