Beyond Euclid #178
Welcome to Beyond Euclid #178, the newsletter for the best mathematics and science stuff of the week. I am Ali, and I curate cool math and science stuff every week to help you have a better week.
Some creatures don’t just live—they express. Take cats, for example.
I don’t think their massive fanbase is just about cuteness—it’s about the way every movement they make carries a kind of elegance. A cat doesn’t just walk out the door. It tilts its head, lifts its tail, and glides through with the grace of an invisible S-curve. When it leaves your lap, it doesn’t hop—it springs, arches, and almost takes off.
When it sniffs something, it doesn't just use its nose—it extends its whole body forward. Even when there’s no prey in sight, it walks on tiptoe like it’s stalking a ghost. During grooming, it’s never random. It’s symmetrical, deliberate, and rhythmically precise. When it stretches its hind leg over its head to clean, it looks like it’s striking the fourth position in classical ballet.
And all of this elegance... usually comes wrapped in a body that looks like it’s about to roll off the couch.
Watching a cat isn’t just watching an animal—it’s like watching a slow, wordless performance. Silent, but full of intent.
This week’s newsletter is in that spirit: searching for the elegant, the measured, the quietly striking. Whether it’s in math, tech, or the shape of a strange object—everything holds a bit of pi, a bit of balance, a bit of intuition. Just like cats. Let’s begin.
Mathematics + Science + Art
• The Longest Pi Article on the Internet: Literally Everything About π. After months of research and writing, the longest article on the number π is finally live. From ancient civilizations to modern computing, from wild world records to everyday uses of pi—this deep dive covers it all. If you’ve ever been curious about the history, beauty, or sheer weirdness of π, this is your rabbit hole.
✍️ The world’s shortest math paper: 2 words. In 2004, John Conway and Alexander Soifer submitted a math paper to The American Mathematical Monthly containing just two words and two diagrams: “n² + 2 can.” The editors were baffled. Initially, the response was that it was “a bit too short.”
Soifer pushed back, asking, “Is there really a connection between quantity and quality?” Eventually, the journal agreed to publish it—not as a full article, but as a filler to avoid blank space on a page. The authors accepted.
🎨 At first glance, Magritte’s The Blank Signature feels like a visual glitch—horse legs both in front of and behind a tree at once. It shouldn’t make sense, but somehow it holds together. That same logic-defying coherence shows up in math too: like √–1, or non-Euclidean space where parallel lines curve. Both challenge intuition, yet play by strict internal rules. In that sense, Magritte and mathematics aren’t far apart—they just twist reality in equally disciplined ways.
📐 This geometric artwork says a lot without spelling anything out. The curves, lines, and proportions point to an underlying order—but they don’t announce it. Everything feels intentional, but how it’s all held together only reveals itself if you really look. It’s precise, measured, and completely quiet about it.
🪑 When a four-legged chair doesn’t sit flat on the floor, most of us either shove a piece of paper under it or grumble and move on. But here’s a better question: how can you place a four-legged chair so that all four legs touch the ground perfectly? The key lies in the Intermediate Value Theorem. In simple terms, the theorem says that a continuous function must pass through every value between two points at least once. So what does this have to do with a wobbly chair?
Think of it like this: when you place the chair on the floor, usually one leg hovers slightly above the ground. If you slowly rotate the chair—keeping it level—the leg in the air will gradually approach the floor, and eventually another leg will lift off. Somewhere during that rotation, the roles must switch. And right in between, the Intermediate Value Theorem kicks in: if one leg is up at the start and a different one is up at the end, then there must be a moment in between where all four legs are touching the ground.
Mathematically, this situation can be modeled using continuous functions and differences in leg height. But the beauty lies in the simplicity: whether you prove it with theorems or just trust your gut, a perfectly balanced position always exists. It’s a small but striking reminder of how deeply math is woven into everyday life. Sometimes, math is just about sitting properly.
Engineering + Physics + Art
🌒 These two pages come from al-Mulakhkhas fi al-Hay’a, a concise astronomy manual written by 13th-century scholar al-Jaghmini. On the left is a diagram of a lunar eclipse, showing the alignment of the Sun, Earth, and Moon. On the right, a circular chart illustrates the phases of the Moon around the Earth.
This book was used in medieval Islamic madrasas to teach the basics of astronomy. It’s based on the Ptolemaic model, but simplifies it with clear visuals and short explanations. In that era, science wasn’t taught with abstraction alone—it was shared through carefully drawn diagrams like these. Even today, looking at these pages reminds us: knowledge sticks better when it takes shape.
🔍 Have you ever stopped to wonder: how many atoms does a car tire lose every time it rotates? At first glance, it sounds like a silly question—but it's actually a perfect example of a Fermi problem, those clever back-of-the-envelope estimates popularized by physicist Enrico Fermi.
A typical car tire lasts around 60,000 kilometers. With a circumference of roughly 2 meters, that adds up to about 30 million rotations before it's worn out. Assuming it loses about 9 kilograms of material over its lifetime, we’re looking at a loss of approximately 0.0003 grams per rotation. Now comes the molecular math: since there are about 5×10²² carbon atoms per gram, that tiny 0.0003-gram loss translates to roughly 10¹⁹ atoms shed with every turn of the wheel. Every corner, every acceleration, every stop—millions of billions of atoms are left behind on the road. You don’t see it. You don’t feel it. But the math makes it real.
🪑 Installed in a public park in Germany, this interactive bench tips to one side when used alone. It only finds balance when two people sit across from each other. Designed by Berlin-based artist Martin Binder, the Balance Bench aims to create not just physical, but social equilibrium as well. Especially in a post-pandemic world, it playfully questions how we manage closeness and distance in shared spaces.
Made of oak wood and powder-coated steel, the bench isn’t just for sitting—it’s for being present with someone else. The message is simple: real balance comes from togetherness. It sparks conversation, demands cooperation, and yes—it’s basically a safe, adult seesaw.🤖 Tired of doing house chores? Meet π0, a robot that folds laundry, wipes tables, and learns just by watching you. It observes human movements and mimics them to get better—show it how to fold a shirt once, and next thing you know, it’s doing a neater job than you. For now, it’s limited to the lab, but for anyone dreaming of escaping housework, it’s a promising glimpse of the future. Turns out, delegating ironing might not be a fantasy after all.
🪑 The chair every American kid sat on. It’s called the Verco 9000. Launched in 1965, sold over 60 million units, and it’s still in schools today. A single-piece plastic seat with tubular steel legs—lightweight, durable, stackable. Pure public utility design. But this isn’t just about design. This chair became part of a shared memory. The one you leaned back on in science class, the one kids bounced on at recess. It’s familiar because everyone had it—or felt like they did. Just a plastic chair, sure—but somehow, a cultural constant. Sometimes the quietest objects are the ones we all remember.
🐾 This business card doesn’t try to sell your service—it makes people smile before they even read your name. Shaped like a minimalist cat, with pointed ears and tiny embossed paw prints wandering across its surface, it’s printed on thick, textured paper that feels more like a keepsake than a card. Designed by Hrund Guðmundsdóttir for a letterpress competition in Reykjavik, it trades hard-sell for soft charm. It doesn’t say “Call me because I’m useful,” it says “Call me because you won’t forget this.”
💻 Maker [Scott Yu-Jan] built a portable setup using Apple’s new M4 Mac Mini, but it’s far from a typical laptop. The screen, keyboard, and Mac Mini are fused into one modular unit—no battery, all wired. It’s not really a laptop; it’s more like something you’d pull out of a hacker’s bag. The build focuses on portability and design, not just function. The Mac Mini is mounted to the side of the keyboard for easier handling, and small TPU rests help the screen close more smoothly. The end result? A slick, eye-catching cyberdeck—maybe not practical, but definitely cool.
🌕 Inspired by an old flip clock, Simone Giertz built a device that tracks the phases of the Moon using 30 rotating flaps—each showing a different lunar stage. As the flaps turn, they mimic the Moon's transition from new moon to full moon in a satisfying, analog way. It doesn’t update automatically, so you’ll need to flip it manually each day—but that’s part of the charm. The design is simple, visual, and surprisingly meditative. Plus, the build files are available for free on Yetch Studio if you want to make your own.
This is the kind of hands-on project that’s perfect to build with kids: it’s creative, teaches about lunar phases, and results in something genuinely beautiful to keep on a desk or shelf. A little science, a little art, and a lot of fun.
News
🎂 People are more likely to die on their birthday—a phenomenon known as the birthday effect. In a study using nearly 2 million death records, deaths on birthdays were significantly higher than average: 183 vs. 156. This spike is statistically solid, even after adjusting for seasonal factors. Theories vary—from psychological stress to risky celebration habits—but the data is clear: birthdays aren't just for cake, they come with a measurable bump in mortality.
💡 Your “Aha!” moments leave a mark on your brain. When a solution suddenly clicks, your brain doesn’t just light up—it remembers better. A new fMRI study found that insight-driven answers (those “aha!” moments) are more likely to stick in your memory, even days later. These moments activate key brain areas like the hippocampus and visual processing regions, increasing communication between them. The stronger the insight, the stronger the memory.
This Week I Learned That
🦴 Why do wet animals shake themselves dry? Because they’ve got these special receptors called C-LTMRs that detect water droplets on their fur and send a signal straight to the brain. The brain goes, “Shake it off.” This reflex isn’t unique—mice, dogs, you name it, they’ve all got it. Staying wet means losing body heat, and that’s no good. So the animal spins 4–6 times per second and gets rid of over 70% of the water in just a few seconds. Basically, it’s like having a built-in spin cycle.
Buy
🌀 Helicone. Designed by artist and mathematician John Edmark, the Helicone might look like a simple wooden object at first—but once you spin it, it transforms into a mesmerizing kinetic sculpture. Made of 38 laser-cut wooden pieces, its design is based on the Fibonacci sequence, allowing it to shift between forms with every twist—sometimes appearing as a helix, other times as a pinecone.
When not in motion, it rests elegantly on a wooden stand, like a sculpture. Inspired by art, math, and nature, the Helicone is a quiet rebellion against the ordinary—visually striking, rhythmic, and completely hypnotic.
⌚ Designed by Japan’s Hachisanmaru, the “Protect A” transforms the Apple Watch into a gadget-core, cyberpunk accessory. With chunky steel housing, faux circuit parts on the strap, and an exposed external crown, it looks more like hacker gear than a smartwatch. Compatible with 40mm and 44mm models, it still keeps health sensors and charging intact. At around $70, it’s not for minimalists—but for those who want their wrist to look like a mini motherboard, it’s perfect.
Bookmark This Gem
🌍 You no longer need to be an astronaut to see Earth from space. UK-based company Sen has installed three 4K cameras on the International Space Station, streaming live footage of our planet 24/7. One shows Earth’s horizon, one focuses directly on the surface, and the third captures the station’s docking area.
But this isn’t just eye candy—it taps into what astronauts call the overview effect: seeing Earth from space can shift your perspective on the planet and humanity. That’s exactly what Sen aims to do—make space and Earth more accessible, informative, and inspiring for everyone.
I love everything about Beyond Euclid! Every time I tune in, I find out something that lets me think in ways about ordinary or extraordinary life of the mind in different ways. Thank you for your posts - they are singular and interesting without being beyond my perception, like little trips out of my head they make me feel freshly arrived.