The Sages established that one’s mekom shevita on Shabbat is square, and thus his teĥum is square as well. This means that if he is spending Shabbat in a field, and his mekom shevita is thus four amot, the measurement is not made by drawing a circle around him with a diameter of four amot. Rather, to determine his mekom shevita we inscribe such a circle in a square with four-ama sides along the four cardinal directions, which adds space to his mekom shevita at the corners. Similarly, if one’s mekom shevita is in a city or town, even if the area is round, we inscribe it in a square or rectangle, adding space at the corners (m. Eruvin 53a).
Then 2,000 amot are measured in each direction. Once again we draw a square or rectangle, which once again grants him additional space in the corners.
This rule, that we square off the city, is derived from the Torah’s description of the area the Levites were given outside each of their cities:
You shall measure off two thousand amot outside the city wall all around. You shall measure off two thousand amot outside the town on the east side (lit. corner; same applies to the other directions), two thousand on the south side, two thousand on the west side, and two thousand on the north side, with the city in the center. (Bamidbar 35:5)
The most straightforward explanation for why we square the teĥum is that it is extremely difficult to measure and mark off a circular boundary. One would need to measure 2,000 amot from almost each and every point of the city’s perimeter. In contrast, when marking off a square boundary, only four measurements need to be made – one in each of the four cardinal directions. After that, a straight line can be drawn in each direction, and the result is the teĥum.
Additionally, this method reflects a spiritual reality. A circle represents the infinite, which has no beginning and no end. A person’s life is circular and cyclical. His actions, wishes, and thoughts repeat themselves cyclically. Even his limbs are circular and cylindrical. This makes it difficult for a person to realize his aspirations. The way to solve the problem is to take one’s “circular” infinite ideas, and give them a “square” finite framework that will help him put them into practice. This is the meaning of teĥum Shabbat, which is meant to provide a framework for absorbing the holiness and blessing of Shabbat. This is why each city belonging to the Levites, who are charged with revealing faith in this world, is surrounded by a square boundary.