So setting here with my brother. We got into a debate on what would be more efficient if we were able to find a big enough circle that made it worth walking in circles. Here is what we came up with.
So we have 2 different size circles. A 1km circle and 2km circle. We are both speed walkers so we used the time it takes us to travel down to our Pokestop (.5km) which only takes 4 minutes. This may be hard to understand but I just got done mathing after a few years off from school. I theorized the smaller circle would be more efficient because if it took 8 minutes to finish walking the whole thing. The game would ping twice, both opposite from each other. Meaning you would get the diameter of the circle.
My brother, however, his hypothesis was a circle that took 16 minutes to walk. A 2km circle would be better and yield more distance/time. You would get 4 pings within the full circumference, rather than the 2. I swayed a little, then decided let’s figure it out! In the picture above (calculations could be wrong), it would be more efficient to find a circle you can hit the opposite side in 4 minutes (the time it takes for the game to ping to the servers). It doesn’t really matter how large the circle is as long as you can reach the other side in 4 minutes.
Now I know what you are all thinking. I said walking in circles was pointless, but I did some thinking and though it’s not the best way. It can still be done, in fact, it may be better and here is why. Say you walk 5km in a straight line and it took you 30 minutes to do so. Well, it would take another 30 minutes to walk back. By that time you have walked 10km and you are probably pretty tired or out of a drink or whatever the problem may be if there is one. Though the distance calculated towards your eggs will be shorter. You could practically take a break any moment and be in the vicinity of your home or vehicle.