Eruvin 51 - Is the residence area (techum) round or square?

Rabbah and Rav Yosef were traveling on the road late Friday afternoon, and they were concerned about their residence area for Shabbat. Rabbah said to Rav Yosef, "Let our Shabbat residence be established under that tree (he knew it) that produces so much fruit that it relieves its owner of paying taxes." Rav Yosef countered, "But I don't know it." Rabbah then quoted in the name of Rabbi Yose, "One who does not know the place can rely on the other one who does." That was not actually true, the rule was not in the name of Rabbi Yose, but Rabbah attributed it to him on purpose, so that Rav Yosef (who was blind) would accept its authority, since Rabbi Yose is known for deep reasoning behind his rulings.

What is the source for the two thousand steps limitations? It comes through a chain of "same word" connections, which ends up with the city of Levites, having a two thousand amot area of space and vineyards around it.

Was the techum area square or round? Rabbi Chanina ben Antignos says that it was round. What about the cities of the Levites, whose area around was square? - He notes that the Torah says "This will be or them the area around," and explains, "This for them" but not this for others. And the other teacher? He understands it, "Like this, for them and for others."

Art: Gustave Courbet - Red Apples at the Foot of a Tree

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