———-Part 1: My obsession with brownies——–

Once, when I was in 9th grade, I polished off nearly an entire pan of brownies all by myself. And then proceeded to place 12th at the New England Cross Country championships a mere few hours later… I’ve loved brownies since.

I’ve made batches and batches of the rich and decadent treats over the years. But the other day, as I was cutting them, I took a second glance, slightly unsatisfied. Just look at their shape! Square, monotone, boring… my inner geometry enthusiast cried out for change.

———-Part 2: Sierpinski’s triangle———-

Look! The Sierpinski triangle, intriguing patterns abound. I was first introduced to this wonderful creation during my 6th grade math class, and have adorned many of my notebook margins with its beauty since. The process is quite simple: you start with a single equilateral triangle, then draw a smaller triangle connecting the midpoints of its sides, then draw smaller triangles connecting the midpoints of the triangles you just created, on and on to infinitum.

———-Part 3: Brilliance———–

In English class, when my teacher was discussing the usage of symbolism in chapter 44 of Moby Dick, I had a revelation. Why not introduce the Sierpinski triangle… to the brownie? With two colors of brownie, I would assemble the gorgeous Sierpinski design, and then, I would have beauty, richness, decadence, and an endless array of patterns all on one plate! Perfection. I was determined to make it happen…

———-Part 4: Intensity———–

Excited, I searched my pantry for brownie ingredients. It didn’t take long to meet my first obstacle: brownie pans are, well, rectangular–clearly, major baking pan companies do not have Sierpinski on the brain. So I must modify! I designed a brownie-cutting pattern that would maximize the number of equilateral triangles I could fit into one pan.

My pan is roughly 8.25”x10.5” with rounded corners… so my largest triangle has side length 7 3/8”. I calculated that I needed to make two pans of dark chocolate brownies and one pan of white chocolate brownies. (My calculations here.) Then, I made the brownies (recipe: white chocolate/dark chocolate duo; Smitten Kitchen February 2011.)

Then, I cut the brownies, using paper triangles to guide me…

…until I got something that looked just like my pattern that I had sketched earlier.

Cut to size…

Then arrange, like so.

I cut the white chocolate brownies and began to fill in the spaces.

Done!

I repeated this process three times, then cut a dark chocolate brownie with the same edge length (7 3/8”) as the above multicolored triangles.

Just rearrange them together and we’re done!

Ta-dah!

———-Part 5: Conclusion————

I am so happy. The whole process, from calculating areas to melting chocolate to cutting brownies to assembly, took over five hours, not including the time it took to write this post. But it’s definitely worth it. Sometimes, when I look back at all the work I’ve done in the pursuit of something so random and out-of-the-norm, I wonder if I am a little crazy. But when I think about it, I realize that I’m just deeply passionate about what I do and at the same time eagerly willing to pursue whatever random ideas that come into my mind. In other words,* I just care a lot.*

And that, my friends, makes it all the more worthwhile.

Oh man….it’s incredible to see where all the creativity takes you. Almost everywhere. :D

Now I see what you did there with that baking you’ve done this afternoon :P

And those look delicious! I should perhaps try some of those on my own.

I saw this and KNEW it was smitten kitchen!

This is SO COOL!

Wow you really like mathematics Luyi!

Um… awesome.

this is one of the coolest things i’ve ever seen. I’m a big fan and i hope you keep it up

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This is Awesome! – Maybe some menger sponge-cake up next?

I just stumbled upon your blog and I just wanted to say that we are so much alike!! And Wow, those brownies look so yummy :) And I’m also a math-lover! People look at me like I have 2 heads when I tell them that, but there’s just something so interesting about math/science/all that nerdy stuff, that just makes me happy :D

Have a lovely day, I hope you enjoyed your brownies!!!

Oh my God I think you’re my hero. I love baking and I run cross country and I appreciate math too!! C: You’ve given me newfound hope to succeed…

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Gosh!! You have cooler ideas than I do!!! Let’s see what my latest cool idea was… Ha ha, I have no cool ideas.

Just let me discuss your project with my students and teachers. I think we should hold a competition in the school using your idea during the Youth Festival or sooner. Keep up the good work.

How long did it take for you to eat that?

Not long, half a morning? I brought it to school and shared it with lots of people :)

This is really cool –we do “math food” for extra credit in my pre-cal class. I may make this. Any other suggestions that might be a little easier would also be greatly appreciated. (I’ve already done the “pi pie” and a square pie “pi r squared”) thanks!

mmm…. looks tasty :)

That’s so awesome!!!