Tag: Mathematics

Reality and Imagination

Reality and Imagination is a series of thirteen images generated by custom, hand-crafted computer code. Each image shows the same virtual sculpture from a different viewpoint. I call it virtual as its shape is solely defined by a mathematical function – an object existing in the human mind, in the platonic realm of ideal objects.…
Geometry of the Motion of a Free Prolate Gyroscope (and the Power of Magnets)

How should I spin the story of the gyroscope this time? Imagine, you have a wonderfully crafted elongated ellipsoid from wood (shaped like a rugby ball). You built some apparatus that make it spin fast about its major axis. Probably you can make it spin with your bare hands – or you ask a tentacled…
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…
Mass Shell

Space and time are rotated into each other. Momentum and energy are as well. This rotation in four dimensions is of an unusual, hyperbolic kind. Which is the source of all so-called paradoxa in special relativity. Best to avoid thinking of clocks, rulers, trains, and observers. Just stick to the geometry. When a classical particle…
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…
Vintage Temperature Waves

There might be three people among my active followers who still remember when this blog was primarily about hard science and tech – without artistic adornments. These were the glory days of the internet, in the early 2010s. When social media had not yet defeated small blogs. We had our German heat pump and energy…
Dare to Be Negative!

Do you remember analog photo negatives? I still have some, tucked away deep in the archives. I always found them eerie and uncanny. Humans turned into zombies with black teeth. Burnt orange, weird cyan and violet everywhere. But what did I expect? We don’t have an intuition for addition or subtraction of colors. Would you…
Circles to Lines (2026)

Circles and lines – that sounded manageable. So, this was one of my first attempts at reviving descriptive geometry. A circle on a sphere is projected into a circle in the equatorial plane under stereographic projection. But if the source circle contains the North Pole, the projection ray in this point becomes tangent to the…
Archaic Mathematical Art – and Poetry – from Code

What is the simplest way of creating art with code? I have been using software frameworks for mathematics and graphics in the past year. They “abstract away” how you actually place the dots on the virtual canvas. But I want something ancient, with a clear-cut boundary. My choice is the language C: created in the…
Rolling Not Slipping – Story of a Twirling Ellipsoid

I can’t help it – I use the first title that pops into my mind! “Rolling, not slipping” is the punchline of a mathematical argument used in classical mechanics, in the theory of the motion of a gyroscope. But I am not going to do it justice in this blog post (apart from a math…
Futuristic T-Shirts for Physics Geeks!

Have I started the elkement.art fashion brand? I have been working on the series Poinsot’s Pixel Spaceship for ages. I have been thinking about releasing wall art, but then I tested a different product – the classical print-on-demand product: T-shirts. And THIS WAS IT! This is the perfect surface I want to print this spaceship-like…
Friendly Sparkling Alien Spaceships

I know, I am again using this metaphor! But once I saw the friendly alien spaceships in these images, I could not unsee them! There is more background information about these sparkling ellipsoid and spheres in my previous post. Today I only want to show you number 2 and 3 in this series of four…
Saying Hello to New Subscribers and Introducing Poinsot’s Pixel Spaceship!

A bunch of you have signed up recently here or via my new store, or you started following this blog via platforms like Mastodon (in the Fediverse)! Thanks a lot for following elkement.art! I want to welcome you all and give you an overview of what to expect here! I have been blogging since 2012,…
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…
LinkedIn Timeline Poetry: Are You Prepared to Own?

Today, I am finding poetry in the posts in my LinkedIn feed! I check out the first post in my feed and pick a short snippet of text without editing it. This becomes the first line of the poem! Only after the first line is cast in stone, I visit the next search result and…
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…