Tag: Geometry

Osculating Circles Revisited

Every squiggly line could be an image of the meandering trajectory of a particle. At each instant, the path has a direction and a curvature. Curvature can be represented by the circle that fits the curve best – the osculating circle. In a two-dimensional world, the osculating circles would lie flat in the same plane…
Diamond Cubic

Once upon a time I analyzed electron diffraction patterns. They looked like this: These patterns are the inverse of the crystal lattices, sort of. The regularity of the dots represents the symmetries of the physical crystal. To identify the material causing a certain pattern, you compared it with sample patterns in a “database”. I am…
Hello, World – from Code to Canvas

I have promised to report on my progress with presenting my digital art on canvas. but I had been sidetracked by inverted drawings. So, I created a first – and very modest – descriptive geometry drawing by code: I have tried to explain here what this software does; it is very different from my other…
Drawing With Code

What does it even mean? I see two main ways of drawing with code: 1) going for a representation of a thing you have in mind, or 2) using an algorithm and elements of randomness to surprise you. Representational I have code-drawn Lissajous curves with code – from a picture in mind before I started.…
Coping with the AI Apocalypse

Painstakingly, I was putting the finishing touches on my analog geometric art – when this video popped into several of my social media feeds: We Need To Talk About AI… by Cool Worlds Podcast Cool Worlds Podcast is run by a team at Columbia University and usually features guests interviewed by physicist David Kipping. This…
Unearthing a Time Capsule and Preserving a Fading Cathedral

My first creative endeavors (as an adult) were not drawings or paintings. It was the early web that made me pick colors by hand and stitch together HTML code snippets. The web of the early 2000s was a very different place from the modern social media era, built from many small independent sites and blogs,…
My Posts Escaped. And So Did I! Or: Math is My Blanket!

I did maintenance work on my blog, touching all the posts. As my blog is also a Fediverse instance needed to take great care that changed blogs did not get posted there again. Of course, some of them escaped, and I had to post – again – writing about this! I found a workaround to…
$Hello to the Fediverse :)$

Hello to the Fediverse :)

Hello, people out there on Mastodon, Pixelfed, or whatever platform you use! You might have seen a weird collection of old posts reposted by my account today! Sorry :) This has been just me cleaning up minor stuff – not knowing that I have to turn off federation explicitly to avoid blasting out these old…
Poinsot’s Paper Spaceship (2025)

I’m presenting the recently completely series of artworks – and related physics blog posts – in its entirety! An ellipsoid is intersecting a sphere. Their intersection line is where the vector of angular momentum is seen to travel along – from the perspective of the spinning gyroscope. Four geometrical drawings, each based on the physics…
Geometry of the Physics of the Gyroscope – on a Coffee Mug!

Construct the Labyrinth from Which You Plan to Escape … has been the motto of the Oulipo movement, French writers and mathematicians who have boosted their creative writing by imposing arbitrary constraints. I had practiced Oulipo long before I knew the term. I just called it Search Term Poetry or Spam Poetry. I have been…
Evil Ellipsoids and Spheres (Poinsot’s Paper Spaceship #4)

Do you remember how photo negatives looked like? The inverted versions of the most common colors looked so unreal. Hues of orange, violet, or cyan that you never saw in the real world. Happy smiling human people looked like turquoise zombies with an evil grin. When creating this geometric drawing, I haven’t been thinking about…
Bumblebees and Ellipsoids (Poinsot’s Paper Spaceship #3)

In the movie Ice Age, Manny the Mammoth says he is not fat – just poofy! It is just the fur! I feel the same must be true for bumblebees – they are fluffy, but not really fat! And yes, these were the things going through my mind, when I created this geometric drawing: A…
Poinsot’s Paper Spaceship #1 – UFO

Louis Poinsot has a crater on the moon named after him … and now, also my series of geometrical drawings. I am taking the ellipsoid and sphere to the third dimension, based on the plan laid out before. Number 1 is an oblate ellipsoid, intersecting the sphere nearly in two circles. It is a classic…
Circles to Circles (2025)

Allow for a repost of sorts! I am looking back, revisting my just completed series Circles to Circles! Here are just the images and the links to all the blog posts with more physics, mathematics, and (sometimes) poetry! Six differently positioned circles, six different points of view. An attempt at showing the beauty of math…
Circles to Circles #5. Following the Rules.

Engineering is the art of creating solutions under constraints. The more rigid the constraints, the more creative you need to get. Art benefits from constraints, too. A long time ago, I discovered the joy of following – my own – silly rules when creating Found Poetry: Creating the labyrinth from which you want to escape.…
Circles to Circles #4. Stereographic Retrospective.

Circles to Circles is a series of six geometric watercolor pencil drawings. I have revealed number one, two, and three, and this is number four: On this blog, I have probably said anything I had to say about stereographic projection … using words, mathematical symbols, and drawings. Today, I rather create a retrospective: This is…
Circles to Circles #3. Using the Invisible Simple Box

When you do your geometry homework, everything fits nicely on a sheet of standard paper. Problems have been carefully designed to make this happen! I had never appreciated this – until I created my own geometry challenges. Either the different views were overlapping too much or interesting features were pushed beyond the edges of the…
Circles to Circles #2. A Friendly Death Star.

My art should speak for itself, as an abstract geometric drawing. But if you are so inclined, you can decode the math. Mathematics shows up twice: In the thing I am depicting, and in the techniques I am using to draw it geometrically. The series Circles of Circles is about stereographic projection of circles onto…