Semi-seriously, connected (orientable) double covers of Möbius strips? (Requires two strips of each colour per model.)
Glue or tape a red strip to a white strip, making a single double-thickness strip that is red on one side and white on the other. (Optionally colour the white side to look like a fruit rind, such as watermelon.)
Make a second unit of the same type.
Place two of these units with red sides facing, making a single quadruple-thickness strip that is white on the outside and red on the inside as if the paper has been cut in half "depthwise."
Treating this quadruple-strip as a unit, create a Möbius strip conventionally: Give a half-twist, and "attach the ends, respecting the laminar division."
Tell math-y people you made a Möbius strip, cut the thickness of the paper in half, and this is what resulted!
As for semi-serious: The model clearly has two sides (one of each colour), and nicely illustrates how "orientable double-covering" amounts to "painting a non-orientable surface and peeling off the paint," i.e., picking a germ of orientation and constructing its connected component in the sheaf of local orientations.
It's fascinating to me that giving someone a "beat down" is the same thing as "beating them up". It implies that beating exists in some sort of non Euclidean space that folds in on itself.
This past October, dozens of mathematicians gathered in Pasadena to create the third version of “Kirby’s list” — a compendium of the most important unsolved problems in topology, the study of deformable shapes.
++ Video is visually appealing, compact (28'). Tries to present the question of finiteness || infiniteness of Universe within the context of relativistic #cosmology. Intros to 2D #topology + #curvature are fair. Publicity for my group's research is nice :).
The relation to 3D topo+curv is absent; there are several bloopers in the narration.
I remember one time I ...found a book w/ pdf.
It was about displaying dynamical systems theory, showing manifolds and so on.
Plots were not made with any programming language, they were actual drawings, pastels, watercolors.
It's the type of book I literally have dreams about, but I think this one exists😅 what was it?
Our redesign for https://topology.pi-base.org finally launched! If you might be teaching #topology someday, I'd love to chat about ways to use it in your #classroom. And we're always looking for students and faculty who want to contribute to its content...
For #ArtAdventCalendar Day 13: Happy birthday to #mathematician Virginia Ragsdale (1870-1945). The Ragsdale conjecture, made in her 1906 dissertation, is amongst the earliest and most famous on the #topology of real & algebraic curves, which stimulated a lot of 20th century research & was not disproved until ‘79. A correct upper bound has yet to be found. In her dissertation she tackles the 16th of David Hilbert’s famous 23 unsolved 🧵1/n