A new application to draw your own snowflakes and save them in PDF format. Clean, cross-platform, open-source, and able to generate closed-polygon vector shape output. *Oh yeah.*

# Category Archives: Mathematics

# Binary Birthday

I am this many.

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.

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# A Sinusoidal Acrylic Bracelet Design

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.

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# 20 millicenturies of Evil Mad Scientist Laboratories

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!

**Quick projects:**

Rubberbands made from old bicycle innertubes.

Light tent made from a lampshade.

Spool spinner from an old fan.

The $1.00 C to D adapter

**Electronics projects**

How to make a Joule Thief from Make: Weekend Projects.

How to make a dark-detecting LED night light.

The Great Internet Migratory Box of Electronic Junk

How to make a Sawed-off USB Key

**AVR microcontroller projects**

Using an ADXL330 accelerometer with an AVR microcontroller

**Kit Projects**

**Crafty Projects**

**Food Hacking**

**CandyFab**

Printing complex shapes: Sugar Chain

Candyfab improvements: higher resolution and edible output

**Papercraft:**

Rotary Fraction Adding Machine

**Observations & silly projects:**

**Lego Projects:**

Forbidden Lego review & build

**Reviews:**

Lee Valley & Veritas Catalog Review

**Teardowns:**

# Sierpinski Cookies

A few months ago we showed you how to make beautiful fractals in polymer clay.

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.

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# Iterative Algorithmic Plastic Sculpture: Fimo Fractals

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.

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# Make your own 1952 Fraction-of-an-inch Adding Machine

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!

# Computing the volume of a cat

How do you compute the volume of a cat?

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.

# Play with your food: Rework your toast

It’s a simple formula, really: hot air gun + bread = interesting toast.

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# 0.999… equals one.

But you knew that, right? Check out the Wikipedia article about different proofs that 0.999… equals 1. It’s really quite interesting to see the wildly different methods that can be used to arrive at the same conclusion. While I’m partial to the Cauchy sequence version, the first of the proofs is my favorite, beautiful in its simplicity:

0.333…. = 1/3

3* 0.333… = 3 * (1/3)

0.999… = (3*1)/3 = 3/3 = 1

Q.E.D. =)