Answer to Question #24465 in Complex Analysis for Harini

Question

Mickey as well as being a very clever mathematician is also a keen gardener and has a fenced allotment which has a square shed placed in one of its corners.In order to celebrate his wife Gilly’s 36th birthday, he decides to allocate a region of his allotment to her and also one to each of their two children, Philly and Tilly.Gilly said “I like how each region has a common vertex at the corner of the shed not in contact with a fence”.Philly, the elder son, was also impressed, thinking “I do like how each of our regions is a different regular polygon whose side length is the same as the width the shed and the shed’s corner with the vertices from the three regions makes a full turn”.Unfortunately Gilly was less impressed by her husband’s design idea saying “I always thought you were irrational but did you really have to make the area of each region proportional to the square root of our ages and what is the baby supposed to do with her plot?”Determine the shape of the regions allocated to Gilly, Philly and Tilly