In an attempt to keep to my workout routine, I have printed out a blank calendar for the current month and charged my 6 year old daughter with putting a sticker on each day I exercise. She is wonderful when it comes to handing out stickers and takes pride in both choosing the sticker and in affixing it to the page as straight as possible. Today I earned a five pointed star. “I put it on straight,” she said with a smile and then after a brief pause, “but it would be right even if I turned it a bit.” There it was, a perfect opening for a math lesson.

I asked her what she meant and she took another star sticker from the pack. “I can put it with this point up but if I turn it and put this point up instead it will still look the same.” My daughter’s statement is akin to a mathematician declaring that the five pointed star has rotational symmetry. I pushed, “How many points are there? Does this always work…will it always look the same when you turn it?” Little by little we talked through how any of the 5 points could be “up” ensuring the sticker would look the same, but that if a point wasn’t up it would be different. She talked about turning it enough or not enough. Mathematically, this has to do with the number of degrees that the star is rotated about its center. As there are 360 degrees in a full turn and we have 5 points which could be pointing up, every time we go 360/5 = 72 degrees we up with the sticker, in my daughter’s words, “looking the same.” In actuality regardless of how the star looks initially rotating 72 degrees as many times as you want will yield an image that looks exactly the same as the one you started with. After my daughter and I talked through the pattern she was observing I told her that mathematicians have noticed this same pattern and called it rotational symmetry. She was delighted by this and started asking if it might work with some of the other stickers she has which gave us an opportunity to play with the concept further. We often think of mathematics as consisting of numbers and equations which, unfortunately, is quite limiting and for many makes the subject feel distant, irrelevant, and even something to be feared. Instead, I urge you to think of mathematics as the study of the patterns that exist all around us. By doing so, a seemingly simple observation by a six-year old pertaining to the way a sticker looks when we turn in it our hands, can become the first step into the elaborate, beautiful, mathematically rich topic of symmetry.