Biblical Math Mystery Solution for PI
by Roy A. Reinhold, revised and expanded August 1, 2010
|In reading the Bible, many people come across a description of the huge sea at Solomon's Temple, which held 2000 baths of water. They read the description in 1 Kings 7:23-26,
and note that this water container was 10 cubits from brim to brim, circular in form, and was 30 cubits in circumference, and 5 cubits in height.
NEW August 1, 2010: Some readers have written about the discrepancy between the 2000 baths of water in 1 Kings 7:26, and the 3000 baths of water mentioned in 2 Chronicles 4:5. It's a worthy question; and I have added a complete new section at the end of this article to give a solution based on the Hebrew in both of those verses. Only one is correct. The answer up front is that from a Hebrew language analysis, we can safely state that the 2000 baths of water is the correct one. The new portion of the article at the end gives the solution.
Skeptics take issue and say that either God didn't know the value for "pi" (3.1415927....) or else it proves that the Bible was written by men, and at the time they had no understanding of the relationship of :
pi = circumference of a circle divided by the diameter = 3.1415927...
The following is an exact possible solution:
Skeptics and non-believers, along with many who think the Bible is well worth studying, read the above verse and think to themselves that this is nonsense. Everyone who has completed High School knows that the circumference of a circle is "pi x diameter" or "pi x 2 x radius". So if the circumference were 30 cubits, and the diameter were 10 cubits, then the ancient value of pi was 3.0, which is not very good.
What I want the reader to think about is whether the text tells you inside diameter or outside diameter, and whether the circumference given is inside circumference or outside circumference?
To get the full picture, we need to know the thickness of the large cast metal container, and that's shown a few verses down in 1 Kings 7:26.
The following graphic from a top view, shows what it would look like, although I am leaving off the fluting of the top of the brim. The thickness of the metal tub or sea was a handbreath.
We all understand that there was fluting outward at the top, like a teacup, but we don't know how far down it started curving outwards. Likewise, the bottom of the sea probably was not abruptly a 90 degree corner, but was probably rounded. While these points would make the analysis more correct, we can ignore them for the purposes of this problem concerning the value of "pi".
The mistake that people make when reading 1 Kings 7:23, is to assume that the value of 10 cubits is the inside diameter, and 30 cubits is the inside circumference; or they assume that both are the outside parameters.
Let's take a look at the situation where 10 cubits is the outside diameter, and 30 cubits is the inside circumference.
First, what is a cubit? 1 cubit = 18 inches (distance from elbow to fingertip)
calculation of pi = circumference / diameter = (30 x 18) / (10 x 18) - (2 x handbreath in inches)
Since I consider myself an average size man, I measured my own handbreath and it is slightly over 4 inches. I have a good engineering ruler with hundreths of an inch, and my handbreath is ~4.05 inches.
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. I would call that 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.
Mystery Solved, the ancient people did have an understanding of PI. In fact, there is no way other than as done in the scriptures, where someone can give three even measurements of the sea and do it with economy of language (using the figures of 5, 10 and 30 cubits to describe all the measurements of the molten sea).
New Subject: The article above mentions 2000 baths of water; how many gallons are in the molten sea? Also, how many gallons are in 1 bath?
First, a couple of liquid measurements to ease the calculations:
1 US gallon = 231 cubic inches = 3.7856 liters
1 cubic cubit = 18 x 18 x 18 = 5832 cubic inches = 25.24675 gallons
From the above scriptures, we know now that the inside circumference of the molten sea at the Temple of Solomon was 30 cubits, and the depth was 5 cubits. The area of a circle is = pi x radius squared, and the volume of the sea = area of the circle x depth.
volume of the sea = 3.1415927 x [(9.5493 / 2) squared] x 5 = 358.0989 cubic cubits
therefore, 2000 baths = 358.0989 cubic cubits = (358.0989 x 25.24675) gallons = 9040.8 gallons
and also therefore, 1 bath = (9040.8 / 2000) gallons = 4.52 gallons
In working on this section of the article, I looked in the dictionaries for a definition of a bath, and the New World Dictionary: Second Collegiate Edition defined a bath as an ancient liquid measurement somewhere between 6 to 10 gallons. Easton's Bible Dictionary defined a bath as 8 gallons and 3 quarts. It is interesting that the measurement in Easton's is almost exactly 2 times as much as calculated from the 1 Kings 7 example above. In looking at a variety of sources, I realized that the reference sources all disagreed about the bath. Therefore, I assume that the above calculation of ~4.5 gallons per bath is correct.
In Ezekiel 45:11-14, in talking about the future 4th Temple that will be built by the Messiah when He comes to reign on the earth, the millennial definitions for just measures are given.
100 kors = 10 bat = 1 homer
1 bat = 1 ephah = 1/10 homer, where a bat is the liquid measure and an ephah is the dry measure
The 2000 or 3000 baths of water controversy?
Many readers of the Bible have noticed that there is a discrepancy in the volume of water held by Solomon's great sea water container at the Temple in 1 Kings 7:26 versus 2 Chronicles 4:5. The former states that it held 2000 baths and the latter states that it held 3000 baths of water. To solve the dilemma, we need to examine the original Hebrew language of the verses in question. Here are the two verses in Hebrew and English:
In examining the Hebrew for both verses above, the Hebrew as shown is good grammatical Hebrew in both verses. Therefore, one has to look at the possibility of the word breaks being wrong in one verse, or the wrong vowelization marks for a word applied by the Massoretes in 400-800 AD.
Most of the Tanakh (Old Testament) was written before the Babylonian captivity of Judah in ~687 BC. They used ancient paleo-Hebrew letters and not the Ashurri Aramaic letters known today commonly as Hebrew block letters. The Jews adopted the Assyrian Aramaic block letters while they were held captive in Babylon, since the whole Aramaic world used them at the time. The Assyrian Aramaic block letters were also a huge improvement over the chicken scratch looking paleo-Hebrew letters.
At the time of Ezra the priest and scholar, after the 70 years of Babylonian captivity, he and perhaps others helping him took all the old Bible manuscripts written in ancient paleo-Hebrew and wrote them using the Assyrian Aramaic block letters (Hebrew letters).
In this case of the apparent scriptural discrepancy between 1 Kings 7:26 and 2 Chronicles 4:5, we know the problem had to occur at the time of Ezra. The reason is that the Greek Septuagint was translated from Hebrew to Greek in ~250 BC, and it has the same problem between the two verses. We know that the discrepancy had to occur before the Septuagint was translated; therefore, assuming it took place in the changeover to block Hebrew letters is likely the source of the problem. All English Bibles today have this same discrepancy between the two verses.
Here is my solution:
1. If the problem is in 1 Kings 7:26, we could say that the vowelization for the word "alpayim (2000)" is wrong. Alafeem is spelled the same and means "thousands", but it is pronounced differently.
If we apply different vowelization making it alafeem and not alpayim, then the last part of 1 Kings 7:26 would read: "it contained thousands of baths".
This would solve the discrepancy using 1 Kings 7:26 by making that verse non-specific, and then the 3000 baths in 2 Chronicles 4:5 would be correct.
However, as I showed in the first part of this article on mathematically solving the mystery of the molten sea, it is impossible for the molten sea to hold 3000 baths based on the actual specific dimensions given for it. Therefore, we have to discard this whole possible solution.
2. The discrepancy therefore must occur in 2 Chronicles 4:5. It is a more complex sentence with multiple verbs, so it is the more likely place for the problem.
Currently, the applicable part of the verse is:
The KJV translation is not what the original Hebrew states, but as I show just above. The translators took liberties to expand the literal verse in the KJV.
My theory for 2 Chronicles is that in going from the continuous script of old paleo-Hebrew, there was no word separation in the old manuscripts. Ezra and others saw what appeared to be "shloshet" which means "3" and it grammatically fits when followed by 1000 (alafeem). However, this is where the discrepancy occurred. The word shloshet should actually be two words "shel shat" with a space between the two words.
shel = belonging to, designated for, according to
If we make this change and also change the pronunciation of alafeem to alpayim (same spelling for both), then we have the following in Hebrew:
This solves the scriptural discrepancy and makes 2 Chronicles 4:5 say 2000 baths in agreement with 1 Kings 7:26. It doesn't add or remove letters from the original Hebrew Bible text; but it recognizes that a simple mistake was made in not separating the letters for shloshet into two words, shel shat. Then the those who translated the Septuagint, and later the Massoretes applying the vowelization to the Hebrew text, carried on the original simple mistake made at the time of Ezra.
Please feel free to e-mail me about any part of the above article. Thanks and shalom.