Problem 2: Consider the regular polygons. Taking the centre of each polygon to be its origin, we can define vectors for the vertices, stretching from the origin at the centre to each vertex. Find explicitly the sum of all vertex vectors for the first four regular polygons (i.e. equilateral triangle, square, regular pentagon and regular hexagon), and find a general result for the sum of the vertex vectors in a regular polygon of any number of vertices. BONUS: For an irregular polygon, at what point of the polygon should we put the origin such that we retrieve a similar result for the sum of the vertex vectors?

Problem 2: Consider the regular polygons. Taking the centre of each polygon to be its origin, we can define vectors for the vertices, stretching from the origin at the centre to each vertex. Find explicitly the sum of all vertex vectors for the first four regular polygons (i.e. equilateral triangle, square, regular pentagon and regular hexagon), and find a general result for the sum of the vertex vectors in a regular polygon of any number of vertices. BONUS: For an irregular polygon, at what point of the polygon should we put the origin such that we retrieve a similar result for the sum of the vertex vectors?