Category: Physics

I am thinking out loud about well-known mathematical physics. Re-learning an re-viving the basics again and again.

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…
Aharonov-Bohm Effect

It is often called the simplest example of topology impacting physics (Topology like “the shape of space”, like coffee mugs being donuts!). Charged particles move under the the influence of electric and magnetic fields. The concept of fields was once introduced to replace action at a distance: If one charge tugs on another, it does…
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…
Postal Scales Now and Then

I’ve tried to stage it properly. But it just looks sad. Functional – and not inspiring: The white plastic casing already starts to yellow at the top, from years of bombardment with UV photons. Its function in our office had been replaced … by not sending invoices or contracts on paper anymore. Edit: The original…
Poetry: Representations

Finally, a revelation! I was asking myself: Why do I often find ancient, terse, illustration-free textbooks easier to follow than their modern, friendly, playful, illustrated, multi-media-enhanced counterparts? Case in point (and I know that not everybody will agree): Paul Dirac’s legendary Principles of Quantum Mechanics or the definitive course on theoretical physics, the volumes by…
Magneto Compass – Inverted Art

It has been quite a while since I have drawn my antique rotary phone as “negative art”. This phone features white letters on black background. At that time I had no idea that white gel pens exist, for drawing such letters. So, I “invented” inverted art – as usual, only to discover that many artists…
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…
Coffee-Powered Stargate

Let me open the Stargate of Diffraction for you, once again! This is as close as I ever got to a plain scientific visualization: No 3D effects, just the intensity of diffracted radiation as a function of position in space. If you use a sun catcher – a film with a diffraction grating – 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…
Spinning Projection – a Tiny Canvas Print, a Long Time in the Making

These spheres and lines have been haunting me. I have been writing about stereographic projection so often – and created so much related geometrical art – that I created a blog post just for curating all the links to my own articles: Stereographic Retrospective. This year, I have created a series of six drawings of…
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…
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…