iiinova — where your digital self keeps evolving

Dave Richeson @divbyzero.bsky.social · 3h

I wanted to see how my calculus students could do creating a closed piecewise parametric curve for an impossible object. They made one side and could choose one of my shapes for the other side. Then I printed the objects. It went well, and I think I can ramp it up a little bit and

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Dave Richeson @divbyzero.bsky.social · 9h

My morning walk to work across the Dickinson College campus.

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Dave Richeson @divbyzero.bsky.social · 18/09/2026

Here are a few more impossible objects. This time, I printed the stand in black and the object in another color. It adds a lot of print time, but I like the final version better.

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Dave Richeson @divbyzero.bsky.social · 17/09/2026

Today in Multivariable Calc, I mentioned the connection between the cross product and quaternions. So I showed them a photo of me with the Hamilton plaque in Dublin from this summer!

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Dave Richeson @divbyzero.bsky.social · 14/09/2026

In contrast, this is the "horizontal" version of the cloud/lightning bolt.

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Dave Richeson @divbyzero.bsky.social · 14/09/2026

Over the weekend, I had an idea: what if, instead of the objects appearing to sit horizontally in front of you, I modified them to appear vertically? Here are four test attempts.

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Dave Richeson @divbyzero.bsky.social · 11/09/2026

Friday afternoon print: lightning/thunder cloud impossible object. 🌧️⛈️🌧️

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Dave Richeson @divbyzero.bsky.social · 07/09/2026

Whenever I had a few minutes over the last few days, I created a new shape for my "impossible objects" library. Want to make a cactus/cowboy boot shape? You can now. I also implemented a visual picker to replace the drop-down menu. I plan to keep adding to it. divisbyzero.github.io/impossible-o...

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Dave Richeson @divbyzero.bsky.social · 05/09/2026

A sword and a shield. The shape of the object is pretty crazy!

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Dave Richeson @divbyzero.bsky.social · 04/09/2026

I am most pleased with how I designed the spinner. We happen to have the bearings for skateboard wheels from years ago when my son and I made a homemade fidget spinner!

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Dave Richeson @divbyzero.bsky.social · 04/09/2026

correct angle (86°). Maybe it is overkill, but it was fun to think about and design.

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Dave Richeson @divbyzero.bsky.social · 04/09/2026

I've been thinking about how to best display and view my impossible objects. Here's what I've come up with so far. The feet fit into the spinner to line up the object. The spinner turns 180°. The window forces the viewer to look down at a 45° angle. And the mirror has a slot to hold it at the

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Dave Richeson @divbyzero.bsky.social · 28/08/2026

Your post isn't showing me anything

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Dave Richeson @divbyzero.bsky.social · 28/08/2026

Since the semester starts in a few days, I thought I'd share a link to the web app I've been working on: divisbyzero.github.io/impossible-o.... It lets you design your own impossible objects! Anyone can view and rotate them in a browser, but you can also download the OpenSCAD file to generate a

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Dave Richeson @divbyzero.bsky.social · 26/08/2026

Thank you, @moduality.bsky.social for pointing out the weird shadows of my impossible objects. That got me to think of yet another way to show how weird they are. Here, a light is shining down from behind at a 45° angle!

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Dave Richeson @divbyzero.bsky.social · 26/08/2026

Ok. One more. Two circles or three?

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Dave Richeson @divbyzero.bsky.social · 24/08/2026

Here are a few more impossible objects: the duck/rabbit illusion and the hand/foot illusion.

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Dave Richeson @divbyzero.bsky.social · 23/08/2026

I am thinking about having my students (~35) design their own impossible objects this semester. That would mean I would have to print quite a few of these. This little guy took about 27 minutes, and it is pretty sturdy. If I put multiple on the build plate, this might be reasonable.

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Dave Richeson @divbyzero.bsky.social · 22/08/2026

Here is another impossible arrow. It occurred to me that you can get the same effect by putting it on a mirror!

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Dave Richeson @divbyzero.bsky.social · 18/08/2026

The "impossible objects" that I've been posting look a little better when the mirror is tipped forward slightly. To look down at a 5 cm object from about 60 cm away and in a mirror 10 cm behind the object, the mirror should be at an angle of approximately 86° to get two 45° views of the object.

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Dave Richeson @divbyzero.bsky.social · 17/08/2026

We got a rental minivan to take our daughter to college. Look at what I found in the footwell under the seats that fold down. 😮😮😮 The Enterprise guy said the previous renters knew they'd lost a hermit crab but couldn't find it. He said he'd try to contact them. "Otherwise, I'll keep it as a pet."

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Dave Richeson @divbyzero.bsky.social · 16/08/2026

Partly because it makes my daughter laugh at my mathematical ridiculousness, I like to take pictures of wallpaper, tiles, and carpet patterns. Here's some wallpaper we saw yesterday. It got a 🤦 from her. I haven't looked at it long enough to see the repeating pattern.

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Dave Richeson @divbyzero.bsky.social · 13/08/2026

Here's a fun puzzle that @cardcolm.bsky.social shared with me: The Bucolic Cube, designed by Yasuhiro Hashimoto. Assemble these identical pieces to obtain a 3x3x3 cube.

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Dave Richeson @divbyzero.bsky.social · 12/08/2026

Thanks! Sure! Here’s a short video.

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Dave Richeson @divbyzero.bsky.social · 11/08/2026

article muse.jhu.edu/pub/6/articl.... It didn't have too much about Byrne's calculus, but it did have this image of the frontispiece. So cool to see that again! Here are some images I made a few years ago of conic sections on circle/circle and circle/line graph paper.

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Dave Richeson @divbyzero.bsky.social · 11/08/2026

At Bridges, @quiteclare.bsky.social spoke about Oliver Byrne and his version of Euclid's Elements. She mentioned that Byrne's last known work (unpublished but in the archives at Trinity College Dublin) was "The Trinal Calculus," which was his attempt to put calculus on a rigorous

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Dave Richeson @divbyzero.bsky.social · 11/08/2026

Recently, I've seen a bunch of "Gen Z translation" videos explaining the slang of today's youth. Those videos remind me of the prank pulled on the NY Times in 1992, when they wrote about grunge, Seattle, and local slang. These terms were all made up by a record label employee.

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Dave Richeson @divbyzero.bsky.social · 10/08/2026

At Bridges, I gave a talk about how to make "impossible objects" from curves defined in terms of functions of x, parametric, polar, and implicit equations. @standupmaths.bsky.social asked if a similar technique could be used for a curve given by an SVG file. Yes! Here are some proofs of concept.

A chicken that has an egg-shaped reflection

An egg that has a chicken-shaped reflection

A sneaker that has a car-shaped reflection

A car that has a sneaker-shaped reflection

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Dave Richeson @divbyzero.bsky.social · 10/08/2026

I left my car in an outdoor parking lot near Washington Dulles Airport for 11 days while traveling. It must have been warm. A sealed seltzer can exploded, and the melatonin gummies melted into one massive gummy.

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Dave Richeson @divbyzero.bsky.social · 08/08/2026

At family day at Bridges I volunteered to help Nick Sayers with his giant pantograph. Trace the outline of the person, and a small copy is drawn by the pen. It was fun for kids and adults of all ages. Here is @ayliean.bsky.social as a model and an artist.

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Dave Richeson @divbyzero.bsky.social · 07/08/2026

I saw this lovely design on the sidewalk in Galway. According to Google, it is a water main stopcock cover. The inscription "uisce" means "water" in Irish, and "WSC-R" stands for Water Service Control - Road.

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Dave Richeson @divbyzero.bsky.social · 07/08/2026

A fun free coordinated motion puzzle from George Bell and Nan Ma.

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Dave Richeson @divbyzero.bsky.social · 07/08/2026

Euclid illustrator Oliver Byrne married someone with last name Rugg. So her married name was the unfortunate Rugg Byrne.

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Dave Richeson @divbyzero.bsky.social · 01/08/2026

More math tourism: the library at Trinity College Dublin. Now with busts of female scholars, like Ada Lovelace (2023).

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Dave Richeson @divbyzero.bsky.social · 30/07/2026

Math tourism: Broome Bridge in Dublin, Ireland, where Hamilton discovered the quaternions!

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Dave Richeson @divbyzero.bsky.social · 22/07/2026

The font was small, I was lazy, and I didn't want to count all the 1s. I copied and pasted into Google: "What is the number 1111111111?" Not the reply I expected.

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Dave Richeson @divbyzero.bsky.social · 13/07/2026

I created this logic/grid deduction puzzle several months ago just to try out vibe coding. I created it for myself and have been enjoying playing it, so I thought I'd share it more widely. I call it Daedalus' Labyrinth. divisbyzero.github.io/Daedalus-Lab... Each segment in the grid must either

Screenshot of the solution to the puzzle

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Dave Richeson @divbyzero.bsky.social · 10/07/2026

everything a 100% blend of its ingredients?" Today, I decided to ask Google's AI to explain it to me. It pointed me to this item of federal code: Title 21 / Chapter I / Subchapter B / Part 101 / Subpart B / § 101.30(b)(3) www.ecfr.gov/current/titl...

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Dave Richeson @divbyzero.bsky.social · 10/07/2026

Who says AI is not useful? Here's today's use case. 🤣🤣🤣 This was my Facebook memory from 15 years ago. (I still think it is funny!) "We just bought this juice today. I don't understand what the '100%' refers to. 100% cranberry juice: no. 100% juice: no. All I can figure is 100% blend. But isn't