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A little known write of the rule book reads
And he make a molten sea, ten cubits from the unmatched brim to the other: it was round all about, and his height was 5 cubits: and a line of thirty cubits did compass it about. (I Kings 7, 23)
The same verse can be prime in II Chronicles 4, 2. It occurs in a list of specifications for the great temple of Solomon, built nearly 950 BC and its interest here is that it gives ? = 3. Not a rattling accurate economic value of course and not even in truth accurate in its day, for the Egyptian and Mesopotamian values of 25/8 = 3.125 and ?10 = 3.162 have been traced to oft earlier dates: though in defence of Solomons craftsmen it should be noted that the item being exposit seems to have been a very large brass casting, where a high degree of geometrical precision is neither manageable nor necessary. There are some interpretations of this which lead to a much better value.
The fact that the ratio of the circumference to the diameter of a circle is constant has been known for so long that it is quite a untraceable. The earliest values of ? including the Biblical value of 3, were almost certainly found by measurement. In the Egyptian Rhind Papyrus, which is dated about 1650 BC, at that place is good evidence for 4 × (8/9)2 = 3.
16 as a value for ?.
The first theoretical calculation seems to have been carried out by Archimedes of Syracuse (287-212 BC). He obtained the approximation
223/71 < ? < 22/7.
beforehand giving an indication of his proof, notice that very considerable edification involved in the use of inequalities here. Archimedes knew, what so many flock to this day do not, that ? does not equal 22/7, and made no claim to have discovered the exact value. If we postulate his best estimate as the average of his two move we obtain 3.1418, an error of about 0.0002.
Here is Archimedes argument.
Consider a circle of radius 1, in which we...If you want to get a full essay, order it on our website: Ordercustompaper.com
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