Andrew D. Hwang

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

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

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

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

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

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.

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Just to report on the state of online commerce since I re-opened 13 months ago: Sales are all but non-existent (which is understandable), and over the past four (4) days my shop received more than one-quarter (~27%) of its all-time visits, i.e., was hit by a distributed entity, likely based outside the US, coming through VPNs (which is comprehensible, but for different reasons). Half of those visits, more than one-eighth of total visits for 13 months, were yesterday.

No referers, no blockable user agent, one page per visit, sucking out about 10 days of typical bandwidth per day, mostly product pages for print-on-demand items. Impossible to know if this was a harvest of AI training data, or wholesale product theft, or a low-grade DDOS attack, or what.

This was not the first time, but the sophistication is increasing. And it's hard to believe my small, independent shop would be the target of a coordinated attack unless all small, independent shops are.

#Math #MathArt #SciArt #3DPrinting

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

#Math #MathArt #SciArt #3DPrinting #StopMotion

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.)

Particularly, the lift of the large loop (encircling both points \(z = \pm 1\)) lies on a holomorphic branch of \(\sqrt{1 - z^{2}}\) defined in the slit plane \(\mathbf{C} \setminus [-1, 1]\).

#Math #MathArt #SciArt

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/

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For newer followers/passersby: I earned my PhD in complex differential geometry in 1993 under the direction of Shoshichi Kobayashi. In 2023 I left academia to preserve some ember of sanity, and am now trying to earn a modest living by designing mathematical jewelry and poster/t-shirt images, and writing about math as a form of public outreach.

All my products for sale are created using software I wrote, together with widely-available libre programs. I warmly invite human visitors to browse my shop/blog:

https://www.diffgeom.com/

The newest addition is an inexpensive set of picture postcards, titled "You Are Here":

https://www.diffgeom.com/product/you-are-here-postcard-pack/

Over a period of 4.5 intensive months in 2024-25 I re-wrote an existing manuscript into "An Invitation to Real Analysis." A short blog post summarizes what is inviting (to both readers/students and instructors) about the book:

https://www.diffgeom.com/blogs/around-the-shop/an-invitation-to-real-analysis/

As appropriate, please order an evaluation copy from Routledge. Every course adoption helps. In sardonic moments while writing I thought, "I'll be lucky if this book earns $0.30/hr." In fact, to date the book *has* earned ~$0.30/hr. But it would be nice to earn even more.

https://www.routledge.com/An-Invitation-to-Real-Analysis/Hwang/p/book/9781032989136

#Math #MathArt #SciArt

"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

"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

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

"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 your consideration.

https://www.routledge.com/9781032989136

The description on the publisher's page was not written by me. More about the book's style and content:
https://www.diffgeom.com/blogs/around-the-shop/an-invitation-to-real-analysis/
[Link edited]

#Math #ITeachmath

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

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