#descriptivegeometry — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #descriptivegeometry, aggregated by home.social.
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Spherical Harmonic
You can build rectangular pulses from wavy sine and cosine functions. You can decompose any function into its harmonics. You can do the same for functions that live on a sphere: Cover the surface of the earth with flag poles, and raise flags everywhere - gradually varying the exact height of the flag. How the position of the flag depends on longitude and latitude - this is the function. If the height varies smoothly from flag pole to flag pole, this is a well-behaved function of the kind […] -
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 alien for help. The symmetry axis of the body, the axis of rotation, and the vector of angular momentum are all aligned. You or the alien or the apparatus fling the ellipsoid into the air, […] -
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 the tangent vectors are confined to. But in three dimensions also the "instantaneous plane" of the motion is changing. There are three vectors that describe the path in each […]https://elkement.art/2026/07/29/osculating-circles-revisited/
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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 moves (classical in the sense of "non-quantum", but relativistic), it is constrained to the mass shell: a three-dimensional hyper-surface in the […] -
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 "expect" red and green adding up to yellow? The exact opposites of our usual, friendly red-yellow-green-blue are uncommon in the real world. I once tried to create […] -
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 sphere and parallel to the equatorial plane. Thus circles containing the North Pole are projected into lines - circles with infinite radii. The drawing shows this […] -
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. I saw the curves as built from wires as thin as possible, or as thick metallic tubes. I have been lucky that I mathematical objects can be compressed so well into code. It would be way more […] -
Vertical exaggeration (Cartography 🗺️)
Vertical exaggeration is a scale that is used in raised-relief maps, plans and technical drawings, in order to emphasize vertical features, which might be too small to identify relative to the horizontal scale.
https://en.wikipedia.org/wiki/Vertical_exaggeration
#VerticalExaggeration #Cartography #DescriptiveGeometry #TopographyTechniques
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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, and I am using orthographic projection as a tool. In a sense this is "orthographic projection of stereographic projection" Circles to Circles #2 by elkement 2025, […]https://elkement.art/2025/05/22/circles-to-circles-2-a-friendly-death-star/
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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 Geometry books. "DG" was taught for the two last years of high school, in grade 7 and 8 (age 17 - 18). I remember it as pure delight - learning how to depict three-dimensional objects […]https://elkement.art/2025/05/16/circles-to-circles-1-on-descriptive-geometry/