The complex unit circle as a two-sheeted cover of the plane with two rays removed

New Items and Future Directions

As we hope you've seen browsing the Differential Geometry math art shop, we like light, color, and shape, and we strive to create mathematical images that surprise the eye!

We're steadily introducing new images on apparel and wall art. We also now offer lines of greeting cards. We'll be introducing more sticker designs in the near future. In the coming months we expect to develop and offer wearable objects: pendants, earrings, and pins. For the longer term we're working on desktop models, many of them solid versions of our existing images.

In the direction of public outreach, we continue to blog about math. The goal is admittedly ambitious: To start from mathematics many school students encounter in some form (such as Cartesian coordinates in the plane, functions, and graphs, or perhaps circles and trigonometry), explained in simple, concrete, welcoming terms, and to build short, friendly bridges toward the mathematics behind our images. These bridges are necessarily selective, but are written to serve in part as guides for further reading elsewhere.

If anything in a post is unclear, ask in the comments! There is no shame in not understanding, and there is benefit for everyone to clarify what is unclear. Your feedback is the fastest way explanations will smooth out to become more valuable for posterity.

Incidentally, we were delighted to learn that mathematical notation can be included in product descriptions and blog posts! Huge Gratitude to Davide Cervone, and everyone who contributes to MathJax!

Even inline notation, such as being able to write the Golden ratio as \(\phi = \frac{1}{2}(1 + \sqrt{5})\) (rather than, say, phi=(1/2)*(1+sqrt(5))), helps keep mathematics clean and manageable. But as the needs for notation become more intensive, conventional notation will become decisive in conveying understanding.

(A note to the math-averse among you: Cartoonists have depicted scientists' and mathematicians' blackboards as thickets of algebraic scrawls for many decades. There is truth to this image, but it results from hasty erasure and expedient fitting of jottings into gaps. The point of notation is clarification, not intimidation! Truthfully, a professional scientist or mathematician does not glance at a complicated, unfamiliar notational expression and learn anything in detail. Instead, mathematical expressions, equations, and inequalities have recursive structure that can be typographically complicated when fully expanded. When we come to expressions of that type, the recursive structure will be expained in bite-sized pieces.)

Our special introductory prices continue through August 2023. We hope browsing our catalog continues to inspire and delight!

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