Tag: Drawing

Celebration of Dispersion

Light is economic. It takes the minimal path. It follows the Principle of Least Time! When light is reflected, the angles of incidence of original ray and reflected ray are the same. This might seem natural. But you can derive it from the Principle of Least Time – also called Fermat’s Principle. If we want…
Dirac’s Belt Trick Through the Years

2021 It started with a humble sketch. This has been the first time I drew something after decades of not touching pencils or brushes. It kicked off an obsession – with art in general, but also with Dirac’s Belt trick. The trick is a demonstration of the underappreciated weirdness of rotations in three-dimensional space. You…
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…
First Encounter

You try to find an object to draw. Ideally, it should already sit on your desk! Ideally, it should be translucent and sparkling! You try to make it look interesting… Adding little rainbows, perhaps? No sun today, so: Fetch the replacement sun! The spectrum of a flashlight is duller than that of the sun. The…
Poinsot’s Paper Spaceship #2 – Zeppelin: Unstable Rotation About the Intermediate Axis.

Subtitle: Why UFOs are more stable than zeppelins. This UFO… … tells a story of rotation. The yellow ellipsoid encapsulates the main features of a rotating rigid body: Its moments of inertia, that is: how masses are distributed in relation to three principal axes. The moment of inertia is larger, if more mass is positioned…
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 #6. The Making Of.

Number 6 is the last one in my series about stereographic projection! In this post, I am looking back at the creation of the whole series! It has started with messy sketches: How to fit the sphere and the circles onto a small sheet of A5 paper? How to make all six of them distinct…
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 – Digital Interlude

I wanted to know: How would it feel to replace ruler and compass with the straight lines and circle tools of drawing software? Procreate (the iPad drawing software) does not have anything like a compass. You cannot measure the length of a line segment either, or parallel transport lines exactly. You can create perfect circles…
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…
Circles to Circles #1. On Descriptive Geometry.

I am not a hoarder. I parted with school memorabilia long ago. When I started reading books on e-readers, the remaining books felt like an odd time capsule. They were not representing my reading self anymore. So, I got rid of most books, too. There was one exception: I still have my high school Descriptive…
The Two Sides of Physics

Classical physics might not get its fair share of attention in contemporary science writing. But it can feel every bit as weird and awe-inspiring as so-called mysterious and spooky quantum mechanics! Statistical physics introduces you to spheres in trillions of dimensions whose volume is concentrated in a thin layer beneath their surfaces. Our intuition fails…
Poinsot’s Gyroscope and the Magic of Precession.

Nobel prize winners have been fascinated by it: You can learn about the underlying mathematics. You can solve differential equations. But do you really feel why it does not fall? When gravity tries to topple a spinning top, the top escapes sideways, sort of, by precessing: The axis of rotation is changing slowly. There is…
“The Over-All Space-Time View”

… is an expression Richard Feynman had used in his 1949 paper Space-Time Approach to Quantum Electrodynamics. It seems to be one of the earliest publications featuring his famous diagrams. Feynman diagrams are related to interactions of particles, and they look like cartoon illustrations of particles bumping into each other. But they are actually mnemonics…
Circles to Circles – a Series in Progress

When I started creating mathematical artworks with code, the result was a series: I developed a virtual 3D sculpture, looked at it from different viewpoints with my virtual camera … and could not decide which “snapshot” I liked best. So, I panned and pivoted my camera and shot up about 10 different still images along…