While designing a new logo for our company I had to solve a version of the geometric problem below. I have repackaged it here in the form of a puzzle that I hope others might enjoy!
The pigeon drawn above in the Cartesian plane:
- consists of a straight line and 5 circle arcs
- is perfectly smooth along its perimeter except for the points labeled B,C,D and E on the graph
- tiles the plane
Assuming that the weight of the pigeon is distributed uniformly across its area, what are the co-ordinates of E such that it balances exactly on its foot?
Not really an answer: I've just prepared the figure below, with the relevant geometric information. But finding the center of mass is too tedious for me...