Watch it Ichy: I'm goin' for the record!
PI in the Bible
By Jochen Katz1 Kings 7:23 He [Solomon] made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim [diameter = 10] and five cubits high. It took a line of thirty cubits to measure around it. [circumference = 30]
Since circumference = PI x diameter as any elementary geometry book will tell you, but the Bible "seemingly" tells us that PI = 3. Since "this is obviously false, therefore the Bible cannot be from God..." is how some people like to reason.
But obviously the wisdom of God is greater than the wisdom of man:
In this case the word for circumference = "line" (
in Hebrew)
But in this verse "line" is written with an extra letter (
).
Since Hebrew has no digits, all letters are also numbers, we can take the ratio of (the gematriacal value of) the unusual word form ( ) to the regular word form ( ). Given that the gematrial letter values are = 100, = 6, and = 5 we find that:
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| 5 + 6 + 100 = 111 | 6 + 100 = 106 | 111/106 = 1.0471698 |
| False number for PI | Ratio | TOTAL |
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1.0471698 | = 3.14150943... |
The real value: PI = 3.1415926...
The difference between 3 x 111/106 and PI is 0.0000832 which is only an error of 0.00026%.
It is interesting to compare the "Solomonic" approximation of PI with the approximations used by the Babylonians and Egyptians.
PI = 3.1415926... Error Babylon : 3 1/8 = 25/8 = 3.125 0.0165926 Egypt : 3 13/81 = 256/81 = 3.16049382... 0.0189012 "Solomon": 333/106 = 3.14150943... 0.0000832Since the ancient Egyptian or Babylonian approximations are much older than the time of Solomon it might be interesting find out what the usually used approximation of PI was at that time (Solomon was King around 1000 B.C.) in this or other parts of the world. Any helpful information on this question would be very much appreciated.
The "sound exegesis" answer: The Bible is not a scientific text book (though sometimes it makes scientific statements) and this specific passage wasn't intended to reveal the value of PI but to give a description of what the temple and its "furnishing" objects looked like. But given that the value "3" is within less than 5% error compared to the real value of PI = 3.14159... this is an acceptable approximation, even though "31 cubits" length would have been the (correctly rounded) answer that we might have expected. But who knows what "rounding" entailed in these days. And in a certain sense "30" is a "rounder" number than "31". And these last remarks are made all under the assumption that this above mentioned astonishing approximation is NOT intended.
Another interesting aspect, the letters used here are the only letters in Hebrew that will reveal this ratio with the difference between the gematriacal value of 3 letters and 2 letters. In other words this is the absolute lowest mathematical sequence in Hebrew to produce this ratio.
Taking into account further information a few verses later, provides us with yet another way of understanding the text. In 1 Kings 7:26 we read about this metal pool:
1 Kings 7:26 It [the above mentioned metal pool] was a handbreadth in thickness, and its rim was like the rim of a cup, like a lily blossom. It held two thousand baths.
which we can imagine to be like:
`\ /' d = the measured diameter between
| | the extreme points of the rim
| |
| | but circumference is measured below
| | the rim at the actually smaller
| | diameter c
\_________________________/
*--------------d-----------------*
|/'
*-----------c------------*
Given this information and assuming that exact numbers are given we could even calculate the width of the rim, if we want to... [that is a home work problem for the interested reader].
I prefer pi
"Pi" and More in Torah
The Bible and the Value of "PI" Does the Bible contain a mathematical error? Not at all! Biblical Value of Pi Solomon and the Molten Sea In describing the temple that King Solomon built for the King of Kings, several articles of furniture are described. One of these pieces is “a molten sea.” II Chronicles 4:2 reads thus, “Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.” A supposed discrepancy has arisen from this passage concerning the mathematical accuracy of the Bible. The value of π (pi) is known to be equal to the circumference of a circle divided by its diameter, The aforementioned scripture states that the molten sea was “ten cubits from brim to brim” and “a line of thirty cubits did compass it round about;” thus, its diameter was 10 cubits, and its circumference 30 cubits. Dividing this circumference of 30 by a diameter of 10 gives a value of exactly 3. This is where the questions arise. It is commonly known that the value of π is approximately 3.14159265358979. In fact, this value has been proven so exactly, that its value is known to hundreds of thousands of digits. Why then does the Bible appear to give the value of π to be 3? A diameter of 10 cubits should yield a circle having a circumference of more that 31.4 cubits--not 30 cubits. Is the Bible just rounding things off? Are the Biblical values just approximate and not really exact? If we see here that the scripture is not exact, what other passages also contain words that cannot be received with complete accuracy? 1 Kings 7:26 It [the above mentioned metal pool] was a handbreadth in thickness, and its rim was like the rim of a cup, like a lily blossom. It held two thousand baths. If the diameter of this bowl was 10 cubits, then the circumference should have been 31.415926 cubits, and not just 30 cubits! Any math student will tell you that the circumference of a circle is found by taking the diameter times Pi (3.14159265358979...), is commonly approximated by 22/7 if great accuracy is not needed. Is this an error? Think again. The answer is so simple! The diameter of 10 cubits is from outer rim to outer rim, the way anyone would measure a circular object. The circumference of 30 cubits, however, was of the inner circle, after subtracting the thickness of the brass (two handbreadths—one for each side) from which the bowl was made. This would be the number needed to calculate the volume of water. line of thirty cubits did compass it round about calculation of pi = (30 x 18) / [(10 x 18) - (2 x 4.05)] = 540 / (180 - 8.10) = 3.1413613 = 3.1414 Let's compare our calculated value of 3.1414 to the real value of "pi", which is 3.1415927. Actually, the parameters given in 1 Kings 7:23-26 gives a direct value for "pi" that is within 2 parts in 10,000, which is fairly accurate. Since the outside diameter of the sea is 10 cubits, what is the inside diameter? inside diameter = circumference / pi = 30 / 3.1415927 = 9.5493 cubits And, since the inside circumference is 30 cubits, what is the outside circumference? outside circumference = diameter x pi = 10 x 3.1415927 = 31.4159 cubits. God makes no mistakes, mathematical or otherwise. The Scriptures do not contain error. By the way, Solomon built this sea in 1000 B.C., long before the Greeks rediscovered Pi (p). We may not understand some things at first glance, but the problem is with us, not with the Bible. Ancient standards of measure vary widely, a cubit is generally taken to be about 18 inches, although there are different types of cubits ("common" and "royal", varying from 17 to 22 inches). A handbreadth is taken to be about 3 inches, sometimes being defined as one-sixth of a cubit. Something else to ponder: First, mathematically, take the etymology of the words Just for the heck of it look up word number "1047" in the Old Testament lexicon. It is "Beth Peor", spelled
1.0471698, which multiplied by 3 is pi. "1047" in the Old Testament lexicon can be transliterated as "pi." Hence, "house of pi." Indeed, truth is stranger than fiction.
and (the Hebrew word used in this verse, versus the usual word for circumference), and you'll find that the ratio of their numeric value (via Gametria) [(5 + 6 + 100)/(6 + 100)] is 1.0471698, which multiplied by 3 is pi. 
. Beth is translated "house of," and the first three letters of the last portion, peh, ayin, vaw could very easily be transliterated as "pi." Hence, "house of pi." Indeed, truth is stranger than fiction.
I believe I'll have another piece of pi, please.
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The old myth of king Click on picture to enlarge it |
The
political value of Solomon's PiMost textbooks on the history of science assert that ancient Near Eastern mathematicans did not know how to compute the circle constant pi, and that the Bible gives the very inaccurate value of pi = 3 for this important number.
They refer to the reported dimensions of the “sea of cast bronze” which king Solomon placed before the Temple he built in Jerusalem, as described in 1 Kings 7:23:
“It was round in shape, the diameter from rim to rim being ten cubits; it stood five cubits high, and it took a line thirty cubits long to go around it.”
Indeed, the Rabbis who wrote the Talmud a thousand years after Solomon asserted this value based on those verses. They may not have been mathematicians, but they knew how to divide thirty by ten and get three. They affirmed as late as the middle of the first millennium CE:
“that which in circumference is three hands broad is one hand broad”.
Scholars of the Enlightenment era were glad to concur with that interpretation because it allowed them to wield this blatant falsehood in the Bible as an irresistible battering ram against the until then unassailable inerrancy of the religious authorities.
Their Colonial era successors further embraced that poor value for Solomon’s pi to belittle the mathematical achievements and abilities of the ancient non- European civilizations, and to thereby better highlight those of their own group.
The views of these scholars survive to the point that this purported lack of mathematical intelligence under the reign of a king renowned for his wisdom is still an article of faith among mainstream historians of science trained to read this obviously primitive value into the text.
One of the most popular books on "A History of Pi" even offers eight translations of that biblical passage into seven different languages, presumably to drive home the point, with the common mainstream method of proof by repetition, that in every one of those translations the diameter remains ten cubit and the circumference thirty1.
However, the disparagers of Solomon’s pi omit half the evidence. The rest of the passage they cite shows their dogma is based on a hit- and- run calculation of the type that would make any undergraduates flunk their exam.
It seems that none of those who so compared the diameter and circumference of Solomon’s Sea of Bronze, as reported in 1 Kings 7:23 and 2 Chronicles 4:2, bothered to read on. Both accounts state three verses later that the rim of said vessel was
“made like a cup, shaped like the calyx of a lily”.
In other words, the rim was flared, and the ten- cubit diameter measured across its top from rim to rim was therefore larger than that of the vessel’s body which “took a line thirty cubits long to go around it”.
The surveyors would hardly have tried to stretch their measuring rope around the proud outside of that rim where it would never stay up. The only practical way to measure such a flared vessel is to stretch the rope around the body below that rim, as suggested on the picture above.
The circumference and diameter reported were thus not for the same circle, and deducing an ancient pi from these unrelated dimensions would be about as valid as trying to deduce your birth date from your phone number.
The volume and shape of Solomon's Sea Moreover, the measuring unit conversions supplied by modern archaeology allow us to compute the inside volume of that vessel and to thereby find its shape. With the stated circumference, wall thickness, and height, only a cylinder can contain the volume of 2,000 bath given in 1 Kings 7:26. The cubit length which had been used in various Jerusalem buildings and tombs of Solomon’s time was 20.67 inches2, according to the archaeologist Leen Ritmeyer who investigated the standards used in those structures. Like the ancient Egyptian cubit of typically similar length, it was divided into seven hand breadths of four fingers each. The bath was a liquid measure of “approximately 22 liters”, as Harper’s Bible Dictionary states. It was one tenth of a “kor” in the well- known dry- measuring system which is also described in Ezekiel 45:14. Its use for liquids is confirmed by eighth century BCE storage jars, found at Tell Beit Mirsim and Lachish, that were inscribed “bath” and “royal bath”3. A liter is 61.0237 cubic inch, so 2000 bath equal 304.04 cubic cubit. As calculated and illustrated in the above diagram, the 2000 bath of water from 1 Kings 7:26 fill that cylinder close to its top, to a height of 4.511 cubit above the inside bottom. The outside height was five cubit, and the bottom was one seventh of a cubit thick, so the 2000 bath leave only a shallow rim of about 0.3461 cubit above the water level, depending on how accurate the "about 22 liter" conversion factor is.
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The rim flare inscribed into the computed rectangle looks indeed like that of a cup, or like the calyx of a lily. |
The height and width of that rim, computed with the proper pi, produce an elegant flare that matches the biblical description. The same holds true for approximations to pi from about 3 1/8 to 3 1/6 which all produce lily- like rims and are all closer to the proper value than the alleged but unsupported pi = three.
These conversions also make it clear that the copyist of the much later4 parallel history in 2 Chronicles 4:6 misread that volume when he gave it as 3,000 bath. No matter how much you fudge the math or squeeze the water, this volume does not fit into a vessel with those dimensions.
The mainstream denial of ancient Pi Solomon’s mathematicians and surveyors, and their ancient colleagues throughout the ancient Levant, were therefore not necessarily the clumsy clods portrayed in current history books. The accuracies of transmitted lengths which Ritmeyer found in the actual dimensions those ancient builders left us in stone show that they worked with great care. It strains belief that their surveyors could have misread the rope around that vessel by almost two and a half feet in a circumference of less than 52 feet. Nor is there any rational reason to assume that the ancient number researchers were so innumerate that they could not have computed a fairly good value of pi, as close to the real one as that of Archimedes, or even closer. They had the same basic mathematical tool kit which Archimedes used many centuries after the Babylonians and Egyptians developed it. They had perhaps also more patience and motivation than Archimedes to continue with the simple but repetitive calculations required for better approximations. However, the backwardness of ancient Near Eastern mathematics has become a cornerstone of the prevailing prejudice against pre- Greek accomplishments. Examining that cornerstone exposes the scholarly bias on which it was founded. The reason for the current denial of ancient pi seems to be that the tool required for the calculation of pi is analytical thinking, the same mode of thought on which all the rest of so- called Western science is based, and which must therefore be Western. Most history books tell us that this superb achievement and gift to all humanity had to wait for the unique genius of the glorious Greeks, and that the invention of inquisitive and logical thinking was the decisive contribution from these purported founders of said science. The Greeks were, in the words of a highly respected Egyptologist born at the height of the English Empire: “... a race of men more hungry for knowledge than any people that had till then inhabited the earth”5 . Reflecting the same then typical attitude which refers to those other people as “that” instead of “who”, an equally respected historian of science quoted approvingly Plato’s partisan remark : “... whatever Greeks acquire from foreigners is finally turned by them into something nobler”6. This cultural bias led some of those afflicted by it not only to disregard obvious facts, as in the case of Solomon’s pi, but even to fabricate evidence, as needed to support their supposed superiority.
