This is a model for optimizing the optimization radius problem in the improved k-means algorithm. The algorithm works to "divide and conquer" by splitting into two points on opposite sides of a circle. The circle's radius is defined by 1/2 the average Euclidean distance from all points to their arithmetic centroid (average coordinate point). The circle's center is the arithmetic centroid of all the points.
The algorithm works to find the quickest relative minimum of this function by binary searching its derivative with respect to x.

N.B: The function here is not how the algorthm actually finds the solution; the function is just graphed with respect to an angle on the circle for the sake of understanding how the algorithm works. Also note that due to the limited interval of x, the algorithm is guaranteed to find a quick solution every time, but the solution is not guaranteed to be optimal (the absolute minimum value calculated through the derivative).