Degrees in regular polygon
This is an expansion of the idea beyond the natural numbers; what if you use this formula for different values of ? Type your choice of into the input box. You can enter fractions by typing 7/2 or 3 + 1/2. Then drag the sliders for and to see what these represent.
This is a response to Dan Meyer's "Discrete Functions Gone Wild!". He expands the function to the rational numbers. But what about negative angles in the range of , like when ? Well, If f(x) is the function in the table, then by a precalculus exercise, . For example, f(4) = -f(4/3); either way, we obtain the vertices of a square, but in the opposite order. Or, f(9/4) = -f(9/5), so we obtain the same vertices with a switch of interior and exterior angles.