You know what I mean right? Like when you look in the mirror and see your reflection staring back at you? That’s a pretty basic form of symmetry it’s called bilateral or radial symmetry. But did you know that there are actually different types of symmetry in math?

First up, we have rotational symmetry. This is where an object can be turned around a fixed point and still look the same. For example, if I draw a circle with a dot in the middle, no matter how many times I spin it around that center point, it’s always going to look like a perfect circle with a dot in the middle.

Next up is translational symmetry. This is where an object can be moved along a line or plane and still look the same. For example, if I draw a repeating pattern of squares on a grid, no matter how many times I move it to the right or down, it’s always going to look like that exact same pattern.

Now reflectional symmetry. This is where an object can be flipped over a line and still look the same. For example, if I draw a letter ‘S’, no matter how many times I flip it horizontally or vertically, it’s always going to look like that exact same letter ‘S’.

There’s also glide reflectional symmetry. This is where an object can be flipped over a line and then moved along the same line. For example, if I draw a triangle with one vertex at the origin (0, 0) and another vertex on the x-axis (-3, 0), no matter how many times I flip it horizontally and move it to the right by 6 units, it’s always going to look like that exact same triangle.

Finally, we have point symmetry or rotational symmetry around a point other than the origin (0, 0). For example, if I draw an equilateral triangle with one vertex at the origin and another vertex on the x-axis (-3, 0), no matter how many times I spin it around that center point (-1.5, -1.5) or any other point along the line connecting those two vertices, it’s always going to look like that exact same equilateral triangle.

The different types of symmetry in math. Who knew there were so many? But hey, now you can impress your friends with all this newfound knowledge.