For the Love of Symmetry

Feb 13, 2020 | Littleton

This week, many people in the US are celebrating Valentine’s Day – a holiday created to celebrate and cherish those we love. Love comes in many forms and Valentine’s Day doesn’t necessarily just have to be something shared between romantic partners. Think of Valentine’s Day as a kid, specifically in elementary school. You also might have celebrated by having a party and you also likely made lots of cards for everyone in your class and maybe a box or folder to receive them in on Valentine’s Day. When it comes to making hearts, often for the creation of Valentine’s Day cards, the standard folding the paper in half, cutting a half of a heart shape, and opening open the paper up to reveal a whole hearts was perhaps one of the first things you learn how to cut with scissors. This, in fact, may have been one of your first experiences in creating something symmetrical. 

Symmetry, or the property of being exactly the same from side to side or around a center, is something that is used for many things in life. It’s actually said to be one of the things humans find most attractive in other humans – perceived asymmetry – as well as something humans use to assess beauty in everything. From animals, to shapes, to plants, to manmade objects and structures symmetry is everywhere and the history of the recognition of symmetry goes all the way back to Plato who agrues in his “Symposium” that the origins of love lie in the search for symmetry. Others, like Pythagoras, were more interested in the symmetry of geometrical figures, like the icosahedron, which is a geometric shape with 20 faces. It was really not until the 19th century that symmetry was discovered in mathematical equations, which started a long pursuit by many mathematicians to keep extracting more about the math behind symmetry. 

So, how do we define symmetry fairly simply in math? It depends on the object you’re dealing with. Rotational symmetry applies to figures like a globe – something entirely spherical whose appearance remains unchanged when you rotate it by less than 360° on a center point. Angle of rotation applies to more polygon shapes and can be found by dividing 360° by the number of sides or vertices (points where two or more lines meet to form an angle) in the shape.

In honor of Valentine’s Day, let’s talk about the paper hearts we used to (or still might!) make and different ways to examine symmetry using them as examples. Say like you take a paper heart you’ve cut out and you fold it in half vertically so that the edges match up exactly. When you unfold it, you’ll notice a line in the middle from the fold. This line is also known as an axis of symmetry, and that the shape on each side of the line is exactly like the other on the other side of the line, or a mirror image. Because one half of it mirrors the other half, the heart has what’s called reflection symmetry. Now fold the heart in the opposite way – horizontally. Does it feel like origami yet?! You’ll notice the sides won’t line up. The shape on one side of the horizontal line created by the fold is really different than the shape on the other side. Because of this, we can’t call the horizontal line created and axis of symmetry. Hearts only have one line a symmetry, which means you can only fold them one way to make a mirror image – that’s why you can create a symmetrical heart by folding a piece of paper the half and cutting out a half of a heart shape in the first place! Other shapes have more axes of symmetry.

Now, let’s take your Valentine into account. If you look at their face directly head on and imagine a vertical line running down the middle of it, similar to the paper heart, do you see their face as symmetrical? Possibly? The reality is while faces appear to be perfectly symmetrical when you look at both sides together as the same time, things change when you look at the side of a face separately. All human faces are slightly asymmetrical, so that one half is a little different than the other. If your Valentine had an exactly symmetrical face, they would potentially look out of the ordinary for a human, and certainly not like themselves. Despite that nobody has an exactly symmetrical face, those who are closer to having a more symmetrical face are often described to be more beautiful. 

Regardless, of symmetry or not, paper hearts or not, or Valentine’s Day parties or not, we at Mathnasium of Littleton hope you have a great Valentine’s Day with those you love and hold dear. And speaking of love, do you love Mathnasium of Littleton? Share the love by liking us and/or writing us a review on Facebook. We love you, too.  

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