This application finds the best packing and largest radius of equal-sized circles, such that they fit in a pre-defined triangle. One solution, as visualized by this application, is given below.

This is a difficult global optimization problem and demands strong solvers. This application uses Maple's Global Optimization Toolbox.

Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 20 circles generates 310 constraint equations.

The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations. The vertices of the triangle can also be modified

Applications like this are used to stress-test global optimizers.