First, SJsinNYC, a big Mazel Tov on the baby. May you have much nachas.
Second, Squeak, After having a chance to look at the gemara in more detail on Shabbos, I will take back my post, but for a different reason. It is clear the language of the Rashbam and Tosfos is completely megumgam, so I don’t know if we even have the correct text of either. (Note, in general, to change a girsa is very difficult to say, and borders on heresy, but for the honor of the rishonim, I think it can be done here. The Rashbam at first mentions that the 5×5 has a diagonal of 8, which even according to the gemaras well-known approxiimation that sqrt(2) =1.4, is wrong, and should read 7. Then he says that a 6×6 has diagonal 8.4, which seems totally irrelevant to the flow. He then brings in the 5×5 again. Possibly, a printer confused the shnei chumshin of the 8.4 with shnei chamishin (5×5). Maybe the Rashbam was trying to use 6×6 as a rough estimate of 4×6 (not 5×5), and say that it equals about 8, as well. (This would be a pshat in the Rashbam’s chada shiura, 4×6~6×6, they share a common dimension.)Then Tosfos fits very well. He first draws a picture of a 4×4 within a 4×6. He shows that the 4×4 has diag 5.6, and adding the two additional amos to get 4×6, means that at maximum, the diagonal of the 4×6 is 7.6, so how could the Rashbam say 8? Plus, if you use the direct diagonal in his picture, rather than the 2-step diagonal, kol shechain that it is less than even 7.6. Then in the second half of Tosfos one would have to change the girsa as well and say that 6×6=36 which is more square amos than 4×6=24 so for that reason, as well, the 6×6 is greater than the 4×6. So we can possibly defend both, but need to change girsos quite a bit.
However, merely because I initially said Chazal didn’t know how to calculate the diagonal is not an insult to Chazal, it just means they weren’t familiar with Pythagoras’s theorem. It is not an insult to say about current physicists that they don’t know cold fusion. It hasn’t been done yet. Note also, that in my original post I didn’t say Chazal didn’t know how to measure with a string, I said one can verify the Pythag thm with a string. In our case, differentiating the diag of a 4×6 from a 5×5 with string would be very hard, as they are so close, only a few percent apart.
Finally, in my second post above it should say that the 1×12 has diag *almost* twice the 5×5, not *more than*.