The Mishna (13b) discusses different possibilities regarding the shape of the Kora (cross beam) that is used to symbolically close the open end of a Mavoy (alleyway). In discussing a round Kora, the Mishna teaches a mathematical rule that the ratio between the circumference of a circle and its diameter is 3:1. The Gemara (14a) shows the source for this principle to be the passages in Sefer Melakhim I (7:23) which describe the various utensils in Solomon’s Temple, including the Yam shel Shlomo – the reservoir of water in the Temple that was used by the priests to wash their hands and feet. This reservoir is described as being ten amot across, with a circumference of 30.
According to the simple reading of the passages describing the Yam shel Shlomo, it was a huge half-globe about five meters in diameter. The globe sat on twelve legs, three on each side, that were shaped like cattle. (Keep in mind that, unlike most of the utensils in the Temple, which have very exact specifications, the Kiyor (=laver or washing station) is not described in the Torah. Therefore it was redesigned to accommodate the needs of the Temple priests at various times. During the Mishkan period it had only two faucets; during the Second Temple a donation from one of the Kohanim allowed it to be designed with 12.)
Already in the medieval period there was recognition that the ratio of circumference to diameter in a circle was larger than 3:1, as is noted by the Tosafot on our page. The popular explanation is that the difference is so small that it was ignored by the Sages. Maimonides, in his commentary to the Mishna, argues that pi is an irrational (and perhaps even a transcendental) number which cannot be expressed using normal numerals. Since it is impossible to state pi in a definitive way, the Sages chose to use a simple estimate that closely matches the true relationship – 3:1.