Publication Year

2001

Keywords

Group theory, chemistry, symmetry, mathematics

Disciplines

Applied Mathematics | Chemistry | Mathematics

Abstract

Symmetry is a concept that is familiar to many people. Symmetry is apparent in nature as well as most architecture that humans find aesthetically pleasing. For instance, many blossoms are very symmetric and the Eiffel Tower contains high levels of symmetry. If you were to place an axis from the center of the four "feet" of the Eiffel Tower through the top peak, you could rotate the Eiffel Tower 90 degrees and the Tower would look identical to the starting arrangement (excluding the two leg elevators and the ticket booths at the bottom of the Tower!). Symmetry has also been found at the microscopic level. Molecules take on different three-dimensional geometric shapes depending on the most stable arrangement of atoms and electrons around the nuclei. Molecules such as water, which is usually described as having a bent geometry, as sen in Figure 1, have easily apparent symmetry. In our example of water, we can see that the left and right sides of the molecule are symmetrical, that is, they are mirror images of each other. This and the other symmetries of the water molecule will be discussed later in this paper.

Department 1 Awarding Honors Status

Chemistry

Department 2 Awarding Honors Status

Mathematics

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