Abstract
The operation (c) of taking the complement of an angle (α) is of order (period) two, since 90° –(90° –α) = α. Similarly, the operation (s) of taking the supplement of an angle is of order two. If we perform these two operations in succession there results an operation (cs), which is of order four since it changes α into α + 90° Hence the group {c, s} generated by c and s is the dihedral rotation group of order 8. This fact follows directly from the general theorem, Two operations of order two generate the dihedral rotation group whose order is twice the order of their product.
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