In a dense downtown area, the buildings are often touching each other. Imagine such a downtown. Now place your right hand on the (imaginary) building next to you and plan on keeping it there. Begin your imaginary walk and don’t let your hand leave the building. Just slide it along. When you encounter a corner, keep your right hand on the building and follow it around to the right.
If it’s a single building with streets on all four sides, you will walk all the way around it and end up back where you started.
And if it’s a solid block of buildings where each one touches the next, you’ll walk all the way around all of them and, no matter how the streets twist and turn, if you keep your right hand on the faces of the buildings and always turn right, eventually you will be back at your starting point.
Riding a bicycle, I used that rule to explore my neighborhood. Instead of using the buildings (houses), I used the curb. I rode on the right and kept the curb continuously on my right. Whenever a street joined the one I was on, the curb went to the right around that corner and so did I. In doing so — always turn right — I never crossed any streets.
On my ride, you can see what happens on a dead end. On bike I followed the curb, and walking I would keep my right hand on the building and loop down and then back out of the dead end.
The picture above is the Google-Earth view of the route around my neighborhood using that rule. According to the GPS on the bicycle that recorded the trip, the route covers 8.63 miles.
(Incidentally, the ride took 40 minutes and I averaged 9.8 MPH, a tad under my goal of 10 MPH. I’ll have to pedal a smidge faster on one, maybe two, of the gentle uphill inclines next time.)
If I cross the street before starting, I wonder how far that will take me?