Techum Shabbos

Techum Shabbos

“Give the Leviim the inheritance of their fathers – cities to dwell in and open areas around the cities... You shall measure outside the city towards the eastern corner 2000 amos, to the southern corner 2000 amos, to the western corner 2000 amos, and to the northern corner 2000 amos, with the city in the center.” (Bemidbar 35, 2-5)

A person may walk in any direction from one’s place of dwelling on Shabbos up to a 2000-amos radius, called a Techum Shabbos. This law is derived or alluded from the verse cited above. Walking beyond this range is “travelling” and not permitted on Shabbos.

Our Sages teach (Eruvin 56b) that when determining the 2000-amos limit, one does not draw a circle around one’s residence.

1. If one resides in a city, then the entire city is one’s residence.
2. Any residence that is within 70 amos of the city is considered as residence of that city and the borders are extended to that point, at which one would then begin the count of 2000 amos.
3. If a city has four corners, we first “square out” the borders to make a rectangle or square. Then, we measure from each side 2000 amos in each of the four directions (learned from the verses above which mention corners). Next, a band around the city is completed by extending the 2000-amah border from each of the four sides until they meet at the corners, forming a larger square around the city.
4. If a city has a different shape such as a circle or triangle, we then extend the border making a square around the city. Further, if a city is wider on one side, we add space on the narrower side to make the square. And then the 2000 amos is counted from that “imaginary” square.
5. Further, every city has an extension of 70 and 2/3 amos of clear space outside its borders prior to beginning the 2000 amos measurement.
6. If two cities are within 141 and 1/3 amos of each other, then the cities are considered as if one city for the purpose of Techum Shabbos, and are combined to make the square to begin the measurement.

Of course, many other details and possibilities exist. Refer to your local orthodox Rabbi for guidance.

A consequence of “squaring out” is that at the corners of the imaginary square, one may walk the length of the diagonal of the square (whose sides are 2000 by 2000) which would exceed 2000 amos. The Gemara calculates this figure to be 2,800 amos using the “simplified formula” of “the diagonal = length of the side times 1.4” from “A” to “C”.

The precise formula (called Pythagorean Theorem) for a diagonal of a square is “diagonal = length of the side times (the square root of 2).” The square root of 2 is an irrational number which be approximated as 1.41421.., a slightly larger number than the simplified 1.4 used by our Sages. This would yield a diagonal of about 2,828 amos for our Techum Shabbos.