Chulin 29 - Can One Divide Exactly In Two Halves?

If in doing the shechitah one cuts exactly half of the pipe's circumference, Rav says that it is valid, because God told Moses not to leave over more than half uncut, and Rav Kahana says that it is invalid, because God told Moses to but the greater part when slaughtering.

An objection against Rav comes from the laws of purity. If one split a ritually impure earthenware oven into two pieces, ostensibly of the same size - they both remain impure, because it is impossible to be precise in anything, and any of the two pieces might be the larger one. However, if it were possible to be precise, the pieces would be pure! But, according to Rav, exactly half is considered like more than half, and thus the pieces should remain impure, which proves that Rav is wrong! Said Rav Pappa in Rav's defense, in an oven both pieces cannot be the larger ones, but in slaughter we care only about the part that is cut.

In the end the Rav's point of view is revised as untenable, and instead we say that the argument is not about shechitah, but about half of all Jews being impure on Passover.

Art: Pieter Harmansz Verelst - A young boy reclining, eating from an earthenware bowl