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| ![Minimum-stick 9-crossing knots][1] **Nines** In our paper ["New stick number bounds from random sampling of confined polygons"][2], my graduate student Thomas D. Eddy and I found many examples of polygonal knots made with fewer edges than... |
| ![Inverse Cayley transform of rotating grid of circles][1] **Rotation Redux** A [recent post by Dave Whyte (a.k.a. @beesandbombs)][2] on Twitter reminded me of my old GIF [_Rotation_][3], which is almost 5 years old (and dates back to before I... |
| ![Fourth power of a square grid in the complex plane][1] **Fourth Power** Continuing the series of conformal transformations ([1][2], [2][3], [3][4]). The first part shows a square grid in the first quadrant under the transformation $z \mapsto... |
| ![Conformal map of upper half-plane to triangle][1] :christmas_tree: The [Schwarz–Christoffel mappings][2] are conformal transformations from the upper half-plane (or unit disk) to convex polygons; the existence of such maps is guaranteed by... |
| ![Inverse Cayley transform of level sets of log][1] `:globe_with_meridians:` Take level sets of the real and imaginary parts of the level sets of $\frac{1}{\pi i} \log z$ in the upper half plane (i.e., the real part is the standard solution of... |
| Apparently emoji are not supported here? I tried to post this with the actual eyes emoji rather than ":eyes:", but got a "Message board not available" error. /cc [@Vitaliy Kaurov][at0] [at0]: https://community.wolfram.com/web/vitaliyk |
| Yes, you're quite right. I realized after the fact that I'm doing something much bigger than the modular group, but never went back and corrected the description. And thanks! Nice to virtually meet you. |
| ![Stereographic projection of rotating cube vertices][1] **Cube Life** The basic idea is simple: I'm rotating the cube around the axis $(1,1,0)$ and stereographically projecting the vertices to the plane. Or rather, I'm thinking of the... |
| By summing over both $i$ and $j$ youÂ’re adding up the entries in the contraction. What you presumably want is something like Table[Sum[?2[[i, j]]*f[[j]], {j, 1, 3}], {i, 1, 3}] Of course, as [@Hans Milton][at0] points out, this is the same... |
| ![Morph between +3-framed and 0-framed 200-gon][1] **Framing** An animated version of a [graphic][2] I produced for my paper ["Stiefel manifolds and polygons"][3], which appears in the _Proceedings of Bridges 2019: Mathematics, Art, Music,... |