Andrew D Hwang

A digital image of a blue-and-cyan banded doughnut overlaid on a photograph of a spring sky bordered by oak trees breaking out in catkins The book's dedication reads, "For everyone possessed of curiosity, honesty, and kindness." The image extends the dedication visually. Math, particularly real analysis, seems larger than us, yet is insubstantial, a creation of minds. Like all human creations made with good intent, math can be weaponized. Publishing a textbook that aims to present a body of traditionally-difficult material is therefore potentially perilous. But there is no way to publish or teach without risk; one can only be explicit about the perils, and enjoin learners to steer clear.

"Vortex" is a remake of the cover image of "An Invitation to Real Analysis" as a postcard. The looming sky torus is the image of a ray of slope π on a square torus, with color along the ray graded to highlight π~=22/7.

www.routledge.com/An-Invitatio...

#MathSky #MathArt #SciArt

Collage of five geometrical drawings - colored in the style of stained glass with watercolor pencils. Orthographic projections of functions used in physics, constructed from their 2D projections: Cones related to the theory of the gyroscope, Lissajous Figures, spins and stereographic projection, a mathematical tower from a spherical harmonic function.

I am using traditional descriptive geometry and watercolor pencils to turn functions used in physics into cathedrals from stained glass.

#MathArt #SciArt

A spherical steel sculpture in a rotating U-mount gleams in the autumn sun. The sphere is divided into hemispheres, each divided into 24 latitude semicircles. The hemispheres' poles are orthogonal.

👀 Looking forward to seeing the final piece!

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Some months back a former colleague took me to an exhibition of George Sherwood's sculptures. "Wind Sphere" comes naturally to mind:

www.georgesherwood.com/outdoor-scul...

#MathSky #MathArt #SciArt

Large hanging crochet granny square artwork with a red theme

Day ☀️♥️

A shiny banded toroidal pendant in an open jewelry box, next to a box top reading Differential Geometry, sitting on a red earth-toned glazed tile surface.

Luminoso is a 1-1/2 inch (40mm) rhodium-plated brass pendant in the shape of a cyclide banded by "diagonal" circles. I have a limited number in stock, and would be delighted to find new happy homes for them!

www.diffgeom.com/product/lumi...

#MathArt #SciArt #Jewelry

Our International Day of Mathematics events includes 2 special magic shows by Tadashi Tokieda at the Chau Chak Wing Museum on Sat 14 & Sun 15 March 12:30 pm

'A magic show' will be for both curious children 🧒 & seasoned scientists alike! 🪄👩‍🔬 🎩

🧮 events.humanitix.com/a-magic-show...

#MathSky

A shiny gold knot with six-fold rotational symmetry in an open jewelry box, next to a box top reading Differential Geometry, sitting on a red earth-toned glazed tile surface.

Harmonia is a 1-3/8 inch (35mm) 18K gold-plated brass pendant in the shape of a torus knot. I have a few left in stock, and would be delighted to find new happy homes for them!

www.diffgeom.com/product/harm...

More about the math:
www.diffgeom.com/blogs/about-...

#MathArt #SciArt #Jewelry

Thank you kindly! 🥰

Abstract art coloring page with pattern of many concentric and overlapping circles.

Looks like my coloring pages are getting popular on Pinterest again.

If you like my Procedural Art coloring pages, inspired by Chemistry and Physics, please buy them from ME instead of someone who stole them from me.

www.patreon.com/posts/858020...

#SciArt #art #Coloring #ArtForSale

A shiny banded toroidal pendant in an open jewelry box, next to a box top reading Differential Geometry, sitting on a red earth-toned glazed tile surface.

Luminoso is a 1-1/2 inch (40mm) rhodium-plated brass pendant in the shape of a cyclide banded by "diagonal" circles. I have a limited number in stock, and would be delighted to find new happy homes for them!

www.diffgeom.com/product/lumi...

#MathArt #SciArt #Jewelry

Thank you for trying out the software!

I'm afraid that (unlike with Pirouette, the Spirograph clone) there's currently no path editing capability. Adding that is on a nebulous to-do list (along with a mode for drawing line segments by clicking their endpoints, IIRC)....

Come to think of it, the same is true of the two non-discrete, non-trivial topologies on a 2-point space, right?

But still....

A screenshot of the program Torus Sketch. On the left is a square scribbled landscape containing a tree, hills, and sky; four translated copies of this scene are visible, two side-by-side, the other two split between the top and bottom of the frame. On the right, the tree, hills, and sky are wrapped around a torus. The tree's trunk reaches through the central hole, the leaves extend over the back at the top, and the sky wraps around the entire outside.

A simple interactive program for drawing on a torus, written in response to a math.stackexchange question. Mathematically, we see the flat plane as a conformal universal cover of a circular torus. Read more:
www.diffgeom.com/blogs/free-o...
#MathSky #ITeachmath

Thank you!

A photograph of a sunset over water, superimposed with a digital image of a sky-filling minimal surface the color and approximate size and shape of a thunderhead.

A shipment of postcards arrived today. Not yet decided whether to put them in the shop (as a wish-you-were-here collection after getting other designs printed), or to use them for promotion.

If you're willing to comment: Do you ever send postcards and/or greeting cards?

#MathSky #MathArt #SciArt

Apparently while I was asleep, part of my brain came up with:

Textbooks are read
Analysis is pleasurable
Unless you bumble into
A set that's non-measurable.

0.5*(🤔+😳)

#MathSky

Part of my confusion is, "Must the solution path start at A and end at B?" Because that does not appear compatible with the stated constraints. (If we can start and end on white squares neighboring A and B, however.... :)

A large orange sphere in the abstract style floats against a graded ocher background.

I have a thing for round spheres, not least because 1. extremal Kähler metric, and 2. isometrically embeds in real 3-space. This fetching (if I may say so) digital image arose unexpectedly in January 2026.

www.diffgeom.com/product/roll...
www.diffgeom.com/product/canv...

#MathSky #MathArt #SciArt

A Phosphene board as seen in the program's interface, comprising a black-on-gold pattern resembling a quincunx of shadowed pyramids seen from directly above. On closer inspection, the board is an 8x8 grid of identical square tiles, each divided diagonally into two right isosceles triangles, half black, half gold.

Over my years in academia, I wrote or helped create a variety of free online mathematical materials. Phosphene is a meditative geometric solitaire that runs in a web browser. I hope you and your students enjoy the software! Read more:
www.diffgeom.com/blogs/free-o...

#MathArt #MathSky #ITeachmath

Probably ought to have bleeted this poster image a week or two back.... 🤔

www.diffgeom.com/product/roll...

#MathSky #MathArt #SciArt

A Pirouette design with 11-fold symmetry, comprising eight bands grading inward from cyan to violet. Successive bands effect counting mod 11 by successive integers starting with 2.

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:

www.diffgeom.com/blogs/free-o...

#MathArt #MathSky #ITeachmath

First page of 'Paperclip graphs', available at https://mathweb.ucsd.edu/~ronspubs/pre_paperclip.pdf. Figure 1 depicts a magic trick that starts by "Putting two paperclips on a strip of paper shaped as an S curve."

Figure 4: From a strip with paperclips to sets of nonintersecting arcs. (a) Strip with paperclips. (b) Starting to pull apart. (c) Making the strip taut.

Figure 5: Going from a set of arcs to a strip with paperclips. Figure 6: Circular representation for arc configurations.

Work tasks today included thinking about a magic trick and Catalan numbers at the same time — living the dream!

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/

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 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/

Any of these delicate earrings would make a fine treat for a math-loving someone in your life. All my jewelry is 15% off with code Bsky26 through Feb 14. Shipping to the US normally takes at most 5 business days.

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

More in alt text.
#MathSky #MathArt #SciArt #Jewelry

Red 20mm nylon earrings in the shape of knotted bands having 7-fold rotational symmetry.

Purple 20mm nylon earrings in the shape of knotted bands having 7-fold rotational symmetry.

Pink 20mm nylon earrings in the shape of knotted bands having 7-fold rotational symmetry.

Through Feb 14, all my nylon earring designs are 15% off with checkout code Bsky26. Orders to the US that ship Monday should arrive comfortably before the 14th.

Anemone is a stylized representation of the complex 2/7-power.

www.diffgeom.com/product-cate...

#MathArt #SciArt #Jewelry #3DPrinting

Filtering Snowflakes Whether you call this triangle Pascal's triangle, Binomial Expansion Coefficients, Yang Hui's triangle, or any other name, it is beautiful. Finding patterns in this triangle is fun - from counting nu...

New post on Fractal Kitty:

www.fractalkitty.com/filtering-sn...

#mathart #pascalsTriangle #binomialExpansion #mtbos #snowflakes #iteachmath

Thank you! I probably ought to have mentioned the torus is a solenoid of slope pi, colored along its length by a gradient from cyan to purple, so the continued fraction of pi starts to emerge, e.g., the prominent banding comes from 22/7 :D

A paperback copy of "An Invitation to Real Analysis" sitting on a glazed tile table. The cover image shows a banded torus filling a lightly-clouded spring sky bordered by trees.

Copies of "An Invitation to Real Analysis" arrived today. (The book came out last September.)

If you're evaluating books for an introductory real analysis course, I'm grateful for your consideration.
www.diffgeom.com/blogs/around...
www.routledge.com/An-Invitatio...

#MathSky

Just to confirm, an "iceberg" is a polygon with integer points as vertices, and with sides that are horizontal, or vertical, or of absolute slope 1?

Through February 14, use the code Bsky26 at checkout for 15% off all my in-stock nylon earring designs.

Shipping within the contiguous US is free, and normally takes no more than 5 business days.

www.diffgeom.com/product/vola...
www.diffgeom.com/product-cate...

#MathArt #SciArt #Jewelry

Thank you kindly!