Andrew D Hwang
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diffgeom.com
Andrew D Hwang
@diffgeom.com
650 followers 500 following 340 posts
The online shop Differential Geometry: Original Math Designs, at www.diffgeom.com.

"Hwang" rhymes with "song" more or less, he/him: Freelance mathematician, mathematical artist (no machine learning), author, difficult to summarize. I block bots
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diffgeom.com
The same design as earrings:
www.diffgeom.com/product/inti...

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My online shop will be closed the week of January 19. I expect to re-open the week of January 26.

#MathSky #MathArt #SciArt #Jewelry
Photograph of sterling silver earrings, about 5/8 x 7/8 in, each in a single curve that traces two large overlapping circles and a smaller inner circle, resembling an eye.
January 11, 2026 at 4:00 PM
diffgeom.com
That suggests the visible explosion is initially all ejecta; the shock waves only become visible once the ejecta are subsonic, and are a lot smaller in radius than intuition might suggest...?

Corrections to my understanding are welcome!
[2/2]
January 10, 2026 at 2:20 PM
diffgeom.com
(Caveat: mathematician, not scientist)
Long-time nit: In existing (still/animated) impact depictions, velocities look wrong to me: Impactor ~20-30 mi/s, but ejecta should be well below escape velocity (~4-5mi/s), and shock waves at speed of sound (in air, water, rock; ~0.2-1mi/s).
[1/2]
#SciArt
January 10, 2026 at 2:19 PM
diffgeom.com
My interpretation of linked rings:
www.diffgeom.com/product/inti...
www.diffgeom.com/product/inti...

#MathSky #MathArt #SciArt #Jewelry
Photograph of Intimo Golden, a shiny 1-3/8 in (35mm) tall gold-plated brass pendant that in a single curve traces two large overlapping circles and a smaller inner circle, resembling an eye. Photograph of Intimo, a shiny 1-3/8 in (35mm) tall rhodium-plated brass pendant that in a single curve traces two large overlapping circles and a smaller inner circle, resembling an eye.
January 9, 2026 at 9:30 PM
Reposted by Andrew D Hwang
kristinhenry.bsky.social
#Genuary 2026 Day 2: Twelve principles of animation.

I'm taking inspiration from the example of how horses run, with body carrying through. But with lizards.

I wrote a bit more about it: www.patreon.com/posts/147034...

#Genuary2026 #Genuary2 #ink #drawing #art #SciArt
My small sketchbook with sketches of varying detail where I'm figuring out the geometry of placing the feet to make the lizard look like it's walking. A finished drawing is in the background.
January 2, 2026 at 10:26 PM
Reposted by Andrew D Hwang
sgoldstine.bsky.social
#ShowMeYourKnits #knitterschoice

Fundamentals of Lace, 2025: the newest #mathart I’m exhibiting at the Joint Math Meetings next week. Details (like the allusion in the name) are through the link and in the alt text.

🧶 #knitsky #mathknitting #symmetries

gallery.bridgesmathart.org/exhibitions/...
The catalog photo of Fundamentals of Lace, a knitted wall hanging. The piece is a rectangle of blue knitted lace lashed to wooden dowels at the top and bottom. The fabric has white, yellow, and red beads knitted into the lace. The rectangle is divided into a 3 x 3 grid of different lace designs, and each section has its own pattern of colored beads that mark the symmetries of the design. The white beads, which are always in vertical or horizontal lines, mark the axes of reflection (mirror) symmetries. The yellow beads (also in vertical or horizontal lines) mark the axes of glide reflection symmetries. The red beads, which are slightly larger and more spaced out, mark centers of rotational symmetry. Fundamentals of Lace after blocking and before attaching to dowels, lying flat on a wooden deck. Each of the nine lace designs is made up from smaller lace motifs arranged in four rows and six columns. Disregarding any beads, the motif in the upper left corner of each design is identical, a rectangle with eyelets along one diagonal and half of the other diagonal forming a lowercase lambda. The part of the motif under the lambda is an eyelet mesh, while the regions above and to the left are solid stockinette. The rest of each design consists of the same motif in various orientations, some like the original, some flipped vertically, some flipped horizontally, and some rotated by 180°. Mathematically, the motif is a “fundamental region” for the design; hence, the title of the work. Fundamentals of Lace, pre-blocking. The lace is rumpled and uneven, and the lines of beads are much wobblier than in the finished work. Algebraically, we can prove that there are exactly nine possible symmetry structures for a design in a non-square rectangular grid repeating in two directions. The structures are expressed by the beaded markings: for instance, the middle panel gives an example of a design with no 180° rotational symmetries that has both reflections and glide reflections, and any repeating design that has evenly spaced, parallel symmetry axes that alternate between reflections and glide reflections and nothing else except translations (just sliding the design without twisting or flipping) has the same abstract symmetry structure.
December 29, 2025 at 1:55 AM
Reposted by Andrew D Hwang
fractalkitty.com
Finished a post today on chords. It would be really easy to keep going and make a Monte Carlo for random chords, rotations of connected shapes, moire strings, shadow art with strings, etc.

www.fractalkitty.com/inquiries-we...
#mtbos #mathart #stringart #decemberAdventure #indieweb
Inquiries-Week 6: Beautiful Chords
Introduction In this inquiry, we explore chords, which are lines drawn across circles, using different rules to create various patterns, curves, and shapes. This inquiry will be different from those ...
www.fractalkitty.com
December 31, 2025 at 6:22 AM
diffgeom.com
Same as for the 6yo, I'd ask probing questions to clarify what the symbol(s) "28" means to them. (And then what "36" means, and what "+" means.)

What happens next depends on the response(s) given.

For example, maybe we count out 28=2*10+8 pennies and 36=3*10+6 pennies and put them in one pile....
December 25, 2025 at 4:17 PM
diffgeom.com
"What's 28?" (Seriously.)

I had not heard of NumberBlocks, but did learn from a former colleague recently that some of their calculus students this fall did not know the difference between addition and multiplication.

What are numbers to a person like that? (Seriously.)
December 23, 2025 at 1:00 PM
Reposted by Andrew D Hwang
sciencesocks.bsky.social
My final holiday ship-out is TODAY at 2 PM PT / 5 PM ET 🎄✨

For the best chance at Christmas delivery, choose UPS 2-day or faster on in-stock ScienceSocks, acrylic jewelry, ornaments & umbrellas 🎁

🔗 sciencesocks.co

Thank you for your support this year!! 💙

Sharing appreciated 🙏
🔭🐡🧪🎨
JWST holiday ornament in tree with Santa hat
December 19, 2025 at 5:39 PM
Reposted by Andrew D Hwang
petraschwer.bsky.social
In case you are still trying to find a present for yourself or a loved one who would like to hear more about what we mathematicians do and how so.... I can only recommend Bessis' book Mathematica. What a wonderful read. I could highlight every other sentence.
#math #maths #mathsky
Cover of Bessis' Mathematica
December 19, 2025 at 2:28 PM
diffgeom.com
1. 😬 I might ought to apologize on behalf of all mathematicians

2. I do suggest she keep the book; working through it (with a classmate the summer after junior year, i.e., ~2 years after U of T uses it) was the first time I understood "dual vector spaces," "tensors," and "differential forms"
December 19, 2025 at 8:34 PM
diffgeom.com
Thank you; I do strive for promptness! :)

Most of the shipping process is outside my control, but just to note for passersby, orders placed in the next hour or so will go out today before first pick-up.
December 19, 2025 at 2:56 PM
diffgeom.com
One never-ending surprise with these space curves is how their appearance changes with angle. Even the comparable band on the complex twisted cubic (t,t^2,t^3) looks non-rigid when it rotates about the "1-axis"! :)
December 19, 2025 at 2:44 PM
Reposted by Andrew D Hwang
vladabotanica.bsky.social
Final touches on my pine cone drawing 🌲✨
I love seeing every tiny scale come to life — so calming to focus on these little details of nature.

#botanicaldrawing #pineconedrawing #natureart #sketchbookart #slowart
December 18, 2025 at 4:04 PM
diffgeom.com
This type of image would (seriously) make fine adult birthday cards.... 🤔
December 19, 2025 at 1:55 PM
diffgeom.com
🎉
December 19, 2025 at 1:47 PM
Reposted by Andrew D Hwang
elkement.art
Thanks - this gave me an idea what to post in my advent calendar today :)

bsky.app/profile/elke...
elkement.art Elke Stangl (elkement) @elkement.art · 24d
#ArtAdventCalendar Day 18

"Lissajous 345", 2024

3D Lissajous figures and their 2D projections, created with code (no AI).

#MathArt #SciArt
3D Lissajous Figures - x=sin(3t),y=sin(4t),z=sin(5t) - and their 2D projections, as glowing lines on dark background and including the projecting rays. Code-generated art by elkement 2024.
December 18, 2025 at 9:04 PM
diffgeom.com
In the 90s as well, MAT 257 was a ... milestone ... in the specialist coursework. :)

Michael Spivak's thin, dense/rich (and to be honest, fraught) book "Calculus on Manifolds" was a common choice of text. Was that the book she used?

Sadly, the course-schedule stars never aligned me with 257....
December 19, 2025 at 1:39 PM
diffgeom.com
Just so. :) @elkement.art and I separately have a thing for these shapely space curves!
December 18, 2025 at 8:49 PM
Reposted by Andrew D Hwang
diffgeom.com
Delicate new earrings are in my shop, and would make excellent budget-conscious last-minute gifts for math-loving people in your life! Shipping within the contiguous US normally takes at most 5 business days.

www.diffgeom.com/product/vola...

More in alt text.

#MathSky #MathArt #SciArt #Jewelry
A pair of delicate natural bronze earrings with a symmetric, pretzel-like appearance. From different viewpoints the appearance changes intriguingly and dramatically. The product page has a virtual animation showing the rotating shape. As shown in the product photograph, the shape may vary slightly from the mathematical ideal. Browse all prototypes and other unique pieces: https://www.diffgeom.com/product-category/jewelry/unique-jewelry/ A pair of delicate polished bronze earrings with a symmetric, pretzel-like appearance. From different viewpoints the appearance changes intriguingly and dramatically. The product page has a virtual animation showing the rotating shape. As shown in the product photograph, the shape may vary slightly from the mathematical ideal. Browse all prototypes and other unique pieces: https://www.diffgeom.com/product-category/jewelry/unique-jewelry/ A pair of delicate rhodium-plated brass earrings with a symmetric, pretzel-like appearance. From different viewpoints the appearance changes intriguingly and dramatically. The product page has a virtual animation showing the rotating shape. As shown in the product photograph, the shape may vary slightly from the mathematical ideal. Browse all prototypes and other unique pieces: https://www.diffgeom.com/product-category/jewelry/unique-jewelry/
December 17, 2025 at 5:46 PM
Reposted by Andrew D Hwang
diffgeom.com
These new earrings are in my shop, and would make excellent budget-conscious last-minute gifts for math-loving people in your life! Shipping within the contiguous US normally takes no more than 5 business days.

www.diffgeom.com/product/vola...

More in alt text.

#MathSky #MathArt #SciArt #Jewelry
An array of eight pairs of colorful, approximately pyramidal nylon earrings. From above, each looks like an equliateral triangle with one vertex downward. From different viewpoints their appearance changes intriguingly and dramatically. The product page shows views from four directions. All my original nylon earrings are on sale through December: https://www.diffgeom.com/product-category/nylon-wearables/
December 17, 2025 at 12:17 AM
diffgeom.com
My oops; here is a link to the sticker pack page :)
www.diffgeom.com/product/viny...

From the Small World department, I taught at the U of T in the mid-to-late 90s, including MAT 267 (ODEs for math specialists) one semester.

The department had lively student cultures; I hope she's thriving!
www.diffgeom.com
December 18, 2025 at 12:16 AM
Reposted by Andrew D Hwang
flyingtrilobite.com
Would love to see the SciArt Feed 🐡 reach 4,000 subscribers by the end of the year.

Pin & Like here:
December 17, 2025 at 4:58 PM