On the Constructibility of n-Division Points of Certain Polar Curves by Area
By Nithin Kannan and Young Kim
Constructing and n-dividing different polar curves through the use of straight- edge and compass constructions are proven using Field Theory. Some of the solved systems include arc length divisions for circles, hypocycloids, and lemniscates. However, little has been done in terms of n-dividing area of pre-drawn polar curves. Using theory allows for a closed determination of the possible n-divisions, since it gives a closed form for possible lengths and angles. Constructibility can be applied to the long-standing ancient Greek “unsolvable” problems, roots of unity in complex analysis, and computer science through binary digits.