Solving Equations in the Dihedral Group D4 of Symmetries of a Square (Get Perfect Squares & Cubes)
The group of symmetries of a square is the Dihedral Group D4 of order 8 consists of elements D4 = {R0, R90, R180, R270, V, H, D, D'}.Which elements are perfect squares and perfect cubes in this group? We can define two functions f:D4 → D4 and g:D4 → D4 by f(x)=x^2 and g(x)=x^3 and make a table of values to answer this question. In other words, we can find all solutions of the simple quadratic and cube equations x^2 = a and x^3 = a in D4 (solve for x). • Abstract Algebra Course, Lecture 1: I... .
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