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I design and sell 100% AI-free mathematical T-shirts, posters, and jewelry. There's a new poster design, Eclipse Horns: www.diffgeom.com/product/post... www.diffgeom.com/product-cate... www.diffgeom.com/product-cate... www.diffgeom.com/product-cate... #MathSky #MathArt #SciArt

A digital scene of a partial solar eclipse at sunset, two cusps visible over a range of desert mountains.

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Matt Henderson @matthen.com · 09/09/2026

My oops: If we drew imaginary rays from the camera to the left side of the frame and right side of the frame, what angle did they make at the camera? (Knowing the lens' focal length may be enough to deduce that, but my geometric optics isn't up to the task :)

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Reposted by Andrew D Hwang

Drawing a picture from the continued fraction of a number. The continued fraction terms drive a Fourier series.

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Based on the question wording: We need to know or find the angular width or height of the photo; then we can do similar triangles with vehicle sizes :)

Ballpark estimate: ~150-170ft, ~15th floor Just estimating a few heights of objects and how many stacked it would take to reach viewing altitude

SunJester @sun-jester.bsky.social · 04/09/2026

Reposted by Andrew D Hwang

Don’t forget, the Thursday after next Thursday (17/9) will be 200 years after the birth of Bernhard Riemann! #MathSky #200YearsRiemann #HistSky

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Andrew D Hwang @diffgeom.com · 31/08/2026

Q: Which solid is the most well-rested? A: A cone, because every day it has two nappes. Q: What did the line send to the coplanar line to say they would never meet? A: A parallelogram. Q: What's analytic and has long ears? A: A holomorphic vector bunny. Will it never end...?!

Andrew D Hwang @diffgeom.com · 22/08/2026

Thank you! To be honest, generation gap: I can't count how many abstraction layers were necessary to parse the reference. :) Did eventually glean that Evangelion is a franchise, but not whether it originates with "Anime" or "genre fiction" or "gaming" or ..., all of which I know from nothing. 😳

Andrew D Hwang @diffgeom.com · 21/08/2026

Please support independent creators as you shop for mathematical back-to-school posters, T-shirts, jewelry, and games: www.diffgeom.org/misc/math_sh... These are difficult times. We are all grateful for your support! #MathSky #MathArt #SciArt

"Collaboration," a postcard image from the collection You Are Here.
https://www.diffgeom.com/product-category/stationery/postcards/

A side-lit blue-gray compound of five cubes 400 feet across and having overall icosahedral symmetry hovers over a late-wintry body of water bordered by jutting, evergreen-covered shores. On a flat dun area in the middle distance, barely-visible figures walk beneath the cubes' bottom vertex.

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Reposted by Andrew D Hwang

samjshah.bsky.social @samjshah.bsky.social · 16/08/2026

I’ve been sick this past week but started to feel much better today. So I started a new #mathart project. 😁 I’m probably a third of the way done. The math… Truchet Tiles: pelletierauger.com/en/projects/... I’m a novice at stained glass so we’ll see if this large thing will work. #mtbos

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Andrew D Hwang @diffgeom.com · 16/08/2026

Love math? Heading back to school? Looking for original, human-designed posters and T-shirts? I invite you to drop by Differential Geometry! www.diffgeom.com www.diffgeom.com/product-cate... www.diffgeom.com/product-cate... #MathSky #MathArt #SciArt

The real projective plane curve defined by x^3 - x^2z + y^2z = 0 against a blue-to-black twilight gradient: The spatial locus is a set of orange lines through the origin; these meet the unit sphere, the double-cover of the projective plane, along a looping bright green curve that is invariant under the antipodal map of the sphere.

At the bottom in large gold letters with black drop shadows are the title "Nodal Cubic" and the curve's polynomial equation.

https://www.diffgeom.com/product/poster-nodal-cubic/

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Andrew D Hwang @diffgeom.com · 09/08/2026

Without more context, "Assume/suppose A and B are sets, and f:A->B [is] a mapping" to set up notation. Defining (specifying) a mapping requires more words, e.g., "For each a in A, define..." <> Loosely, I use "let...be" as "assume...denotes," as in "Let f:R->R be the mapping defined by...."

Andrew D Hwang @diffgeom.com · 09/08/2026

Another human-created design in a prospective second set of postcards. The overlay is the silhouette of my pendant design Luminoso. www.diffgeom.com/product/lumi... I hope the image evokes looming mystery, ephemerality, holism, mathematical elegance. #MathSky #MathArt #SciArt #Postcard

A photograph of treetops silhouetted at against a darkening pastel pink mackerel sky. In the sky floats a set of six swirling bands, each lying on a cyclide.

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Last spring I introduced a set of original, human-created math postcards for just $15+postage: www.diffgeom.com/product/you-... Your purchase goes toward printing a second set of eleven new designs, including the second image! #MathSky #MathArt #SciArt

A glossy gallery card showing eleven picture postcards, each a striking (if I may say) digital mathematical overlay on an original photograph.

A photograph of a grassy park on a summer day. Filling the cumulus-dotted sky above a line of trees in the medium distance are three enormous gray-white ribbons spiraling around an imaginary sphere.

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6. The (equally-spaced) set x+(x'-x)Z is contained in A ("b/c additive groups"), and spacing is smaller than length(J). 7. Particularly, J contains a point of A. J was arbitrary, so A is dense in R. [3/3]

5. Assume J is an arbitrary real interval. Pick a positive integer N so that 1/N is less than length(J). Subdivide [0,1] into N equal-length pieces. Since A ∩ [0,1] is infinite, some piece contains at least two points, say x, x'. [2/3]

Write c=β/α. Outline of a low-tech approach to showing the set A = Z+cZ = {m+nc: m, n in Z} is dense in R: 1. A+Z = A 2. m+nc = m'+n'c iff m=m' and n=n' 3. For each n, Z+nc = {m+nc: m in Z} has a unique element in [0,1] (floor and ceiling of nc) 4. A ∩ [0,1] is infinite [1/3]

Andrew D Hwang @diffgeom.com · 06/08/2026

This is real and not complex...?

Andrew D Hwang @diffgeom.com · 06/08/2026

I design and sell mathematically-accurate metal and nylon jewelry inspired by differential and algebraic geometry, and topology. I warmly invite humans to browse! www.diffgeom.com/product-cate... www.diffgeom.com/product-cate... #MathSky #MathArt #Jewelry #3DPrinting

A gallery of 15 photographs of shiny mathematical pendants and earrings at Differential Geometry.

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Andrew D Hwang @diffgeom.com · 24/07/2026

👀 and 🥰 The fluid animation is surprising and delightful, yet you make it look effortless! #MathArt #SciArt

Roo Nelo @rooneloart.bsky.social · 24/07/2026

Reposted by Andrew D Hwang

I received a wonderful postcard set from @diffgeom.com. I love them so much that I thought I’d squeeze in a little rough animation. If you like math art, check out his online store: diffgeom.com

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Andrew D Hwang @diffgeom.com · 19/07/2026

Candidate member for a second set of original mathematical postcards. The first set, You Are Here, is just $15 plus postage: www.diffgeom.com/product/you-... #MathSky #MathArt #SciArt

Photograph of a blue sunset sky with sunlit clouds, and silhouettes of high tree branches at bottom. The sky is filled by a sphere with graceful spiral bands climbing to the zenith.

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Andrew D Hwang @diffgeom.com · 17/07/2026

Specifically, add \usepackage{graphicx} %[sic; pkg name ends with x] to the preamble, and replace the \input line with \includegraphics{figures/descriptivename.pdf} FWIW, ePiX has a shell script "elaps" that compiles a tikz figure into a PDF. www.diffgeom.com/blogs/free-o...

diffgeom.com

ePiX: Drawing for LaTeX – Differential Geometry

Andrew D Hwang @diffgeom.com · 17/07/2026

The last time I used tikz directly, the in-document computation substantially slowed the compile. If that is still an issue, it's possible to modify Chris's good strategy by separately compiling each tikz snippet into a stand-alone PDF image and using \includegraphics instead of \input. [1/2]

Andrew D Hwang @diffgeom.com · 14/07/2026

FWIW, the introductory textbook manuscript ams.org/open-math-no... speaks of bases as ordered sets. It's possible a careful revisiting would reveal minor logical inconsistencies needing tweaks, but I am not aware of major inconsistencies with common usage.

ams.org

AMS Open Math Notes: View Listing

Advancing research. Creating connections.

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Andrew D Hwang @diffgeom.com · 09/07/2026

Yes provided we're speaking of 1. linear transformations acting on a 2. (real or complex) vector space 3. equipped with an inner product. (2 and 3 could be combined into "real/complex inner product space" since "length" and "angle" are part of the context). IIRC, angle/length here are unoriented :)

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Andrew D Hwang @diffgeom.com · 02/07/2026

www.diffgeom.com/product/harm... Browse all my original jewelry designs: www.diffgeom.com/product-cate... #MathSky #MathArt #SciArt #Jewelry

Photograph of Harmonia, a shiny 1-3/8 in (35mm) gold-plated brass pendant in the looping shape of a stylized flower with six petals. The piece has a shiny inverted trapezoidal bail fitted with a gold long-and-short loop chain and sits in a white-lined dark red display box.

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Andrew D Hwang @diffgeom.com · 01/07/2026

Just went into the kitchen to see what time it is....

Photograph of a microwave clock reading "End."

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Andrew D Hwang @diffgeom.com · 30/06/2026

In case it's of interest, there's a (gratis, privacy-scrupulous) Spirograph clone that runs in a browser, which you're welcome to point students to: diffgeom.org/software/Pir... #MathSky #MathArt #SciArt

diffgeom.org

Pirouette

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Andrew D Hwang @diffgeom.com · 28/06/2026

The complex unit circle (z^2+w^1=1), a smooth complex curve in complex 2-space, projects to the z-plane as a 2-sheeted branched cover. These poster images show two standard ways of forming sheets. www.diffgeom.com/product/roll... www.diffgeom.com/product/roll... #MathSky #MathArt #SciArt

The complex circle as two graphs defined on the plane with two rays removed, the top half dark blue with a gold coordinate grid, the bottom half showing just the coordinate grid. The top half resembles the skull of a crested dinosaur. The set of real points is an ordinary circle in the real plane, whose axes are marked.

The complex circle as two graphs defined on the plane with the real interval [-1,1] removed, one half dark blue with a gold coordinate grid, the other showing just the coordinate grid. Each graph is a plane with a slit stretched into a real circle, the top half along one side of the slit, the bottom half along the opposite side. The set of real points is an ordinary circle in the real plane, whose axes are marked.

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Andrew D Hwang @diffgeom.com · 23/06/2026

My oops for the omission: It's a line L that gets stretched by some scalar factor c. If c is non-zero, and we scale the plane by 1/c, the composition is a linear transformation fixing L pointwise and shearing along L (particularly, translating lines parallel to L along themselves).

Andrew D Hwang @diffgeom.com · 23/06/2026

In the hope it helps, 1. The single real eigenspace is a shear axis up to scaling 2. Some years back I wrote an interactive web program for exploring geometry of plane linear transformations, and the relationship with matrices diffgeom.org/software/Lin... #MathSky

diffgeom.org

Geometry of Linear Transformations

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Andrew D Hwang @diffgeom.com · 22/06/2026

A human-designed image of real vs. complex calculus: Ranges of virtual mountains uniformly approximate a continuous, nowhere-differentiable function; the sky medallion depicts a conformal map from a disk to a radially-slit disk. www.diffgeom.com/product/post... #MathSky #MathArt #SciArt

The human-designed poster image Lotus, Dawn: A thin band of pink dawn glows above mountain range silhouettes grading from black in the foreground to dark blue at the horizon. The sky is filled by a circular design, pink at the center shading to light purple at the rim, whose gold coordinate grid resembles a lotus.

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Andrew D Hwang @diffgeom.com · 20/06/2026

Good to know this exists, but ... yikes 😬

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Original, human-designed poster images depicting the multi-valued complex inverse functions ("Riemann surfaces") log and arcsin. www.diffgeom.com/product/roll... www.diffgeom.com/product/roll... #MathSky #MathArt #SciArt

The complex logarithm, a blue-bronze helicoidal surface glowingly side-lit, whose longitudinal sections are real logarithm graphs.

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A bit loosely, if we let "a" grow without bound and fix b, the equation (x/a)^2+(y/b)^2=1 in the real plane "converges to" (y/b)^2=1, which defines two horizontal lines. With more care: It depends how exactly sum-of-distances grows as the foci move apart (e.g., we might get one line counted twice).

Longer answer: "Unisex T-shirts" are Bella-Canvas 3001, while "Softstyle" are Gildan 64000. Manufacturers' links: www.bellacanvas.com/3001 www.gildan.com/us/en/64000-... [2/2]

bellacanvas.com

3001 | BELLA+CANVAS ®

BELLA+CANVAS 3001

Discover t-shirts for wholesale and other apparel from Gildan for high quality printing. We provide quality at every level, and the right apparel to fit every need.

Short answer: Unisex shirts are side-seamed and have a logo on the left arm, while softstyle shirts have no side seams/logo. Based on shirts I own, the cut and fabric are pretty similar between the two. [1/2]

gildan.com

Gildan

Unisex Softstyle T-Shirt: Parabolic Ascent – Differential Geometry

Thank you for your interest! Just FYI (no obligation), the design is now available, including: www.diffgeom.com/product/unis... www.diffgeom.com/product/unis...

diffgeom.com

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In school you may have learned a parabola is a section of a circular cone by a plane parallel to a generator...? "Parabolic Ascent" (2023) is an original, no-AI image designed to convey this striking fact. www.diffgeom.com/product/post... www.diffgeom.com/product/viny... #MathSky #MathArt #SciArt

A unit grid of glowing green lines extends to the horizon in the black of space. The parabola y=x^2, plotted in blue with gold dots at integer points, looks perfectly circular. The parabola's equation in gold floats above the vanishing point.

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Just to note, I'm unable to access the article itself, and grateful for your summary!

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Separate hot take: I'd like to see mathematicians move away from eponyms ("Gaussian," "Eulerian," "Einsenstein,"...). 1. They're unevocative/confusing for students. 2. They're seldom historically accurate. 3. They're ambiguous ("Cauchy's theorem"). 4. They can be underwhelmingly insulting. #MathSky

I don't disagree with Kyle, but do think there is benefit to pictures that explicitly depict important symmetries. So: If fundamental domains were primary, I'd omit the third axes. Since conveying symmetries appears to be the point, I'd lean toward keeping the third axes.