diffgeom - Network

One of many ways to depict an infinite binary tree.https://diffgeom.com/products/binary-medallion-gold-wall-art-poster#Math #MathArt

One of many ways to depict an infinite binary tree.

https://diffgeom.com/products/binary-medallion-gold-wall-art-poster

#Math #MathArt

Has anyone re-joined Shapeways? If so, has anything noteworthy changed?#3dPrinting #math

Has anyone re-joined Shapeways? If so, has anything noteworthy changed?
#3dPrinting #math

Conic sections cut in a fixed horizontal plane by a rotating...

Conic sections cut in a fixed horizontal plane by a rotating cone.

https://diffgeom.com/products/conic-sections-phosphor-wall-art-poster
https://diffgeom.com/products/conic-sections-phosphor-unisex-short-sleeve-t-shirt
#Math #MathArt

Conic sections cut in a fixed horizontal plane by a rotating...

Conic sections cut in a fixed horizontal plane by a rotating cone.

https://diffgeom.com/products/conic-sections-forge-wall-art-poster
https://diffgeom.com/products/conic-sections-forge-unisex-short-sleeve-t-shirt
#Math #MathArt

While looking for something else, I recently came across a bit of physics memorabilia, a poster for a lecture at UC Berkeley by Hans Bethe....

While looking for something else, I recently came across a bit of physics memorabilia, a poster for a lecture at UC Berkeley by Hans Bethe. The physical sciences lecture hall was overflowing. What stays in memory are (i) Bethe's energy unit for a supernova, the "foe" for (ten to the) fifty-one ergs, and the fact that neutrino pressure (!!) is substantially responsible for blowing off the collapsing star's outer layers.

#Physics #Astrophysics #Math

At the start of October 2024, I agreed to rework an introductory real analysis manuscript for CRC Press. Yesterday I delivered the...

At the start of October 2024, I agreed to rework an introductory real analysis manuscript for CRC Press. Yesterday I delivered the manuscript. Details will follow in coming weeks as they become available.

If you teach introductory/intermediate real analysis, or are a school teacher looking for a friendly desk reference, please do consider the book. It relies systematically on adversarial games to explain the definitions of analysis: limits, continuity and uniform continuity, integrability, compactness,.... There are over 630 exercises, many with answers/solutions in the back. A complete solution manual will be available to instructors.

The book starts with chapters on the language of mathematics and on the natural numbers, then gives axioms for the reals and works its way through the fundamental theorems of calculus, construction of elementary functions, metric spaces, and a sampling of approximation theorems (including construction of the reals as a completion of the rationals). Everything (except sets and elements) is defined, and aside from the division algorithm for integers, everything is proved. There are fun destinations, including transcendentality of \(e\), an analytic definition of \(\pi\), the many faces of exponentiation, the product-of-chord-lengths theorem in the unit circle, irrational windings on a square torus, and the evaluation of \(\zeta(2n)\) for positive integer \(n\).

I took considerable care with self-containment and internal consistency, logical structuring, simplicity and expository clarity, navigability, and other matters. Whether my intentions succeeded, naturally, is up to you, the reader.
#math #mathematics #ITeachMath

If \(\alpha\) is irrational, the path\[(x, y) = (\cos t + \cos(\alpha t), \sin t + \sin(\alpha t))\]maps the real line to a dense subset of...

If \(\alpha\) is irrational, the path
\[
(x, y) = (\cos t + \cos(\alpha t), \sin t + \sin(\alpha t))
\]
maps the real line to a dense subset of the disk of radius \(2\). If we plot points for regularly-spaced \(t\), with spacing not a rational multiple of either \(2\pi\) or \(2\pi/\alpha\), we get some indication of the geometry of this path, and how sensitively it depends on \(\alpha\).

If you have a minute (60 frames at one frame per second), each image shows the result of plotting points with \(t\) an integer, starting at \(0\) and with \(100\) points in each of \(60\) shades from red to gold. As we step through the frames, the real parameter \(\alpha\) increments along an interval of length \(1/10\) centered at \(\sqrt{3}\).

#Math #MathArt

Artist and artists' rights activist Jingna Zhang recently gave a talk at NeuIPS (in the workshop on Creativity and Generative AI) titled...

Artist and artists' rights activist Jingna Zhang recently gave a talk at NeuIPS (in the workshop on Creativity and Generative AI) titled "Photography, Go, and AI." Highly recommended:

https://www.zhangjingna.com/blog/2024/12/20/photography-go-ai

Reading the words of some of the world's most skilled Go players, one can hardly avoid thinking of Kyuzo in Kurosawa's Hachi no Ronin (The Seven Samurai) who, having devoted his entire life to mastering the art of sword-wielding, is shot in the back at a distance by a cornered bandit.

#AI #MachineLearning #LLMs

A poster image showing units mod \(n\) for \(2 \leq n \leq 50\). A version of this image appears in the book "Sets, Groups, and...

A poster image showing units mod \(n\) for \(2 \leq n \leq 50\). A version of this image appears in the book "Sets, Groups, and Mappings," written for a one-semester algebra-based introduction to proofs for math majors.

https://bookstore.ams.org/amstext-39

#math #mathematics #MathArt

An animation loop inspired by a new poster image "Crystallogram" but with fewer dots, seen from farther away, and reframed, shows...

An animation loop inspired by a new poster image "Crystallogram" but with fewer dots, seen from farther away, and reframed, shows a cube of points as we move in a circle around the vertical axis.

https://diffgeom.com/products/crystallogram-wall-art-poster

#Math #Mathematics #MathArt

Jewelry discounts of 10-60% continue at Differential Geometry! I'm hoping to find happy homes for 2024 inventory, as well as for unique...

Jewelry discounts of 10-60% continue at Differential Geometry! I'm hoping to find happy homes for 2024 inventory, as well as for unique pieces and seconds. Orders to the US placed in the next week should arrive well in time for the holidays.
https://diffgeom.com/collections/earrings
https://diffgeom.com/collections/pendants
https://diffgeom.com/collections/the-workshop
https://diffgeom.com/collections/jewelry-seconds
https://diffgeom.com/collections/nylon-adornments

https://diffgeom.com/

#math #Mathematics #Jewelry

The Mathematical Art Digital Exhibition (MADE) at Queens College (CUNY) is live, and features work by at least a few people at...

The Mathematical Art Digital Exhibition (MADE) at Queens College (CUNY) is live, and features work by at least a few people at Mathstodon:
https://math.qc.cuny.edu/made-gallery
A huge Thank You to @mathzorro!
#math #mathematics #MathArt

A limited number of jewelry seconds at Differential Geometry need and deserve good homes, and are priced to sell with discounts of 40 to...

A limited number of jewelry seconds at Differential Geometry need and deserve good homes, and are priced to sell with discounts of 40 to 60%. In most cases, a piece's contours diverge slightly from the mathematical ideal.

https://diffgeom.com/collections/jewelry-seconds

#MathArt #Jewelry

https://diffgeom.com/products/pulse-sculpture-aluminum#math #mathematics #MathArt

https://diffgeom.com/products/pulse-sculpture-aluminum

#math #mathematics #MathArt

I'm regretfully shelving the Anemone family of jewelry designs indefinitely. Each piece was made of gold-plated brass by Shapeways....

I'm regretfully shelving the Anemone family of jewelry designs indefinitely. Each piece was made of gold-plated brass by Shapeways. There is one of each Anemone pendant (18K) and two brooches (rose or 18K) in the shop.

All jewelry at Differential Geometry is discounted (an additional) 10% from the shop price through 2024, subject to stock.

https://mathstodon.xyz/@diffgeom/112813138293077973 (Anemone 5,2)
https://mathstodon.xyz/@diffgeom/112685156749488663 (Anemone 7,2)
https://mathstodon.xyz/@diffgeom/112702623307692990 (Anemone 7,2)
https://mathstodon.xyz/@diffgeom/112735255946839247 (Anemone 7,3)
https://mathstodon.xyz/@diffgeom/112785153507944239 (brooches)

https://diffgeom.com/collections/earrings
https://diffgeom.com/collections/pendants
https://diffgeom.com/collections/the-workshop

#math #mathematics #MathArt #Jewelry

Laser-cut aluminum struts for a 6.5-inch version of "Pulse" arrived. There was some hope of selling user-built kits, but it turns...

Laser-cut aluminum struts for a 6.5-inch version of "Pulse" arrived. There was some hope of selling user-built kits, but it turns out aluminum is harder to assemble than fiberboard, and does not hold together by friction. I expect to have a couple of assembled models ready for sale in the near future.

#math #mathematics #MathArt #3D #LaserCutting

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...

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

"Pulse" is a new T-shirt and poster design at Differential Geometry, a portrait of the graph\[z = \frac{x\sin\sqrt{x^{2} +...

"Pulse" is a new T-shirt and poster design at Differential Geometry, a portrait of the graph
\[
z = \frac{x\sin\sqrt{x^{2} + y^{2}}}{\sqrt{x^{2} + y^{2}}}
\]
sliced parallel to the \((x, z)\)-plane.

https://diffgeom.com/collections/pulse?_pos=1&_psq=Pulse

#math #mathematics #MathArt

In anticipation of the approaching holidays and as a loose first birthday card for mathematical jewelry designs at Differential Geometry,...

In anticipation of the approaching holidays and as a loose first birthday card for mathematical jewelry designs at Differential Geometry, I've assembled a postcard-sized gallery showing the shop's regular offerings. (Not shown are nylon designs and production-ready prototypes.)

As you shop for the math-loving people in your life, please consider supporting artists and designers here and elsewhere on social media!

diffgeom.com

#Math #Mathematics #Jewelry

Differential Geometry has an ever-growing variety of mathematical images on posters (and other wall art) and T-shirts (as well as hoodies...

Differential Geometry has an ever-growing variety of mathematical images on posters (and other wall art) and T-shirts (as well as hoodies and sweatshirts), now including kids' sizes! My mission is to design images that are appealing to non-mathematicians, but also inviting the mathematically-curious into further engagement and study.

As you holiday-shop for the math-lovers in your life, please keep me and other small shops at Mathstodon and elsewhere in mind!

https://diffgeom.com

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The shop's newest item is hand-boxed holiday cards, featuring the mathematical image "Winter Light." Although this image was designed as an offering of peace and beauty rather than primarily as mathematical illustration, it does contrast complex analysis (the orb quasi-tesselated by loxodromes -- the image of a Cartesian grid under suitable complex exponentiation) and real analysis (the ranges of virtual mountains approximating a Weierstrass continuous, nowhere-differentiable function), using five-pointed stars to suggest quasi-crystalline snow:

https://diffgeom.com/products/winter-light-greeting-cards-box-of-10

#math #mathematics #MathArt