Klein bottles are an entertaining mathematical idea–a shape with no volume. A Klein bottle is basically a tube where the inside is connected to the outside. Making a Klein bottle in our 3D world requires a bit of cheating to work, by adding a hole in one of the walls of the tube to provide a place for an intersection.
The most common physical realization is a glass Klein bottle, which you can ogle and buy at Acme Klein Bottles. They also sell wonderful knit Klein bottle hats which can be bought with a matching mobius strip scarf. I was lucky enough to be given a set as a gift, and it is cozy and bright and wonderful. My only complaint is that the narrow neck of the Klein bottle makes it hard to pull it inside out (or right side out, since it is the same thing) to play with it.
I have found that the concept of a mobius strip is more understandable when you can hold it in your hands and turn it around and around, and I thought the same would be true with a Klein bottle, if only it were a little more flexible than my hat. With that in mind, here’s how to make a simple fabric Klein bottle you can play with from two sleeves of a worn out shirt. Continue reading →
In electronics, it is common to talk about single sided circuit boards. The most common type is a circuit board that only has printed wiring on one side, and components on the other side. There are also surface-mount boards, where all the wiring and components sit on one side. But aren’t all of those reallyjust two-sided circuit boards where you only put components on one of the sides?
Here we present a method of making your own authentic single-sided circuit board. Continue reading →
Have you ever heard of the unary number system, i.e., base-1 numerals? That’s the formal designation of tally marks– a means of representing a number symbolically by using symbols, where the number represented is equal to the number of symbols. While easy to grasp, it’s also a rather inefficient system, so we don’t find too many uses of them in modern life. One of the places that we do (almost) always use the unary system is on birthday cakes, where a birthday cake has one candle per year. This is fine for small numbers, but positioning, lighting and blowing out candles becomes impractical past a certain point.
Here’s a better way: A binary birthday candle. It consists of a single candle with seven wicks, where the wicks that are lit represent the birthday individual’s age in binary. This single candle design works flawlessly to represent any age from 1 to 127, never requiring anyone below the age of 127 to blow out more than a mere six candles at a time. Continue reading →
Sleek sinusoids for your wrists. Laser-cut acrylic.
A free design from Evil Mad Scientist Laboratories, complete with dowloadable files so that you can make your own. (And isn’t this a good time for your first laser project?)
In case you haven’t been bitten by this particular bug yet, here’s a quick intro. Laser cutters are an awesome tool in the modern DIY arsenal. This type of laser is a lot like a laser printer, but uses deep infrared carbon dioxide laser that can cut or engrave most plastics. You can find these at hacker spaces like NYC Resistor and membership shops like TechShop and The Sawdust Shop, so it’s finally getting to the point that almost anyone can learn to use one. However not everyone lives by a laser shop, so sites such as Ponoko, Pololu, and Big Blue Saw offer laser cutting services and enable you to submit jobs from anywhere.
Our bracelets are cut from a single sheet of acrylic (using a laser, obviously!) in concentric wavy rings to form a nesting set of various sizes. The light plays through the transparent acrylic in fun and fascinating ways. Continue reading →
Happy birthday to us! Evil Mad Scientist Laboratories is now two years of age. Collected below is a “Best of Evil Mad Scientist” for the past year: Some of our favorite projects that we’ve published over the last twelve months. Here’s to the next year!
Take that idea, run with it, and where do you end up? In the kitchen, making Sierpinski cookies! These cookies, made from contrasting colors of butter cookie dough, are a tasty realization of the Sierpinski carpet, producing lovely, edible fractals.
As with our earlier project involving clay, you can make these by using a simple iterative algorithmic process of stretching out the dough and folding it over onto itself in a specific pattern. Continue reading →
One of our favorite shapes is the Sierpinski triangle. In one sense, a mere mathematical abstraction, on the other, a pattern that naturally emerges in real life from several different simple algorithms. On paper, one can play the Chaos Game to generate the shape (or cheat and just use the java applet).
You can also generate a Sierpinski triangle in what is perhaps a more obvious way: by exploiting its fractal self-similarity. Continue reading →
Last weekend we took a trip to Urban Ore in Berkeley, where I found an incredible gem: this “Fraction of an Inch Adding Machine.” It’s a simple to use device that lets you add any number of fractions– from 1/64 to 63/64– quickly, automatically, correctly, and without thinking about it.
As proudly proclaimed on the bezel itself, this calculator design is covered under patent Des. 169941, submitted in 1952, and granted a 14-year term in 1953. Forty years after the patent has expired, it’s painfully obsolescent, and yet remarkably charming. The design is so simple and so obvious in how it works, and yet… there’s something almost magical about it.
But enough talk. Want to play with one? Using our pdf pattern and some office supplies, you can make a working replica in 5-10 minutes and try it out yourself!
Dunking it in water doesn’t work– you only get the volume of the rat-like creature that lives inside the cat; much like the feeble alien within a Dalek. (And, if your answer had anything to do with contour integrals, get real.)
Here is a low-tech method that works: Using successive approximation, determine the smallest box that the cat will fully enclose itself in, and measure the size of that box. Cats tend to leave a few appendages hanging out of the corners– you may need to assist with folding the cat into the box for the final stages of approximation.
This cat is approximately 648 cubic inches in volume.