Andrew D Hwang

@diffgeom

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.

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Andrew D Hwang@diffgeom· 2d

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/

Andrew D Hwang@diffgeom· 9d

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.

Andrew D Hwang@diffgeom· 11d

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.

Andrew D Hwang@diffgeom· 12d

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.

Andrew D Hwang@diffgeom· Jul 19

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.

Andrew D Hwang@diffgeom· Jul 2

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.

Andrew D Hwang@diffgeom· Jul 1

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

Photograph of a microwave clock reading "End."

Andrew D Hwang@diffgeom· Jun 27

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.

Andrew D Hwang@diffgeom· Jun 21

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.

Andrew D Hwang@diffgeom· Jun 19

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.

The complex arcsine, an infinite stack of cross-joined, doubly-slit planes in shades of blue and bronze that meet along a glowing green vertical sine curve.

Andrew D Hwang@diffgeom· Jun 18

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.

Andrew D Hwang@diffgeom· Jun 13

The wall art image "Monuments, Fog" depicting (the real or imaginary part of) the complex exponential function, from near the origin looking along the positive real axis. www.diffgeom.com/product/roll... Browse all posters: www.diffgeom.com/product-cate... #MathSky #MathArt #SciArt

A brooding, monochrome digital landscape made of sine waves fading to white whose amplitude grows exponentially with distance, looking like massive piers of rock in fog.

Andrew D Hwang@diffgeom· Jun 8

Eight new limited-edition 2-3/4" stickers, including the designs shown. Price includes shipping! www.diffgeom.com/product-cate... #MathSky #MathArt #SciArt

Product scan of Seussian green plumes on a blue background with six-fold quasi-symmetry, flow lines of a (scaled) complex polynomial vector field.

Product scan of a black-and-white checkerboard of ellipses and hyperbolas defined by the complex sine function, with squares shrinking toward the common foci, which lie on the vertical axis. The sticker is kiss-cut, but has enough margin that it can be trimmed square.

Andrew D Hwang@diffgeom· Jun 7

Eight new limited-edition 2-3/4" stickers, including the designs shown. Price includes shipping! www.diffgeom.com/product-cate... #MathSky #MathArt #SciArt

Product scan of a circular sticker, a spiral design grading from bright green at the outside through shades of light-medium blue, to dark violet near the center, resembling a rounded, organic portal.

Product scan of a spherical black-on-white diatom-like string design with icosahedral symmetry.

Product scan of a spherical pattern comprising two families of latitudes relative to perpendicular axes through the equator; namely, coordinate curves when a sphere is written as a union of two graphs. The bottom hemisphere is green, the top is medium cyan, and the equator is gold.

Andrew D Hwang@diffgeom· Jun 6

Eight new limited-edition stickers, including the designs shown. Price includes shipping! www.diffgeom.com/product-cate... #MathSky #MathArt #SciArt

Product scan of warm red-gold rose curves on a sphere, resembling mitosis, illustrating a non-rotational conformal action.

Product scan of luminous reflecting gold rays in a dark blue disk, looking like a beacon blazing from a cusp-shaped peak.

Product scan of a lotus-shaped coordinate grid in moonlight colors from medium green-blue at the center to dark blue near the edge. The grid depicts a conformal mapping from the unit disk to the radially-slit unit disk.

Andrew D Hwang@diffgeom· May 24

You know how geodesic flow on a generic ellipsoid is chaotic...? www.diffgeom.com/product/unis... I sell exclusively at diffgeom.com. If you find my designs elsewhere, they were ... harvested. #MathSky #MathArt #SciArt

A product image showing a purple T-shirt with a nearly-circular design on the chest, a tracery of light blue-green curves, forming several caustics, on a faintly luminous blue-purple background.

Andrew D Hwang@diffgeom· May 20

For those of you evaluating real analysis books or self-studying, please consider An Invitation to Real Analysis: www.routledge.com/An-Invitatio... There is a 2-page "Clarifications and Corrections" linked here: diffgeom.org/books/index.... #MathSky #ITeachMath

The cover of "An invitation to Real Analysis." The bottom half depicts a fair but not cloudless sky edged in the bottom corners by reaching branches of tall oaks tinged with spring green. A torus wrapped by a blue-and-cyan solenoid curve of slope pi fills the sky.

Andrew D Hwang@diffgeom· May 12

When I was a student, descriptions of multi-valued functions by suitably-joined slit planes rankled. This frame attempts a more accurate portrait for the complex unit circle. The animation is here: mathstodon.xyz/@diffgeom/11... #MathSky #MathArt #SciArt

A graph of the complex unit circle looking like two crested dinosaur skulls base-to-base; the top half is gold mesh, the bottom is solid blue with gold coordinate curves. Below this surface sits a portion of the z-plane, the surface's image under projection along the vertical axis, in solid blue with gold coordinate curves. Three bright blue-green meteors trace closed loops around z=-1, z=1, and both point; continuous lifts of these paths are shown on the complex unit circle.

Andrew D Hwang@diffgeom· May 10

Typically a trefoil knot has 3-fold rotational symmetry. By suitably rotating a quarter turn in 4-space, however (using stereographic projection to/from the 3-sphere), we can instead arrange 2-fold symmetry about multiple axes: www.diffgeom.com/product/inti... #MathSky #MathArt #SciArt #Jewelry

Photograph of unboxing a pair 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.

Andrew D Hwang@diffgeom· Apr 26

Do you remember the fun of sending and receiving postal mail? Do your peeps think math is all about computation and formulas? Do you have a Secret Thing for conformal group actions? If so, order a set of math postcards today! www.diffgeom.com/product/you-... #MathSky #MathArt #SciArt

A set of 11 glossy picture postcards, each a looming digital mathematical overlay on an original landscape photograph, fanned out on a glazed tile surface. In the middle sits a gallery card showing all the cards in a 4x3 array.

Andrew D Hwang@diffgeom· Apr 24

These colorful nylon earrings, "shadows" of a singular disk in complex 3-space, would make a fine graduation gift for a math-loving Someone! I have a limited supply in stock. Price includes shipping within the US. 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 April with code DG1:
https://www.diffgeom.com/product-category/nylon-wearables/

Andrew D Hwang@diffgeom· Apr 22

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! www.diffgeom.com/blogs/about-... #MathSky #MathArt #SciArt

A frame-filling toroidal surface diagonally-colored by black and white squares like a 1950s diner floor.

Andrew D Hwang@diffgeom· Apr 19

Last month I completed a set of mathematical picture postcards. Each is a reminder that math is beautiful and powerful and larger-than-life, yet resides in the mind. Printed for snail mailing, but also suitable as small, inexpensive decor. www.diffgeom.com/product/you-... #MathSky #MathArt #SciArt

A 4x3 array of glossy picture postcards, each a looming digital mathematical overlay on an original landscape photograph. In the bottom left corner sits a gallery card of the same size. The assemblage exhibits the Droste effect to one level.

Andrew D Hwang@diffgeom· Apr 17

Luna has the shape of a cyclide banded by "diagonal" circles. (More in alt text.) I have a small number in stock, and would be delighted to find new happy homes for them! www.diffgeom.com/product/luna... Use "DG1" at checkout through April for 10% off. #MathSky #MathArt #SciArt #Jewelry

A 1 inch (25mm) rhodium-plated brass 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.

Andrew D Hwang@diffgeom· Apr 3

When clouds drop below a distant horizon at our elevation or lower, we see curvature of the earth. #MathSky #MathArt #SciArt

A photograph of a sky dotted with cumulus to the horizon. Amidst the clouds, as if present in the scene, floats a large torus tessellated by blue-purple hexagons.

Andrew D Hwang@diffgeom· Mar 30

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

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.

Andrew D Hwang@diffgeom· Mar 28

Help me celebrate 1 year of my shop's new look: Through April, everything at diffgeom.com is 10% off with code "DG1"! <> Luminoso is a 1-1/2 inch (40mm) rhodium-plated brass pendant in the shape of a cyclide banded by "diagonal" circles. www.diffgeom.com/product/lumi... #MathArt #SciArt #Jewelry

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.

Andrew D Hwang@diffgeom· Mar 19

"Bubble," a postcard image (digital overlay) depicting a seductive sham of apotheosis. 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. #MathSky #MathArt #SciArt

An enormous transparent sphere looms over frozen water and a distant shore under a foreboding sky. Gray spiral bands swoop upward toward a bright spot at the zenith. Beautiful mathematics to some; a dangerous sham promise of power and apotheosis to others.

Andrew D Hwang@diffgeom· Mar 16

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. #MathSky #MathArt #SciArt

A photograph of a frozen body of water with tall evergreens on the near shore and rays of sun streaming through broken clouds. The sky is filled by a torus whose surface is a purple-green jeweled honeycomb.

Andrew D Hwang@diffgeom· Mar 8

Working on a set of mathematical postcards, both digital "scenes" and overlays on photos. Here we see the parabola y=x^2, a conic section, as a circle. For now this is a 3-inch matte black self-adhesive sticker: diffgeom.com/products/par... #MathSky #MathArt #SciArt