← Feed

Posts

• Post #4466801

  Spurred by a couple of recent posts, here is a short list of online math shops: https://diffgeom.org/misc/math_shops.html #math #mathematics #MathArt

• Post #4466800

  Over my years in academia, I helped create a variety of free online mathematical materials. Pirouette is a Spirograph clone that runs in a web browser. I hope you and your students enjoy the software! Read more: https://www.diffgeom.com/blogs/free-online-math-materials/pirouette/ #Math #MathArt #ITeachmath

• Post #4466799

  "An Invitation to Real Analysis" has gone to press, and is available for pre-order on August 21. The book was substantially shaped by my own experiences, in person and at math.stackexchange, clarifying common confusions and conceptual hurdles. If you teach real analysis in English at levels from "introduction to proofs for math undergraduates" to "rigorous course for quantitative fields" (say), or are self-studying, I am very grateful for you...

• Post #4466798

  When I was a student, the descriptions of multi-valued complex graphs obtained by suitably-joined slit planes always rankled, at least a little. This unit circle \(z^{2} + w^{2} = 1\) with a portion of the \(z\)-plane at bottom, animated to show three loops lifted continuously, depicts all the Standard Business about holomorphic branches of \(\sqrt{1 - z^{2}}\) in singly- or doubly-slit planes with what accuracy 3-space can accommodate. (The imaginary part of \(w\) is projected away.) Particul...

• Post #4466797

  #Math #MathArt #SciArt #3DPrinting #StopMotion

• Post #4466796

  Another stop-motion loop of a 3D-printed nylon model, this time of an Enneper-type minimal surface. Because the surface is invariant under the composition of reflection in the equatorial plane and rotation by 1/12 of a turn about an orthogonal axis, the reflection in the CD may be surprising. #Math #MathArt #SciArt #3DPrinting #StopMotion

• Post #4466795

  This commercially 3D-printed torus knot plays off the classic barber pole illusion, converting rotation about an axis into an appearance of non-rigid "smoke-ring roll." I had it printed in late summer 2024 for an AMS session talk on continuous group actions and visual illusions, and as a prospective mobile (shown) or desk toy. <> Just to report on the state of online commerce since I re-opened 13 months ago: Sales are all but non-existent (which is understandab...

• Post #4466794

  An animated version of the postcard "Nimbus," part of the mathematical postcard set "You Are Here." https://www.diffgeom.com/product/you-are-here-postcard-pack/ #Math #MathArt #SciArt

• Post #4466793

  An animation based on a prospective postcard image. The pewter conformal honeycomb torus was drawn using the LaTeX picture environment (ePiX+PSTricks). #Math #MathArt #SciArt

• Post #4466792

  A 3D-printed rigid nylon object filmed on a phonograph turntable. Under continuous lighting there are fewer possibilities for this type of visual illusion than under a strobe light: Invariance under a continuous action of the additive reals is a lot more restrictive than invariance under an action by the additive integers. John Edmark has created pieces that are truly spectacular when strobe-lit: https://www.johnedmark.com/phi #Math #MathArt #SciArt

• Post #4466791

  When revolved about its axis, this torus knot appears to undergo "smoke-ring roll." Because the model isn't completely smooth, you may have to de-focus your attention a little to see this. #Math #MathArt

• Post #4466790

  This mowed hillside immediately suggested a logistic differential equation. Still, the closeness of fit after picking a couple of parameters (not too carefully) was surprising. #Math #MathArt #MathInTheWild #SciArt

• Post #2326320

  A blog post explaining the math behind the image "Cyclide Check" in what I hope is a friendly, step-by-step way. This is fun material, especially if you're teaching or taking or otherwise fond of multivariable calc or linear algebra. (Also, the action by unit complex scalar multiplication on the real 3-sphere is a motivating example of a principal circle bundle, arising in a variety of mathematical settings.) https://www.diffgeom.com/blogs/about-math/cyclide-check/ &a...

• Post #994439

  "Collaboration," a new postcard design. This is the tenth image in a series of digital overlays. I'm working toward packaging these as sets at https://www.diffgeom.com #Math #MathArt #SciArt

• Post #745770

  I'm working on a set of mathematical postcards, some entirely digital but several digital overlays on photographs. Here, a conformally-parametrized torus tessellated by regular hexagons looms in an afternoon sky about last Wednesday. #Math #MathArt

• Post #745762

  "Bubble," a postcard image (digital overlay). As mathematicians in 2026, we need to be Very Careful we are not inadvertently developing virtual tools of enormous power for those of questionable judgment and inhuman values. #Math #MathArt #SciArt