What is Symmetry?


Symmetry is, by definition, the "mutual relation of the parts of something in respect of magnitude and position" or the "relative measurement and arrangement of parts." That is, according to the Oxford English Dictionary. However, when we see symmetrical objects, we do not think in such terms; we do not refer to a remembered definition. To us, if an object is similar in shape or size, it is symmetrical and that is all there is to it.

However, there is more to it than that. Symmetry is an extremely important idea and, as you will see within this web site, a part of almost everything-from music to magic, from chemistry to crossword puzzles. It is such a part of our daily life that we don't notice it and, so take symmetry for granted, that we don't study it or memorize the definition.

But, here on this website- Here on this webpage, we will take a stand! Today, we will reclaim symmetry (and its cousin, tesselations) for the common man-for every man!!!

And, now, back to reality. For our purposes, we will refer mainly to four types of symmetry:
  1. Reflectional Symmetry: If there is a line that cuts the image in two so that one side is the mirror image of the other. Also known as line symmetry, mirror symmetry, or a flip.

  2. Rotational Symmetry: A rotation and is specified by its center and an angle. Also known as a turn.

  3. Translational Symmetry: Results from shifting a figure in a specified distance in a certain direction. Also known as translating or a slide.

    And, finally, the mother of all symmetries (WARNING: Not for the weak of heart):

  4. Glide Symmetry: A combination of reflectional symmetry and translational symmetry: a reflection and a translation along the line of reflection. Also known in certain math circles as the moonwalk.

So, basically, a pattern is symmetric if there is at least one symmetry (rotation, translation, reflection, glide reflection) that leaves the pattern unchanged.



Tesselation


A dictionary will tell you that the word "tessellate" means to form or arrange small squares in a checkered or mosaic pattern. The word "tessellate" is derived from the Ionic version of the Greek word "tesseres," which in English means "four." The first tilings were made from square tiles.

Another dictionary will tell you that the word "tesselate" comes from Latin tessera "a square tablet" or "a die used for gambling." Latin tessera may have been borrowed from Greek tessares, meaning "four," since a square tile has four sides. The diminute of tessera was tessella, a small, square piece of stone or a cubical tile used in mosaics. Since a mosaic extends over a given area without leaving any region uncovered, the geometric meaning of the word tessellate is "to cover the plane with a pattern in such a way as to leave no region uncovered." By extension, space or hyperspace may also be tessellated.

The dictionaries tell you all this but the mantra of our group, TEAM SYMMETRY, is: Never trust anyone you can't see.

So, we recommend instead clicking here for Alex's definition. You can trust him because, besides being the most handsome member of the Yale undergraduate population, he'll give you his home address. So, if he's wrong, you can go beat him up. Would Mirriam Webster do that?

So, here's the info:

Or call him at:


If you're angry or a nice attractive girl, give him a call, pay him a visit, beat the stuffing out of him. And, maybe, if you're lucky, he'll do his Rod Serling impression for you.


Page author: Alex Timbers