1) HALACHAH: WRITING A SEFER TORAH ON "KLAF"
OPINIONS: The Gemara cites a Beraisa which relates that the Chachamim asked Rebbi how tall must a Sefer Torah be, and he responded that a Sefer Torah written on Gevil, a type of thick parchment, must be six Tefachim tall. When they asked him how tall it must be when written on Klaf, a thinner type of parchment, he said that he did not know.
It is a Halachah l'Moshe mi'Sinai that a Sefer Torah must be written on the type of parchment known as Gevil (as the Beraisa in Shabbos 79b states, and as the RAMBAM writes in Hilchos Tefilin 1:8). Why, then, did Rebbi respond that he did not know how tall a Sefer Torah must be when written on Klaf? Rebbi should have said that a Sefer Torah may not be written on Klaf at all.
The Rishonim (RABEINU CHANANEL cited by the RAMBAN, and RASHBA) prove from this Gemara that a Sefer Torah may be written on Klaf. However, they disagree about whether it must be written l'Chatchilah on Gevil, or whether it may even be written l'Chatchilah on Klaf.
(a) RABEINU CHANANEL writes that l'Chatchilah one may not write a Sefer Torah on Klaf, for Rebbi did not write such a Sefer Torah (nor did Moshe Rabeinu). Rather, Rebbi's words indicate that a Sefer Torah is valid only b'Di'eved when it is written on Klaf. This is also the view of the RAMBAN and the RAMBAM (Hilchos Tefilin 1:9). (This indeed is the practice of the communities of Teiman (Yemen), who are stringent to write Sifrei Torah only on Gevil.) When the Halachah l'Moshe mi'Sinai teaches that a Sefer Torah must be written on Gevil, it means that l'Chatchilah it must be written on Gevil.
(b) The RASHBA writes that one is permitted l'Chatchilah to write a Sefer Torah on Klaf, in contrast to the simple understanding of the Halachah l'Moshe mi'Sinai in Shabbos (79b). He cites proof from the Yerushalmi, and he asserts that the fact that Rebbi did not say that l'Chatchilah one should not write a Sefer Torah on Klaf shows that it may be done even l'Chatchilah. Moreover, the Rashba proves that it may be done l'Chatchilah from the fact that the masses of people conduct themselves today this way ("Puk Chazi Mai Ama Davar"). (I. Alsheich)
2) THE DEATH OF RAV ACHA BAR YAKOV
QUESTION: The Gemara relates that Rav Acha bar Yakov wrote only one Sefer Torah, and it happened to come out with the proper measurements, its height equal to its circumference, which is a very difficult feat to accomplish (especially with the first Sefer Torah one writes). The Rabanan "set their eyes upon him" and he died.
Why did the Rabanan set their eyes upon him? What is wrong with writing a Sefer Torah that comes out to have the correct measurements? It does not seem that they merely gave him an "Ayin ha'Ra" which caused him to die, because such a thing would not come about through the Rabanan but only through lowly people who do not like to see others succeed.
ANSWER: The CHASAM SOFER answers that the Rabanan may have thought that since the first Sefer Torah that he wrote came out with the exact measurements, Rav Acha bar Yakov must have used the Divine Name to make it happen. They felt it was not appropriate to use the Name of Hash-m for such a purpose, and therefore they set their eyes upon him. The punishment for using the Divine Name for a personal purpose is written in Avos (4:7): "d'Ishtamesh b'Saga Chalaf." (I. Alsheich)

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3) FITTING THE SEFER TORAH INTO THE ARON HA'KODESH
QUESTION: The Gemara quotes a Beraisa which states that a Sefer Torah's height must be equal to its circumference. Rebbi states that the height of a Sefer Torah must be 6 Tefachim. The Gemara presents a formula that calculates the diameter of a cylindrical shape as one third of its circumference. According to that formula, the diameter of a Sefer Torah must be one-third of its length (which is equal to its circumference), or 2 Tefachim.
The Gemara questions this measurement from another Beraisa in which Rebbi Meir states that the Sefer Torah of Moshe Rabeinu rested inside the Aron ha'Kodesh. The Beraisa explains that 12 of the 15 Tefachim of the length of the Aron (which was 2 and 1/2 Amos, or 15 Tefachim, long) were taken up by the two Luchos, each of which was 6 Tefachim long. An additional Tefach was taken up by the thickness of the walls, and the remaining space of 2 Tefachim was the space in which the Sefer Torah was placed.
The Gemara asks, how could the Sefer Torah have fit into those 2 Tefachim? If the height of a Sefer Torah is 6 Tefachim, then its width (diameter) must be 2 Tefachim. However, since a Sefer Torah is rolled from its two sides towards the middle, there must be additional space left between the two rolls. Consequently, the Sefer Torah would need more than just 2 Tefachim of space.
The Gemara's question is difficult to understand. Perhaps the Sefer Torah rested on its side (with one roll on top of the other), and thus it took up less than two Tefachim of space in the Aron. (The RASHBA writes that its width was only one Tefach. This is difficult to understand, though, because a calculation of its dimensions shows that it was more than a Tefach wide, as the RASHASH asks. The PNEI SHLOMO addresses this question and gives an answer for the Rashba.) Since the Sefer Torah was rolled up on two sides towards the middle of the Sefer Torah, if one roll rested on top of the other, together they would take up less than two Tefachim of width. Why does the Gemara assume that the Sefer Torah was not placed in the Aron in this manner? (RAMBAN, RASHBA)
ANSWERS:
(a) The RASHBA answers that it is not reasonable to suggest that the Sefer Torah was placed on its side, because that is not a proper position in which to place a Sefer Torah. It is disrespectful to the Sefer Torah to put it down in such a fashion.
(b) The Rashba answers further that even if the Sefer Torah was placed on its side, it still would not fit properly in the dimensions of the Aron, for in such a case the space in which the Sefer Torah was placed would be too large. There would be a Tefach of space left between the Sefer Torah and the Luchos (as mentioned above, the Rashba himself maintains that the width of the Sefer Torah was only one Tefach), and, consequently, when the Aron would be moved, the Sefer Torah might fall over.
The Rashba adds that this answer also explains why the Gemara does not suggest another possible position in which the Sefer Torah might have been placed. If the Sefer Torah had been placed upright, with the front of the two rolled sides facing the Luchos, it would have stood in a space of one Tefach. Seemingly, this position would answer the Gemara's question of how the Sefer Torah stood in the Aron. The Rashba resolves this question with the same answer: the Sefer Torah could not have been placed upright in the Aron, because when the Aron would be moved the Sefer Torah would lean into the Tefach of space between it and the Luchos, and it would not remain upright.
The Rashba gives another answer to his second question. It is simply improper to place a Sefer Torah in an upright position. The Rashba adds, however, that he has seen that in all places it is in fact the practice to place a Sefer Torah in an upright position. (He concludes that placing the Sefer Torah on its side is not respectful, and those who do so should be admonished.) (I. Alsheich)