My Sweatshirt

In just four days of wearing my new favorite sweatshirt on campus for the first time I got four separate complements on it. Three people asked me where they could buy it. Since then I've received dozens of compliments, mostly from strangers who, although they don't know me, know an elegant math expression when they see it.

Unfortunately, this sweatshirt is not explicitly for sale anywhere. I had it custom made because I couldn't find anything like it.

My Euler's Identity Sweatshirt


I love my sweatshirt, I'd sell it on a store like CafePress if I could find one that sells black sweatshirts. Since I can't, the next best thing is to provide the instructions to get one.

The image: You can get the image I used for the screen-printing here. However, the company I used for the screen-printing required you to upload an inverted version of the image (at least as of the last time I used their services), which you can download here. If one doesn't work try the other.

The company: The company I used to screen-print the image is Blue Cotton. I chose the Hanes Pullover sweatshirt (Printing -> Sweats -> Hooded Sweatshirt -> F170 Hanes Pullover Hood), but they do offer other sweatshirts. The Hanes sweatshirt has the advantage of having the lowest polyester content (90% cotton) of any of their sweatshirts, which is a good thing for a screen print and has the side benefit of being very comfortable.

The image sizing: For my sweatshirt, an extra-large, I chose to make the image 9.5 inches wide (be sure you lock the width/height ratio when scaling the image on the sweatshirt) and centered it 2 inches below the collar (you'll have to eyeball this measurement). It took a long time for me to decide on those dimensions, but I finally did and I think they're perfect, which is saying something. You might want to scale the width for sweatshirts of different sizes, my rough guess would be to subtract/add .75 to 1 inches per size smaller/larger.

So all you have to do is go to the website, select your sweatshirt, upload the image, set the width/placement, and order it.

Background for the sweatshirt

I'm a math major, and I like elegance. Euler's Identity is my favorite mathematical expression: it's a simple expression of universal truth via constants. It's fascinating how the five most fundamental constants of math are all uniteable in a single, simple expression.

In addition to math, I like t-shirts. I tend to treat t-shirts as billboards for things that I like -- you won't find a blank shirt in my drawer. As need had it, in winter of '07/'08 I found myself in need of a new sweatshirt. Like the rest of my upper-body apparel, I wanted it to say something interesting. I wanted the sweatshirt to be "nice-ish" so that I could wear it to "nice-ish" events, so I didn't want a busy/complicated design. it had to be simple, yet elegant. Settling on a simple expression of Euler's Identity was easy. My second stipulation was that the sweatshirt had to be black.

I started my search at the obvious place for a weird request like that: CafePress. I found a couple of sweatshirts with Euler's Identity, but a) They had obnoxious brand logos, and b) Cafepress doesn't sell black sweatshirts. After an extensive search of the Internet, it became obvious that no one offered anything like what I was looking for (shocking, considering the obvious demand). So I decided to have the shirt custom screen-printed.

The design of the sweatshirt

Thus I was faced with two tasks. The first task was creating the image I wanted to be screened onto the sweatshirt. The second task was finding someone to screen-print the image. Neither task turned out to be as simple as it might seem.

Creating the image was difficult because the only decoration for the black sweatshirt was going to be the bold, white text of Euler's Identity. Thus the styling of the text was very important. In order to truly do the equation justice, and make the sweatshirt look as simply elegant as possible, the font had to be perfect. Not fancy, but not boring. Just slightly elegant.

Getting the image screen-printed turned out to be difficult because there were two major conditions for the screen-printing: I had to be able to have a transparent background, and I was not going to order in bulk. Most custom screening companies violated the former of these two requirements, and the few that allowed background colors required bulk orders. In addition, some companies didn't offer sweatshirts in black.

The final solution

Finally, however, a solution was reached. I designed the image using the "i" and "pi" symbols generated by a Linux-based LaTeX front-end called eqe. I generated the rest of the equation using characters from the Tahoma font in the Linux-based image editor KolourPaint. I needed a very large size image to achieve a sufficient DPI, which was recommended to be at least 90. Both programs allowed me to create the images at a large size with excellent quality, but not a size quite large enough. So I used Gimp to expand the size and I used its anti-aliasing feature to keep the font's smooth despite being enlarged. The result is shown here. (This is a scaled-down version of the image, for bandwidth reasons. Click the image to download the full-size image, the one you would use for actual screen-printing.)

Euler's Identity

View the inverted version.

I also found a company, called Blue Cotton that allows one to screen-print an image, choose a color to make transparent, and doesn't require a bulk order. (Choose Printing -> Sweats -> Hooded Sweatshirt -> F170 Hanes Pullover Hood.) Thrilled to have a working image and a working company, all I had to do was manually place the image on the sweatshirt. I spent (no joke) probably 3 hours total moving the image around on the shirt, higher, lower, bigger, smaller, trying to get it just the right size and at just the right height. Finally I decided on a 9.5 inch width at 2 inches below the collar, which I am pleased to say is the perfect size/placement (for an XL).

Close-up picture of the screen-printed text on the sweatshirt.

Also, kudos go out to my girlfriend for her extreme patience with me. The sweatshirt was a Christmas present from her to me. Being a nit-picky perfectionist, it was decided that I had actually best do the bulk of the designing. I didn't even finish the design until the end of January. Giving it to me was an excellent idea, and it's one of my all-time favorite articles of clothing.