truthsharer,
Sure leeches are back in style, however not even close to the amounts that Dr. Rush and physicians in his day made use of.
Stating that Chazal were not interested in experimentation is 100% wrong. When it came to relying Halachicay on any scientific theory they absolutely experimented an example is in the first perek of Kesubos. Another example would be Rosh Hashonah which clearly contains numerous examples of evidence based calculations resulting from observation in calculating the Molad and other parts of Kiddush HaChodesh.
Further more this point was actually emphasized by Rav Chaim Volozhiner in Shaar Daled of Nefesh HaChayim where he discusses the need to be expert in certain anatomy’s such as grasshoppers in order to properly rule on them in regard to what is the proper “lishmoh” of Torah learning.
As for the statement of Pi, that’s a pretty bad example as the Gemorah (Sukah) there states clearly it is rounding out meausements because of Lo Duk, furthermore the Gemorah on Amud Beis expliclty rounds up the area needed for a circular circle.
The theory that Chazal did not experiment comes from the fact that Galileo proved many parts of Aristotle’s theory through experimentation, consequently people have decided that it must be Chazal had the same approach.
However anyone who has studied Takmud knows the comparisons have no basis in reality as Chazal clearly show the need for experimentenation before relying on any theory in a Halachic manner.