Yes, this is an *approximation*. Even *if* you can justify the use here, it still gives an approximation and not the actual value. In fact, the approximation given is worse than the typical 22/7 often used as an approximation and much worse than the next continued fraction estimate of 355/113.<quoted text>
"Now that you have some background information, let's look at the actual numbers:
Here again is the quote being referred to:
"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." — First Kings, chapter 7, verses 23 and 26
The bowl is said to have had a circumference of thirty cubits and a diameter of ten cubits. The diameter is said to be "from one rim to the other", so this would be the outer diameter; that is, the diameter of the outer mold used to make the bowl.
The circumference is not specified as being the inner or outer circumference, but since using the outer circumference would give us the "ideal" bowl (with no width or thickness), let's instead use the inner circumference, which also, reasonably, would have been the circumference of the mold used to form the inside of the bowl. That is, we will use the two measurements which were necessary for the casting of the piece.
Using eighteen inches for one cubit, we have the following:
outer diameter: 10 cubits, or 180 inches
outer radius: 5 cubits, or 90 inches
inner circumference: 30 cubits, or 540 inches
To find the "Jewish" or "Bible" value for pi, we need to have the inner radius. Once we have that value, we can plug it into the formula for the circumference and compare with the given circumference value of 540 inches.
Since the thickness of the bowl is given as one handsbreadth, then the inner radius must be:
90 – 4 = 86 inches
Let's do the calculations:
inner radius: 86 inches
inner circumference: 540 inches
The circumference formula is C = 2(pi)r, which gives us:
540 = 2(pi)(86)
540 = 172(pi)
Solving, we get pi = 540/172 = 135/43 = 3.1395348837..., or about 3.14.
Um... Isn't "3.14" the approximation we all use for pi? Perhaps those Phoenicians were fairly accurate after all."
The point is that various estimates of pi (some contradicting) were common in all societies because the area of a circle of given diameter (or radius) is a useful thing to know. It turns out that the Babylonians were somewhat better at these approximations than the Egyptians. None-the-less, it wasn't until the third century BC that Archimedes first *proved* some estimates for pi, obtaining that 223/71<pi<22/7.