Explanation #1: [One checks] at the beginning of the 80 days, at the end of 80 days, and in the middle of 80.

Support: We can explain like this what it says in Megilah (19a) regarding [sewing together parchments of] a Megilah. It says that if he made three stitches of sinews it is Kosher, and it says "as long as they are Meshulashin" (evenly spaced), i.e. at the beginning of the parchment, in the middle and at the end.

Explanation #2: There Rashi explained that there is from the beginning of the parchment until [the first stitch of] the sinew like from [a stitch of] the sinew to the next, both above and below.

Support: The case in Makos (9b) is surely like this regarding Arei Miklat. "V'Shilashta" - they should be Meshulashin, that [we pick cities that are evenly spaced]; there is from the south [of Eretz Yisrael] until Chevron like from Chevron until Shechem and from Chevron until Shechem is like from Shechem until Kadesh and from Shechem until Kadesh is like from Kadesh until the north;

We do not say that they should be at the head (e.g. south) of Eretz Yisrael, and the [other] end, and in the middle.

And here Rashi explained that they should be evenly spaced in three parts. If he sees it today, he checks it on day 26 and a half from now, and again after [another] 26 [and a half days... and again] on day 80.

It seems that Rashi explained so according to the way [it is explained] in Makos. However, it is not totally like there, for [if so] he should have explained that he checks at the end of 20, and at the end of 40, and at the end of 60, so there will remain 20 after the last Bedikah just like before the first Bedikah, and one cannot explain so at all! (If so, the Bedikah ends at 60 days. Why does it say 80?!)

Rather, it is like I explained initially, like it connotes in Yevamos (80a) regarding a Seris Chamah (one who does not develop like a normal male). It explains that it is anyone who did not have a time of Kashrus (before becoming a Seris);

[The Gemara] asks that we should be concerned lest he became healthy in the middle, and answers that since he was stricken at the beginning and at the end, we are not concerned. This connotes that the three times are at the beginning, end and middle!

Assertion: It seems that villages Meshulashin in Eruvin (57a) is unlike here, and unlike in Makos. (Rather, they are in a triangle.)

Observation: In Zevachim (25b), the text says d'Tanya ha'Tzorem.

Distinction: The end of the verse "uv'Artzechem Lo Sa'asu" discusses even the Beitzim - any places that castrates, and even through drinking a sterility potion we forbid in Shabbos (110b);

Regarding a Mum, it is not considered an exposed Mum, like [the Gemara] explains the reason below.

Explanation #1 (Rashi): The skin and the meat were peeled off and the bone was left exposed, like "Asher Pitzel" (Yakov peeled sticks).

Question: In the wording of the Mishnah and the Gemara, it should have said "v'Niklaf"!

Explanation #2: "It is Mefatzel the bone" into two. This is like Mefutzalos regarding horns, in Chulin (59b). They branch to here and here.

Support: The Tosefta (4:7) teaches "or the end of the tail was Mefutzal to two bones."

Question: One must be meticulous to deduce whether there are four in all, or four of white (i.e. not Techeles) and four of Techeles, and also whether we discuss before doubling the threads, that when he doubles them they are 16, and now the eight threads that we do are for the sake of white, for we rule like Beis Shamai in Menachos (41b), and if one of them snapped, it is Pasul;

And even though we are Machshir when Techeles was cut and only white remains, all of [our four doubled threads nowadays] are for the sake of white.

Inference: The Sifri in Ki Setzei connotes like this, that the four threads are of each kind;

It taught there "how many Gedilim are made? There are no less than three threads, according to Beis Hillel. Beis Shamai say that there are four of Techeles and four of white, of four fingers each, and the Halachah follows Beis Shamai.

Question: In Menachos (38b), it says that R. Yirmeyah mi'Difti inserted eight [folded] strings through the corner, which are 16 ends. Mar brei d'Ravina did as we do. (He put four unfolded strings through the corner.) This connotes that most do like Mar brei d'Ravina!

Answer: Perhaps [Mar brei d'Ravina] explained that the four white and four Techeles that Beis Shamai say are after he doubled them, i.e. two threads of each kind before they were doubled.

Consequence: According to this, what we do nowadays is half for the sake of white, and half for the sake of Techeles.

Disclaimer: However, the three that Beis Hillel say, you are forced to say that they are before they were folded, for one cannot find three (an odd number) after folding. Now (according to this answer, the three of Beis Hillel are) unlike the four of Beis Shamai (according to Mar brei d'Ravina).

Explanation #1 (Rashi): [We ask how much] hangs below the corner of the garment, for they do not put it truly in the end of the garment. Rather, they raise it three fingers according to Beis Hillel, and four according to Beis Shamai.

Question: Regarding distancing from the corner, we require like [the width of] the joint of the thumb. It mentions within three fingers only to exclude above (further than) three.

Explanation #2: Rashi's other Perush is correct. We ask how much is Meshuleshes - how much is in the Gedil (windings), aside from the Anaf (what hangs straight), which is not Gedil. Beis Shamai say that it is four fingers.

Consequence: Now, the beauty of Tzitzis is a third Gedil and two thirds Anaf. The Gedil is four fingers, and the Anaf is eight fingers. They are 12 fingers in all.

Support: The Sifri connotes like this. The four [threads] of white are four fingers each.

Explanation #3: In Menachos (38b) Rashi explained [that the Tana'im discuss how much] Anaf hangs down, aside from the Gedil. [Beis Shamai say] four fingers.

Consequence: According to this, the beauty of Tzitzis is two fingers of Gedil and four of Anaf.