Eiruvin 4:8-9

Eiruvin 4:8

If a traveler on the road when Shabbos arrives doesn’t know of a landmark where he can establish his Shabbos residence, or if he just doesn’t know how to establish a Shabbos residence while traveling, so he says “My Shabbos residence is in my place,” his place acquires him 2,000 cubits in each direction. Rabbi Chanina ben Antigonos says the 2,000 cubits are in the shape of a circle; the Sages say that we inscribe the circle in a square so that he benefits from the corners. (If a circle with a 2,000-cubit radius is inscribed in a square, the diagonal distance from the center to a corner is approximately 2,800 cubits.)

Eiruvin 4:9

The Sages say that a needy person (i.e., a traveler without food) can make an eiruv techumin (to establish his Shabbos boundary) with his feet alone. Rabbi Meir limits this process to a needy person but Rabbi Yehuda said that the rich can also do so. A rich person happens to use food because it’s just easier for him to have someone place food at the spot he desires to set his eiruv than it is to travel there himself when Shabbos begins.