For those of you chemistry students out there, you know that the benzene ring is one of the most prevalent ring structures found in organic chemistry, and this chemical compound finds itself involved in many chemical reactions and even enmeshed in the ring structures of innumerable organic compounds. Moreover its versatility as a chemical reagent allows it to be used to synthesize drugs, plastics, gasoline, synthetic rubbers and dyes. So what does this have to do with math and in particular geometry?
The benzene ring is the principal chemical comprising a group called “aromatic compounds.” Benzene is called aromatic because it has a sweet pleasant smell and so do the other compounds of this family. In fact, at one point benzene was used as an after shave because of its pleasant smell. It was only when its toxic properties were discovered that it was discontinued for many of the commercial uses that it found itself employed in. Composition-wise benzene is made up of six carbon atoms and six hydrogen atoms bonded together in what is known as a de-localized system. Basically this means that the bonds are neither single nor double but a mix of the two. This is another amazing fact of the electron being able to be in more than one place at one time.
At any rate, the math “tie-in” is that the six carbon and six hydrogen atoms are arranged in a nice regular hexagonal ring structure which lends this particular aromatic stability and, because of this structure, gives it a predilection for forming all kinds of useful and interesting compounds. These include nylon and other synthetics; styrenes (precursors of many polymers) and plastics; rubbers and lubricants; and drugs and pesticides. Could it be more than coincidental the regularity of the benzene ring structure and its omnipresence in compounds and nature? I think this is a rhetorical question given that the deeper we plumb into the mysteries of mathematics the more keenly we see relationships to nature and the world around us.
For high school students now studying those properties of polygons—-particularly hexagons—-such as area, internal and external angles, and lines of symmetry, you might now see that such study is not a waste of time after all. You see geometric shapes and their concomitant properties really do find place in the world. Only through their study are we prepared to unleash the interesting uses of such ordinary geometric shapes.
Joe is a prolific writer of self-help and educational material and is the creator and author of over a dozen books and ebooks which have been read throughout the world. He is a former teacher of high school and college mathematics and has recently returned as a professor of mathematics at a local community college in New Jersey.
Tags: organic chemistry