In 1 Kings 7 (King James version), we read the description of Solomon’s molten sea:
And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.
…which I take is some kind of bath. Superficially, it seems to state that , since the circumference of a circle of diameter given by . But what if “round about” doesn’t strictly means “perfect circle”?.
What if Solomon’s bath is an ellipse? A ellipse is described by the equation:
which is a scaled circle. The parameters and control the shape of the ellipse:
The circumference of the ellipse is
Solving the above for , with one of the axes fixed, say (because it has “ten cubits from one brim to the other”), we find:
Solomon’s bath is only 10% longer than wide. Not an outrageous ellipse.
So it could be that the Bible’s description of Solomon’s ritual bath is mostly accurate, and “round about” only means “rounded”. Most likely, however, is that the idea was that . The Egyptians, for example, while they didn’t seem to even have the concept of a constant such as , computed the area of a circle using th of a square with a side the same length as the diameter (that’s in the Rhind Mathematical Papyrus, problem 48). That’s already much better estimation for ; it implies , that’s less than 1% error!