why do we need, by korahas haKerem, besides the 4 amois needed laavoidas each side, 8 amois in the middle in order to have 2 sodois hachouvim in order not to be botel laKerem. Why wouldn't 4 amois be hochouv enough to stay by itself without being botel to any side
Dovid, Paris France
I found that the Yalkut Bi'urim of the Metivta edition (p. 38, note 56) on Eruvin 3b (where the Gemara also discusses Korachas ha'Kerem) asks your question.
1. However, it seems to me that the explanation is as follows.
Rashi to Eruvin 3b (DH v'Im) writes that the 4 Amos which must be left l'Avodas ha'Kerem are "k'Kerem Dami" -- these 4 Amos next to the Kerem are considered to possess an identical status to the Kerem itself. Since these 4 Amos serve the Kerem, they are considered Halachically as part of the Kerem.
2. According to this, the edge of the Kerem, where the Kerem finishes, is 4 Amos further away from where the vineplants cease to grow. It follows that if one wants to sow seeds, he must leave a distance of 4 Amos from the edge of the Kerem. Since the edge of the Kerem is 4 Amos away from where the vineplants cease to grow, this means that one must add on 4 Amos after the edge of the Kerem and only there may he begin to sow. Therefore, one must leave a total of 8 Amos on each side from where the vineplants cease to grow.
3. Since we have seen that there is a Kerem on each side of the empty middle territory, it follows that one leaves 4 Amos from each Kerem on either side. Since there is a full-fledged Kerem on each side of the empty middle terrritory, sowing seeds is permitted only if one leaves a significant space after the Kerem. Less than 4 Amos is not considered a significant space.
4. This is what Rashi (3b, DH v'Im) means when he writes that if there is 8 Amos in the center, when one splits this into two he is left with a "Makom Chashuv" on each side. This is required because the Kerem on either side is a Makom Chashuv, so if there is not a Makom Chashuv next to the Kerem this area will become Batel to the Kerem and one may not plant there. Therefore, if there is less than 8 Amos in the center this means that there is not a Makom Chashuv to go next to the Kerem on either side, so the Kerem will override the area of less than 4 Amos and one may not sow there.
5. In other words, since there is a full-fledged Kerem on each side of the center area, one needs a Makom Chashuv next to each Kerem to distance the Kerem from the seeds. One Makom Chashuv is not sufficient to distance 2 Keramim from the seeds.