The Sierpinski Valentine, Cardioids, and Möbius Hearts

Welcome to this week’s Math Munch!

With Valentine’s Day this Thursday, let’s take a look at some mathy Valentine stuff. If you’re searching for the perfect card design for your valentine, search no more. Math Munch has you covered!

Sierpinski Valentine

xkcd creator Randall Munroe

Above you can see a clever twist on the classic Sierpinski Triangle, which I found on xkcd, a wonderfully mathematical webcomic. You can read more about xkcd creator Randall Munroe in this interview from the Sept. 2012 issue of Math Horizons. (pdf version)

Ron Doerfler designed another math-insprired Valentine’s Day card, which you can check out here. The image to the left is only part of it. Don’t get it? Well it’s a reference to a mathematical curve called the cardioid (from the Greek word for “heart”). Look what happens if you follow a point on one circle as it rolls around another. You’ll have to imagine it tipped the other way so it’s oriented like a typical heart, but that curve is a cardioid. The second animation was created by the amazing and previously featured Matt Henderson. If you have a compass, then you can make the second one at home.

A cardioid generated by one circle rolling around another

A completely different way to generate a cardioid

Pop-up Sierpinski Heart Card

Really though, nothing says “I Love you” like a Möbius strip. Am I right? Here’s a quick little project you can do to make a pair of linked Möbius hearts. You can find directions here on a blog called 360, or you can watch the video below. Oh, and as if that wasn’t enough great stuff, here’s one more project from the 360 blog, a pop-up version of the Sierpinski Heart!

Mobius strips are really cool. Its pretty neat that by creating a half twist before completing a loop you can create a object with one side and one edge. I love this idea of the chained Mobius hearts. I tried making it and the first few times I did it wrong but I finally was able to create it! It’s really awesome that how they twined together when completed.

Mobius strips are quite interesting, the way he makes it is pretty cool. I learned that the Mobius strip hearts are a mathematical object, discovered about 450 years ago.

These are fabulous, thank you!

Thanks! Glad you enjoyed it. Check back next week for more goodies. ;)

I *love* it (pun intended). I can’t wait for my students to begin their quarterly Math Munch project(s). Great stuff you guys are doing on here.

Portland, OR Math Teacher

Hey Thanks, Kayla!! I can’t wait either. :)

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Mobius strips are really cool. Its pretty neat that by creating a half twist before completing a loop you can create a object with one side and one edge. I love this idea of the chained Mobius hearts. I tried making it and the first few times I did it wrong but I finally was able to create it! It’s really awesome that how they twined together when completed.

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Mobius strips are quite interesting, the way he makes it is pretty cool. I learned that the Mobius strip hearts are a mathematical object, discovered about 450 years ago.